Quotients of triangle groups acting on surfaces of genus 2 to 101 ----------------------------------------------------------------- Below is a list of all quotients of ordinary hyperbolic triangle groups that act on a compact Riemann surface of 2 to 101, up to isomorphism, duality/triality and reflection. These were found by Marston Conder (University of Auckland) with the help of the "LowIndexNormalSubgroups" routine in Magma, in August 2006, and first put online in February 2007. Some enhancements were made to the notes on reflexibility of the group actions in February 2015. The notation "Tg.n" is used for the nth quotient of genus g. The "Triangle type" indicates the three positive integers p, q and r in the defining presentation < x,y,z | xyz = x^p = y^q = z^r = 1 > for the ordinary (p,q,r) triangle group. Such a triangle group is spherical (genus 0) if 1/p + 1/q + 1/r > 1, Euclidean (genus 1) if 1/p + 1/q + 1/r = 1, or hyperbolic (genus > 1) if 1/p + 1/q + 1/r < 1. In particular, by the Riemann-Hurwitz formula, this list includes all "large" groups of orientation-preserving automorphisms of compact Riemann surfaces of genus 2 to 101, where "large" means that |G| > 12(g-1) where g is the genus and G is the conformal automorphism group. The action is called "reflexible [m]" if there exists an involutory automorphism of the quotient that inverts the images of two of the three generators x, y and z. This is the same as hypermap reflexibility. The action is called "reflexible [n]" if two of more of p, q and r are equal, and there exists an involutory automorphism of the quotient that swaps the images of two of the three generators x, y and z with the inverse of the other. For example, this happens if p = q and the involutory automorphism swaps the image of x with the image of y^{-1}, and vice versa. This is equivalent to an extension of the (p,p,r) triangular action to an action of a larger group with NEC signature (0; +; [p]; {(r)}). In all other cases the action is irreflexible, or "chiral". Total number of quotient groups in list below: 20810 Note that in the previous version of this list (published in 2007), the actions called "chiral" were those that are chiral as actions of groups on maps or hypermaps, or in other words, "reflexible [m]". There were 2785 such actions (from the total of 20810). In this new list (below), 602 of those 2785 are described as "reflexible [n]", while the other 2183 remain chiral (with regard to both kinds of reflexibility). The previous version is available at the webpage www.math.auckland.ac.nz/~conder/TriangleGroupQuotients101-Previous.txt Marston Conder February 2015 Genus 2 T2.1 : Triangle type {2,3,8} Group order 48 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z * y * x * z * y^-1 * z^-1 * x * z ] T2.2 : Triangle type {2,4,6} Group order 24 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^6 ] T2.3 : Triangle type {2,4,8} Group order 16 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-1 * x * y^-1 * z^-2 ] T2.4 : Triangle type {2,5,10} Group order 10 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-5 ] T2.5 : Triangle type {2,6,6} Group order 12 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^6 ] T2.6 : Triangle type {2,8,8} Group order 8 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^3 * z^-1 ] T2.7 : Triangle type {3,3,4} Group order 24 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^4, z * y * x^-1 * y^-1 * x ] T2.8 : Triangle type {3,4,4} Group order 12 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^4 ] T2.9 : Triangle type {3,6,6} Group order 6 Action reflexible [m,n] Defining relators: [ x^3, y^-1 * x^-1 * y^-1, y * z^-1 ] T2.10 : Triangle type {4,4,4} Group order 8 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, z^-1 * x^-1 * y ] T2.11 : Triangle type {5,5,5} Group order 5 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y * x^-1 * y, x * z^-1 ] Genus 3 T3.1 : Triangle type {2,3,7} Group order 168 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^-3 * x * y * z^-3, y * x * z * y * x * z * y^-1 * z * y^-1 * z^-1 * x * z ] T3.2 : Triangle type {2,3,8} Group order 96 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^-4 * x * y * z^-3, z * y * x * z * y^-1 * z * y^-1 * z^-1 * x ] T3.3 : Triangle type {2,3,12} Group order 48 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, x * z^2 * y^-1 * z^-3 ] T3.4 : Triangle type {2,4,6} Group order 48 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^6 ] T3.5 : Triangle type {2,4,8} Group order 32 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z^-2 ] T3.6 : Triangle type {2,4,8} Group order 32 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-4 * x * y * z^-3 ] T3.7 : Triangle type {2,4,12} Group order 24 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-2 * x * y^-1 * z^-3 ] T3.8 : Triangle type {2,6,6} Group order 24 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^6 ] T3.9 : Triangle type {2,7,14} Group order 14 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-7 ] T3.10 : Triangle type {2,8,8} Group order 16 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z^-1 * y^2 * z^-1 ] T3.11 : Triangle type {2,8,8} Group order 16 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-8 ] T3.12 : Triangle type {2,12,12} Group order 12 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^5 * z^-1 ] T3.13 : Triangle type {3,3,4} Group order 48 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^4, z * x^-1 * y^-1 * x * y^-1 * x ] T3.14 : Triangle type {3,3,6} Group order 24 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-1 * x * z ] T3.15 : Triangle type {3,3,7} Group order 21 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z * y * x * z ] T3.16 : Triangle type {3,4,4} Group order 24 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^4 ] T3.17 : Triangle type {3,4,12} Group order 12 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^4 ] T3.18 : Triangle type {3,9,9} Group order 9 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-2 * z ] T3.19 : Triangle type {4,4,4} Group order 16 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^4 ] T3.20 : Triangle type {4,4,4} Group order 16 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y^4 ] T3.21 : Triangle type {4,4,6} Group order 12 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z * y^-1 * x * z ] T3.22 : Triangle type {4,8,8} Group order 8 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^4, y * z^-1 ] T3.23 : Triangle type {4,8,8} Group order 8 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * y, z * x^-1 * z ] T3.24 : Triangle type {7,7,7} Group order 7 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^-2 * x * y^-1, x * z^-1 ] T3.25 : Triangle type {7,7,7} Group order 7 Action reflexible [m] Defining relators: [ x^-2 * y, x * y * z, z * x^-1 * z ] Genus 4 T4.1 : Triangle type {2,3,12} Group order 72 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * z * y * x * y^-1 * z^-1, x * z^3 * y^2 * z^-4 ] T4.2 : Triangle type {2,4,5} Group order 120 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^-2 * x * y * z^-2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T4.3 : Triangle type {2,4,6} Group order 72 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z * y * x * y^-1 * z^-1 * x, z^6 ] T4.4 : Triangle type {2,4,10} Group order 40 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-6 * x * y * z^-3 ] T4.5 : Triangle type {2,4,16} Group order 32 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-4 * x * y^-1 * z^-3 ] T4.6 : Triangle type {2,5,5} Group order 60 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^-5, z^-2 * x * y * z^-2, (z^-1 * y)^3 ] T4.7 : Triangle type {2,6,6} Group order 36 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^6 ] T4.8 : Triangle type {2,6,6} Group order 36 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^6 ] T4.9 : Triangle type {2,6,12} Group order 24 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y^6 ] T4.10 : Triangle type {2,9,18} Group order 18 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-9 ] T4.11 : Triangle type {2,10,10} Group order 20 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z * y^-7 * z ] T4.12 : Triangle type {2,16,16} Group order 16 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-7 * z ] T4.13 : Triangle type {3,3,6} Group order 36 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^-2 * x^-1 * z * y^-1, z * x^-1 * y^-1 * x * y^-1 * x ] T4.14 : Triangle type {3,4,4} Group order 36 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^4, (y * z^-1)^2, z^4 ] T4.15 : Triangle type {3,4,6} Group order 24 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z * y * x^-1 * z ] T4.16 : Triangle type {3,5,15} Group order 15 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-5 ] T4.17 : Triangle type {3,6,6} Group order 18 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-6 ] T4.18 : Triangle type {3,6,6} Group order 18 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^2 * z^-1 ] T4.19 : Triangle type {3,6,6} Group order 18 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-6 ] T4.20 : Triangle type {3,12,12} Group order 12 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, z^-1 * y^2 * z^-1 ] T4.21 : Triangle type {4,4,5} Group order 20 Action reflexible [n] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-1 * y * x * z^-1 ] T4.22 : Triangle type {4,4,5} Group order 20 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^2 * y^-1 * x^-1 * z^2 ] T4.23 : Triangle type {4,4,8} Group order 16 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z * y * x^-1 * z^2 ] T4.24 : Triangle type {4,6,12} Group order 12 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^-2 * x^-1 * z ] T4.25 : Triangle type {5,10,10} Group order 10 Action reflexible [m] Defining relators: [ x * y * z, y * x^-1 * y, z^-1 * x^2 * z^-1 ] T4.26 : Triangle type {5,10,10} Group order 10 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-5, y * z^-1 ] T4.27 : Triangle type {6,6,6} Group order 12 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^-1 * x^2 * z^-1 ] T4.28 : Triangle type {9,9,9} Group order 9 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^2 * x^-1 * y^2, x * z^-1 ] Genus 5 T5.1 : Triangle type {2,3,8} Group order 192 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^8, z^3 * y * z^-1 * x * z * y^-1 * x * y^-1 * z^-2 * x ] T5.2 : Triangle type {2,3,10} Group order 120 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, (y * z^-2 * x * z)^2 ] T5.3 : Triangle type {2,4,5} Group order 160 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^-2 * x * y * z^-2, (y * z^-1)^4 ] T5.4 : Triangle type {2,4,6} Group order 96 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^6, z * y * z^-1 * x * y^-1 * z^-2 * x ] T5.5 : Triangle type {2,4,8} Group order 64 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z * y * x * y^-1 * z^-1 * x, (y * z^-1)^4 ] T5.6 : Triangle type {2,4,8} Group order 64 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^8 ] T5.7 : Triangle type {2,4,12} Group order 48 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-12 ] T5.8 : Triangle type {2,4,20} Group order 40 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-6 * x * y^-1 * z^-3 ] T5.9 : Triangle type {2,5,5} Group order 80 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^-5, z * y * x * y^-1 * z^-1 * x, z^-2 * x * y * z^-2 ] T5.10 : Triangle type {2,6,6} Group order 48 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z * y * x * y^-1 * z^-1 * x ] T5.11 : Triangle type {2,6,15} Group order 30 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-2 * x * y^-1 * z^-2 ] T5.12 : Triangle type {2,8,8} Group order 32 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, z * y * x * y^-1 * z^-1 * x ] T5.13 : Triangle type {2,8,8} Group order 32 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y^8 ] T5.14 : Triangle type {2,11,22} Group order 22 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^2 * y^-8 ] T5.15 : Triangle type {2,12,12} Group order 24 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^3 * y^-7 * z ] T5.16 : Triangle type {2,20,20} Group order 20 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z * y^-8 ] T5.17 : Triangle type {3,3,4} Group order 96 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^4, z * y^-1 * z^-1 * x^-1 * z * y * x ] T5.18 : Triangle type {3,3,5} Group order 60 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, x^-1 * z * y^-1 * x * z^2, z^2 * y^-1 * x^-1 * z^2 ] T5.19 : Triangle type {3,4,4} Group order 48 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^4, y * z^-1 * x^-1 * y * z^-1 ] T5.20 : Triangle type {3,4,4} Group order 48 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^4, z^4, y * z^-1 * x^-1 * y^-1 * z ] T5.21 : Triangle type {3,6,6} Group order 24 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, (y * z^-1)^2 ] T5.22 : Triangle type {3,15,15} Group order 15 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-4 * z ] T5.23 : Triangle type {4,4,4} Group order 32 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^4, z^-2 * x^-1 * z * y^-1 ] T5.24 : Triangle type {4,4,4} Group order 32 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2 ] T5.25 : Triangle type {4,4,6} Group order 24 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^6 ] T5.26 : Triangle type {4,4,10} Group order 20 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^2 * y^-1 * x * z^2 ] T5.27 : Triangle type {4,8,8} Group order 16 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, (y * z^-1)^2 ] T5.28 : Triangle type {4,8,8} Group order 16 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^2 * z^-1 ] T5.29 : Triangle type {6,12,12} Group order 12 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^6, y * z^-1 ] T5.30 : Triangle type {11,11,11} Group order 11 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^-3 * x * y^-2, x * z^-1 ] T5.31 : Triangle type {11,11,11} Group order 11 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-2 * x * y^-1 ] Genus 6 T6.1 : Triangle type {2,3,10} Group order 150 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-5 * x * y^-2 * z^-4 ] T6.2 : Triangle type {2,4,6} Group order 120 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (z^-1 * y)^3, z^6 ] T6.3 : Triangle type {2,4,9} Group order 72 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-4 * x * y * z^-4 ] T6.4 : Triangle type {2,4,14} Group order 56 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-9 * x * y * z^-4 ] T6.5 : Triangle type {2,4,24} Group order 48 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-8 * x * y^-1 * z^-3 ] T6.6 : Triangle type {2,5,10} Group order 50 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^-5, x * z * y^-1 * z^-2 ] T6.7 : Triangle type {2,6,8} Group order 48 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^8 ] T6.8 : Triangle type {2,6,8} Group order 48 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^2 * y^2 * x * z ] T6.9 : Triangle type {2,9,9} Group order 36 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^9 ] T6.10 : Triangle type {2,10,15} Group order 30 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z * y^-2 * z^2 ] T6.11 : Triangle type {2,13,26} Group order 26 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^13 ] T6.12 : Triangle type {2,14,14} Group order 28 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^14 ] T6.13 : Triangle type {2,24,24} Group order 24 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^3 * y^-8 ] T6.14 : Triangle type {3,3,5} Group order 75 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^2 * y^-1 * x^-1 * z^2 ] T6.15 : Triangle type {3,3,13} Group order 39 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z^-2 * x^-1 * y^-1 * z^-1 ] T6.16 : Triangle type {3,7,21} Group order 21 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-1 * z * y^-3 * z^2 ] T6.17 : Triangle type {3,8,8} Group order 24 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-8 ] T6.18 : Triangle type {3,18,18} Group order 18 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-5 * z ] T6.19 : Triangle type {4,4,7} Group order 28 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^3 * y * x * z^3 ] T6.20 : Triangle type {4,4,12} Group order 24 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^2 * y * x^-1 * z^3 ] T6.21 : Triangle type {4,5,20} Group order 20 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^-5 ] T6.22 : Triangle type {4,6,6} Group order 24 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, z * y^-1 * x * z, y^2 * x * z^-1 ] T6.23 : Triangle type {4,6,6} Group order 24 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^6 ] T6.24 : Triangle type {4,16,16} Group order 16 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, z^-2 * y * z^-1 ] T6.25 : Triangle type {5,5,5} Group order 25 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-5, y^-5 ] T6.26 : Triangle type {5,15,15} Group order 15 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y^-2 * x * y^-1, z^-2 * x * z^-1 ] T6.27 : Triangle type {5,15,15} Group order 15 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-5 ] T6.28 : Triangle type {7,14,14} Group order 14 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^-2 * y * z^-1 ] T6.29 : Triangle type {7,14,14} Group order 14 Action reflexible [m] Defining relators: [ x * y * z, y * x^-1 * y, z^2 * x^-1 * z^2 ] T6.30 : Triangle type {7,14,14} Group order 14 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-7, y * z^-1 ] T6.31 : Triangle type {13,13,13} Group order 13 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^-4 * x * y^-2, x * z^-1 ] T6.32 : Triangle type {13,13,13} Group order 13 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y * x^-2 * y^2 ] T6.33 : Triangle type {13,13,13} Group order 13 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^3 * y^-1, y^3 * z^-1 ] Genus 7 T7.1 : Triangle type {2,3,7} Group order 504 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^-3 * x * y * z^-3, y * z^-1 * x * z * y * z^-1 * x * z^2 * y * z^-2 * y * z^-2 * x * z^2 ] T7.2 : Triangle type {2,3,12} Group order 144 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, y * x * z^2 * y * x * y^-1 * z^-2 * x * z ] T7.3 : Triangle type {2,4,16} Group order 64 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-2 * x * z * y^-1 * z^-4 ] T7.4 : Triangle type {2,4,16} Group order 64 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-6 * x * z^5 * y^-1 * z^-4 ] T7.5 : Triangle type {2,4,28} Group order 56 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-9 * x * y^-1 * z^-4 ] T7.6 : Triangle type {2,6,9} Group order 54 Action chiral Defining relators: [ x^2, x * y * z, y^6, y * z^-1 * y^2 * x * z ] T7.7 : Triangle type {2,6,9} Group order 54 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-4 * x * y * z^-4 ] T7.8 : Triangle type {2,6,12} Group order 48 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, y * z^-1 * x * y^-1 * z^-2 ] T7.9 : Triangle type {2,6,21} Group order 42 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^2 * y * z^-1 * x * z^3 ] T7.10 : Triangle type {2,7,7} Group order 56 Action reflexible [n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^-7, x * y^-3 * z^-1 * y * z^-1 ] T7.11 : Triangle type {2,15,30} Group order 30 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^15 ] T7.12 : Triangle type {2,16,16} Group order 32 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^16 ] T7.13 : Triangle type {2,16,16} Group order 32 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y^6 * z^-2 ] T7.14 : Triangle type {2,28,28} Group order 28 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^13 * z^-1 ] T7.15 : Triangle type {3,3,6} Group order 72 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T7.16 : Triangle type {3,4,6} Group order 48 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y^-1 ] T7.17 : Triangle type {3,4,12} Group order 36 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1 ] T7.18 : Triangle type {3,8,24} Group order 24 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-2 * z * y^-3 * z^2 ] T7.19 : Triangle type {3,9,9} Group order 27 Action chiral Defining relators: [ x^3, x * y * z, y^-2 * x * z ] T7.20 : Triangle type {3,9,9} Group order 27 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^2 * z^-1 * y^4 * z^-2 ] T7.21 : Triangle type {3,21,21} Group order 21 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-1 * z * y^-4 * z ] T7.22 : Triangle type {4,4,8} Group order 32 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z * y * x^-1 * z^2 ] T7.23 : Triangle type {4,4,8} Group order 32 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z * y * x^-1 * z^2 ] T7.24 : Triangle type {4,4,8} Group order 32 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^4 * y^-1 * x^-1 * z^3 ] T7.25 : Triangle type {4,4,8} Group order 32 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^-1 * z^-1 * x^-1 * z^2 ] T7.26 : Triangle type {4,4,14} Group order 28 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^3 * y * x^-1 * z^3 ] T7.27 : Triangle type {4,6,12} Group order 24 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^6 ] T7.28 : Triangle type {4,10,20} Group order 20 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^-3 * z^2 ] T7.29 : Triangle type {6,6,6} Group order 24 Action reflexible [m,n] Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z^-1 * y * x * y^-1 ] T7.30 : Triangle type {6,9,18} Group order 18 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y * x^-2 * y^2 ] T7.31 : Triangle type {6,9,18} Group order 18 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^6 ] T7.32 : Triangle type {8,16,16} Group order 16 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-8, y * z^-1 ] T7.33 : Triangle type {8,16,16} Group order 16 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-3 * y^2 ] T7.34 : Triangle type {8,16,16} Group order 16 Action reflexible [m] Defining relators: [ x * y * z, y * x^-1 * y, z^2 * x^-2 * z^2 ] T7.35 : Triangle type {15,15,15} Group order 15 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^-5 * x * y^-2, x * z^-1 ] Genus 8 T8.1 : Triangle type {2,3,8} Group order 336 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^8, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T8.2 : Triangle type {2,3,8} Group order 336 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^8, y * x * z * y * z^-2 * x * z * y * x * y^-1 * z^-3 * x * z ] T8.3 : Triangle type {2,4,18} Group order 72 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-13 * x * y * z^-4 ] T8.4 : Triangle type {2,4,32} Group order 64 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-6 * x * z^5 * y^-1 * x * y^-1 * z^-3 ] T8.5 : Triangle type {2,6,6} Group order 84 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^6, x * y^-1 * z * y^2 * x * y^-1 * z^-1 ] T8.6 : Triangle type {2,6,10} Group order 60 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, x * z^4 * y^-1 * x * y^-1 * z^-4 ] T8.7 : Triangle type {2,6,24} Group order 48 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-3 * x * y^-1 * z^-4 ] T8.8 : Triangle type {2,8,12} Group order 48 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, x * z * y * x * y^-1 * z^-3 ] T8.9 : Triangle type {2,10,20} Group order 40 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y^10 ] T8.10 : Triangle type {2,17,34} Group order 34 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^17 ] T8.11 : Triangle type {2,18,18} Group order 36 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^18 ] T8.12 : Triangle type {2,32,32} Group order 32 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^15 * z^-1 ] T8.13 : Triangle type {3,3,4} Group order 168 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^4, (x * z * y^-1 * z^-1)^2 ] T8.14 : Triangle type {3,3,4} Group order 168 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T8.15 : Triangle type {3,4,8} Group order 48 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-1 * z^2 ] T8.16 : Triangle type {3,6,6} Group order 42 Action chiral Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, z^-2 * y^2 * z^-1 * y ] T8.17 : Triangle type {3,6,6} Group order 42 Action chiral Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y * z^-1 * x^-1 * y^-1 * z^-1 ] T8.18 : Triangle type {3,10,10} Group order 30 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y * z^-1 * y^6 * z^-1 * y ] T8.19 : Triangle type {3,24,24} Group order 24 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-2 * z * y^-5 ] T8.20 : Triangle type {4,4,9} Group order 36 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^5 * y^-1 * x^-1 * z^3 ] T8.21 : Triangle type {4,4,16} Group order 32 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^4 * y^-1 * x * z^3 ] T8.22 : Triangle type {4,12,12} Group order 24 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, z^-1 * y^3 * z^-1 * y ] T8.23 : Triangle type {5,6,6} Group order 30 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^-5, y^6 ] T8.24 : Triangle type {5,20,20} Group order 20 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-5 ] T8.25 : Triangle type {5,20,20} Group order 20 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-5 ] T8.26 : Triangle type {6,6,12} Group order 24 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z * y * x^-1 * z^2 ] T8.27 : Triangle type {6,8,8} Group order 24 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, y * z^-1 * x^-1 * y * z^-1 ] T8.28 : Triangle type {9,18,18} Group order 18 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-9, y * z^-1 ] T8.29 : Triangle type {9,18,18} Group order 18 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^2 * x^-1 * z^2 ] T8.30 : Triangle type {10,10,10} Group order 20 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^-2 * x^2 * z^-2 ] T8.31 : Triangle type {17,17,17} Group order 17 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^5 * x^-1 * y^3, x * z^-1 ] T8.32 : Triangle type {17,17,17} Group order 17 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-3 * x * y^-2 ] T8.33 : Triangle type {17,17,17} Group order 17 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^-3 * y^2 ] Genus 9 T9.1 : Triangle type {2,3,12} Group order 192 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, y * x * z * y * x * z * y^-1 * z * y^-1 * z^-1 * x * z, z^-1 * x * z^2 * y * x * z * y^-1 * z^-2 * x * y^-1 * z^-1 ] T9.2 : Triangle type {2,4,5} Group order 320 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^-2 * x * y * z^-2, z * y^-1 * z^2 * y * x * z * y^-1 * z * y^-1 * z^-1 * x ] T9.3 : Triangle type {2,4,6} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^6, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z ] T9.4 : Triangle type {2,4,6} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^6, (y * z^-1)^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T9.5 : Triangle type {2,4,8} Group order 128 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^8, z * y^-1 * z * y^-2 * z^-2 * x * z ] T9.6 : Triangle type {2,4,8} Group order 128 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z * y * x * y^-1 * z^-1 * x, z^8 ] T9.7 : Triangle type {2,4,8} Group order 128 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^8 ] T9.8 : Triangle type {2,4,8} Group order 128 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, y^-1 * z * y^-1 * z * y^-1 * z^-2 * x * z ] T9.9 : Triangle type {2,4,12} Group order 96 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y^-1 * z^-3, (y * z^-1)^4 ] T9.10 : Triangle type {2,4,12} Group order 96 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-1 * x * z^5 * y * x * y^-1 * z^-4 ] T9.11 : Triangle type {2,4,12} Group order 96 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-3 * x * z^2 * y * z^-1 * x * y * x * y^-1 * z^-3 ] T9.12 : Triangle type {2,4,20} Group order 80 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-15 * x * y * z^-4 ] T9.13 : Triangle type {2,4,36} Group order 72 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-13 * x * y^-1 * z^-4 ] T9.14 : Triangle type {2,5,5} Group order 160 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^-5, z^-2 * x * y * z^-2, x * y^-1 * z * y^-2 * z^-2 * y * z^-1 ] T9.15 : Triangle type {2,5,6} Group order 120 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^-5, (y * z^-2)^2 ] T9.16 : Triangle type {2,5,6} Group order 120 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^-5, z * y * x * y^-1 * z^-1 * x, z^6 ] T9.17 : Triangle type {2,6,6} Group order 96 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^6, z^6, x * z * y^-2 * z^-1 * y * z^-1, z^-1 * y * x * y^-1 * z * y^-1 * z^-1 ] T9.18 : Triangle type {2,6,6} Group order 96 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, (z^-1 * y)^3 ] T9.19 : Triangle type {2,8,8} Group order 64 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^8 ] T9.20 : Triangle type {2,8,8} Group order 64 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^8 ] T9.21 : Triangle type {2,8,8} Group order 64 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y^-3 * z^-1 * x * z, y * x * y^-2 * z^3 ] T9.22 : Triangle type {2,8,8} Group order 64 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^8 ] T9.23 : Triangle type {2,8,8} Group order 64 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^-2 * z * y^-1 * z^-1 ] T9.24 : Triangle type {2,8,24} Group order 48 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-2 * x * y^-1 * z^-3 ] T9.25 : Triangle type {2,8,24} Group order 48 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y^8 ] T9.26 : Triangle type {2,12,12} Group order 48 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z^-1 * y^3 * z^-2, z * y * x * y^-1 * z^-1 * x ] T9.27 : Triangle type {2,12,12} Group order 48 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-12 ] T9.28 : Triangle type {2,12,12} Group order 48 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y^-2 * z^2 * y^-6 * z^2 ] T9.29 : Triangle type {2,14,21} Group order 42 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-4 * z^3 ] T9.30 : Triangle type {2,19,38} Group order 38 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^8 * y^-10 ] T9.31 : Triangle type {2,20,20} Group order 40 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^9 * y^-9 * z ] T9.32 : Triangle type {2,36,36} Group order 36 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^17 * z^-1 ] T9.33 : Triangle type {3,3,6} Group order 96 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x ] T9.34 : Triangle type {3,3,19} Group order 57 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z * y * z^-1 * x * z^2 ] T9.35 : Triangle type {3,4,4} Group order 96 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^4, z^4, (x^-1 * z * y)^2, (z^-1 * y)^3 ] T9.36 : Triangle type {3,4,4} Group order 96 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^4, z^4, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T9.37 : Triangle type {3,4,12} Group order 48 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y ] T9.38 : Triangle type {3,5,5} Group order 60 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^-5 ] T9.39 : Triangle type {3,5,5} Group order 60 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, (y * z^-1)^2, z * x^-1 * y^-1 * x * y^-1 * x, y^-5 ] T9.40 : Triangle type {3,6,6} Group order 48 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-1 * z^-1, y^-1 * z^-1 * x^-1 * z * y^-1 ] T9.41 : Triangle type {3,10,30} Group order 30 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^3 * z^-1 * y^4 * z^-2 ] T9.42 : Triangle type {3,27,27} Group order 27 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^2 * z^-1 * y^6 ] T9.43 : Triangle type {4,4,4} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, z^-2 * x^-1 * z * y^-1, x * z^-1 * y * x * z * y ] T9.44 : Triangle type {4,4,4} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, z^-2 * x^-1 * z * y^-1, (x * z^-1 * y)^2 ] T9.45 : Triangle type {4,4,4} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, z^-1 * y * x^2 * z * y ] T9.46 : Triangle type {4,4,4} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^4 ] T9.47 : Triangle type {4,4,6} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^2, z^6 ] T9.48 : Triangle type {4,4,6} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x * z, (y^-1 * x)^3 ] T9.49 : Triangle type {4,4,6} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x^4, z * y^-1 * x * z, y^4 ] T9.50 : Triangle type {4,4,6} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^6 ] T9.51 : Triangle type {4,4,10} Group order 40 Action reflexible [n] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, y^-1 * z^-1 * x^-1 * z^2 ] T9.52 : Triangle type {4,4,10} Group order 40 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^6 * y * x * z^3 ] T9.53 : Triangle type {4,4,18} Group order 36 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^5 * y^-1 * x * z^3 ] T9.54 : Triangle type {4,7,28} Group order 28 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^-7 ] T9.55 : Triangle type {4,8,8} Group order 32 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-1 * z^2 * y^-5 ] T9.56 : Triangle type {4,8,8} Group order 32 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, z^-1 * y^2 * z^-1, y * x^-2 * z * x^-1 ] T9.57 : Triangle type {4,8,8} Group order 32 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-1 * z^2 ] T9.58 : Triangle type {4,8,8} Group order 32 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1 ] T9.59 : Triangle type {4,8,8} Group order 32 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y^-2 * z * y^-2 * z^3 ] T9.60 : Triangle type {4,8,8} Group order 32 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y * z^-1 ] T9.61 : Triangle type {4,24,24} Group order 24 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y^5 * z^-1 ] T9.62 : Triangle type {4,24,24} Group order 24 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^3 * z^-2 ] T9.63 : Triangle type {6,8,24} Group order 24 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^6 ] T9.64 : Triangle type {6,12,12} Group order 24 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^6 ] T9.65 : Triangle type {7,21,21} Group order 21 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-1 * x^3 * y^-2 ] T9.66 : Triangle type {7,21,21} Group order 21 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-7 ] T9.67 : Triangle type {7,21,21} Group order 21 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z * x^-2 * z^2 ] T9.68 : Triangle type {8,8,12} Group order 24 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z * y^-1 * x * z ] T9.69 : Triangle type {8,8,12} Group order 24 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z * x^-2 * z^2 ] T9.70 : Triangle type {10,20,20} Group order 20 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-10, y * z^-1 ] T9.71 : Triangle type {10,20,20} Group order 20 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^3 * x^-1 * y^3 ] T9.72 : Triangle type {19,19,19} Group order 19 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^6 * x^-1 * y^3, x * z^-1 ] T9.73 : Triangle type {19,19,19} Group order 19 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^2 * x^-2 * y^3 ] T9.74 : Triangle type {19,19,19} Group order 19 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^2 * x^-1 * y^2 ] T9.75 : Triangle type {19,19,19} Group order 19 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y * x^-2 * y^2 ] Genus 10 T10.1 : Triangle type {2,3,8} Group order 432 Action chiral Defining relators: [ x^2, y^3, x * y * z, z^8, z * y * x * z^2 * y * x * z * y * z^-1 * x * y^-1 * z^-2 * x * z ] T10.2 : Triangle type {2,3,9} Group order 324 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^-4 * x * y * z^-4, z^2 * y * z^-1 * x * z * y * x * y * x * z * y^-1 * z^-1 * x ] T10.3 : Triangle type {2,3,12} Group order 216 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^7 * y^-1 * x * z^4 ] T10.4 : Triangle type {2,3,15} Group order 180 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, y * x * z^2 * y * x * z * y^-1 * z^-1 * x * z^2, z^-4 * x * z * y^-1 * x * z^2 * y^-1 * z^-1 ] T10.5 : Triangle type {2,3,18} Group order 162 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^6 * y * z^-5 * x ] T10.6 : Triangle type {2,3,24} Group order 144 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, x * z^3 * y^-1 * z^-4 ] T10.7 : Triangle type {2,4,5} Group order 360 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^-2 * x * y * z^-2, (z^-1 * y)^5 ] T10.8 : Triangle type {2,4,6} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^6, (y * z^-2 * y * z^-1)^2 ] T10.9 : Triangle type {2,4,6} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^6, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1 ] T10.10 : Triangle type {2,4,7} Group order 168 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (z^-1 * y)^3, z^-3 * x * y * z^-3 ] T10.11 : Triangle type {2,4,8} Group order 144 Action chiral Defining relators: [ x^2, x * y * z, y^4, z^8, y * z^-2 * x * y^-1 * z^-2 * y * z^-1 ] T10.12 : Triangle type {2,4,12} Group order 108 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (z^-1 * y)^3, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T10.13 : Triangle type {2,4,22} Group order 88 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-17 * x * y * z^-4 ] T10.14 : Triangle type {2,4,40} Group order 80 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-15 * x * y^-1 * z^-4 ] T10.15 : Triangle type {2,6,6} Group order 108 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^6, z^6, x * z * y^-2 * z^-2 * y ] T10.16 : Triangle type {2,6,6} Group order 108 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^6, z^6, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T10.17 : Triangle type {2,6,6} Group order 108 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^6, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z ] T10.18 : Triangle type {2,6,12} Group order 72 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^6 ] T10.19 : Triangle type {2,6,12} Group order 72 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z * y * x * z^4 * y^-1 * x * y^-1 * z^-3 * x * z ] T10.20 : Triangle type {2,6,12} Group order 72 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-2 * x * z^2 * y * z^-1 * x * y^-1 * z^-5 ] T10.21 : Triangle type {2,6,30} Group order 60 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, x * z^4 * y^-1 * z^-5 ] T10.22 : Triangle type {2,8,8} Group order 72 Action chiral Defining relators: [ x^2, x * y * z, z * y^-3 * z^-1 * x * y^-1 ] T10.23 : Triangle type {2,9,18} Group order 54 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-3 * z^-1 * y^2, y^-9 ] T10.24 : Triangle type {2,12,24} Group order 48 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-2 * y^2 * z^-2 ] T10.25 : Triangle type {2,21,42} Group order 42 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^10 * y^-10 ] T10.26 : Triangle type {2,22,22} Group order 44 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^11 * y^-9 * z ] T10.27 : Triangle type {2,40,40} Group order 40 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^9 * y^-10 ] T10.28 : Triangle type {3,3,4} Group order 216 Action chiral Defining relators: [ x^3, x * y * z, y^3, z^4, z * y * x^-1 * y^-1 * z^-1 * x * z^2 * y * x ] T10.29 : Triangle type {3,3,4} Group order 216 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^3, z^4, z * y * x^-1 * y * x^-1 * z * y * z^-1 * x^-1 ] T10.30 : Triangle type {3,3,6} Group order 108 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^6 ] T10.31 : Triangle type {3,3,9} Group order 81 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^3, z^-1 * x^-1 * y^-1 * x * z * y ] T10.32 : Triangle type {3,3,9} Group order 81 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-3 * x^-1 * z^2 * y^-1 ] T10.33 : Triangle type {3,3,12} Group order 72 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^-2 * x^-1 * z * y^-1 ] T10.34 : Triangle type {3,3,21} Group order 63 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z * y^-1 * z^-1 * x^-1 * z^2 ] T10.35 : Triangle type {3,4,4} Group order 108 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * y * x * y^-1 * z^-1 ] T10.36 : Triangle type {3,4,4} Group order 108 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^4, z^4, y * x^-1 * y * x^-1 * y^-1 * x * z ] T10.37 : Triangle type {3,4,6} Group order 72 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-2 * x^-1 * z * y^-1, (z^-1 * y)^3 ] T10.38 : Triangle type {3,6,6} Group order 54 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^6 ] T10.39 : Triangle type {3,6,6} Group order 54 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, y * x^-1 * y^-1 * x * z * y, y^6 ] T10.40 : Triangle type {3,6,6} Group order 54 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, (z^-1 * y)^3 ] T10.41 : Triangle type {3,6,6} Group order 54 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, y^6 ] T10.42 : Triangle type {3,6,14} Group order 42 Action chiral Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y * z^-1, y * z^-1 * x^-1 * z * y ] T10.43 : Triangle type {3,11,33} Group order 33 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^11 ] T10.44 : Triangle type {3,12,12} Group order 36 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-4 * z * y^-1 * z * y^-4 * z ] T10.45 : Triangle type {3,12,12} Group order 36 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, z^-1 * y^2 * z^-1 ] T10.46 : Triangle type {3,12,12} Group order 36 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^2 * y^-3 * z * y^-4 * z ] T10.47 : Triangle type {3,30,30} Group order 30 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^3 * z^-1 * y^5 * z^-1 ] T10.48 : Triangle type {4,4,4} Group order 72 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, z^-1 * x * y^-1 * x * z * y^-1, y^-1 * z * y^-1 * x * z * x^-1 ] T10.49 : Triangle type {4,4,4} Group order 72 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^4, z^4, z^-1 * y * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^2 ] T10.50 : Triangle type {4,4,11} Group order 44 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^11 ] T10.51 : Triangle type {4,4,20} Group order 40 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^6 * y * x^-1 * z^3 ] T10.52 : Triangle type {4,6,12} Group order 36 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^-2 * x^-1 * z * y^-1 ] T10.53 : Triangle type {4,14,28} Group order 28 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^-5 * z^2 ] T10.54 : Triangle type {5,6,30} Group order 30 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^6 ] T10.55 : Triangle type {5,25,25} Group order 25 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^-4 * z ] T10.56 : Triangle type {5,25,25} Group order 25 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^-3 * x^-1 * z^2 ] T10.57 : Triangle type {6,6,6} Group order 36 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^6 ] T10.58 : Triangle type {6,6,6} Group order 36 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^6, y^6 ] T10.59 : Triangle type {6,6,6} Group order 36 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, (x * y^-1)^2, y^6 ] T10.60 : Triangle type {6,6,15} Group order 30 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^2 * y * x * z^2 ] T10.61 : Triangle type {6,24,24} Group order 24 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^2 * x^-1 * z^2 ] T10.62 : Triangle type {8,12,24} Group order 24 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^8 ] T10.63 : Triangle type {8,12,24} Group order 24 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-1 * x^3 * z^-2 ] T10.64 : Triangle type {9,9,9} Group order 27 Action reflexible [n] Defining relators: [ x * y * z, x * y^-1 * x * z^-1, z * y^-1 * x * y^-1 ] T10.65 : Triangle type {9,9,9} Group order 27 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y^-1 * x^3 * y^-2, z^-1 * x^3 * z^-2 ] T10.66 : Triangle type {11,22,22} Group order 22 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^4 * y^-2 ] T10.67 : Triangle type {11,22,22} Group order 22 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^2 * x^-1 * y^2 ] T10.68 : Triangle type {11,22,22} Group order 22 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^5 * z^-1 ] T10.69 : Triangle type {11,22,22} Group order 22 Action reflexible [m] Defining relators: [ x * y * z, y * x^-1 * y, z^-4 * x^2 * z^-2 ] T10.70 : Triangle type {11,22,22} Group order 22 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-11, y * z^-1 ] T10.71 : Triangle type {12,12,12} Group order 24 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-1 * x^2 * z^-1 ] T10.72 : Triangle type {21,21,21} Group order 21 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^7 * x^-1 * y^3, x * z^-1 ] T10.73 : Triangle type {21,21,21} Group order 21 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-4 * z, y^2 * x^-1 * y^2 ] Genus 11 T11.1 : Triangle type {2,4,6} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^6, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, x * z * y^-1 * z * y^-2 * z^-2 * y * z^-1 * y ] T11.2 : Triangle type {2,4,8} Group order 160 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, x * z * y^-1 * z * y^2 * z^-1 * x * y^-1 * z^-1 ] T11.3 : Triangle type {2,4,8} Group order 160 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y * x * z * y^2 * z^-1 * x * z * y^-1 ] T11.4 : Triangle type {2,4,12} Group order 120 Action chiral Defining relators: [ x^2, x * y * z, y^4, z * y * z^-1 * x * y^-1 * z^-1 * x * z ] T11.5 : Triangle type {2,4,24} Group order 96 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-1 * x * z^5 * y * x * z^2 * y^-1 * z^-2 ] T11.6 : Triangle type {2,4,24} Group order 96 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-19 * x * y * z^-4 ] T11.7 : Triangle type {2,4,44} Group order 88 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-17 * x * y^-1 * z^-4 ] T11.8 : Triangle type {2,6,6} Group order 120 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^6, z^6, (y * z^-2 * y)^2, z^-1 * x * z * y^2 * x * y^-1 * z^-1 ] T11.9 : Triangle type {2,6,8} Group order 96 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z * y * z^-1 * x * y^-1 * z^-2 * x ] T11.10 : Triangle type {2,6,8} Group order 96 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, y^-1 * z * y^-2 * z^-2 * x ] T11.11 : Triangle type {2,6,33} Group order 66 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^6 * y^-1 * z^-4 * x ] T11.12 : Triangle type {2,8,8} Group order 80 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^-1 * z * y^-2 * z^-1 * x * z ] T11.13 : Triangle type {2,8,8} Group order 80 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^-2 * z^-1 * y * z^-1, y^8 ] T11.14 : Triangle type {2,8,16} Group order 64 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, x * z * y * x * z * y * z^-4 ] T11.15 : Triangle type {2,8,16} Group order 64 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-2 * x * z * y^-1 * z^-4 ] T11.16 : Triangle type {2,12,12} Group order 60 Action chiral Defining relators: [ x^2, x * y * z, z^-2 * y^2 * z^-1 * y ] T11.17 : Triangle type {2,23,46} Group order 46 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^12 * y^-10 ] T11.18 : Triangle type {2,24,24} Group order 48 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^13 * y^-9 * z ] T11.19 : Triangle type {2,24,24} Group order 48 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y^-2 * z^2 * y^-8 ] T11.20 : Triangle type {2,44,44} Group order 44 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^11 * y^-10 ] T11.21 : Triangle type {3,4,4} Group order 120 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^4, z^4, (x * z * y)^2, z^-1 * y * x^-1 * y^-1 * x * z * y^2 ] T11.22 : Triangle type {3,8,8} Group order 48 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, z * y * x^-1 * y^-2, z^-2 * x^-1 * z * y ] T11.23 : Triangle type {3,8,8} Group order 48 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, (y * z^-1 * y)^2 ] T11.24 : Triangle type {3,33,33} Group order 33 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^10 * z^-1 ] T11.25 : Triangle type {4,4,4} Group order 80 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, z^-1 * y * x^-1 * y^2, x^-1 * y * z^-1 * x^-1 * z * x^-1 * z ] T11.26 : Triangle type {4,4,4} Group order 80 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y^-2 * z^-1 * x^-1 * z * y^-1 * z ] T11.27 : Triangle type {4,4,6} Group order 60 Action chiral Defining relators: [ x * y * z, x^4, y^4, z * y * x^-1 * y * x ] T11.28 : Triangle type {4,4,12} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^12 ] T11.29 : Triangle type {4,4,12} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z * y^-1 * z^-1 * x^-1 * z^3 ] T11.30 : Triangle type {4,4,12} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3 ] T11.31 : Triangle type {4,4,22} Group order 44 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^4 * y^-1 * z^-3 * x * z^3 ] T11.32 : Triangle type {4,6,6} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x^4, z * y^-1 * x * z, y^6, y * z^-1 * y * x * y^-1 * z^-1 ] T11.33 : Triangle type {4,6,6} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, y^6 ] T11.34 : Triangle type {4,6,6} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * z * y^-1, y^6 ] T11.35 : Triangle type {4,8,8} Group order 40 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z * y * x^-1 * z * y^-1 ] T11.36 : Triangle type {4,8,8} Group order 40 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z^-1 * x^-1 * z * y^-1 ] T11.37 : Triangle type {4,16,16} Group order 32 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-1 * z^2 * y^-2 * z * y^-1 * z ] T11.38 : Triangle type {4,16,16} Group order 32 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y^-2 * z * y^-4 * z ] T11.39 : Triangle type {6,10,15} Group order 30 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^-3 * x^-1 * z^2 ] T11.40 : Triangle type {8,8,8} Group order 32 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, z * y^-1 * x^2 * z * y^-1 ] T11.41 : Triangle type {8,8,8} Group order 32 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^-3 * y^-1 * z^-1 ] T11.42 : Triangle type {12,24,24} Group order 24 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^12, y * z^-1 ] T11.43 : Triangle type {12,24,24} Group order 24 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-5 * y^2 ] T11.44 : Triangle type {23,23,23} Group order 23 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^8 * x^-1 * y^3, x * z^-1 ] T11.45 : Triangle type {23,23,23} Group order 23 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-4 * x * y^-3 ] T11.46 : Triangle type {23,23,23} Group order 23 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-3 * x * y^-2 ] T11.47 : Triangle type {23,23,23} Group order 23 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^2 * x^-1 * z^2 ] Genus 12 T12.1 : Triangle type {2,4,15} Group order 120 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-1 * x * z^8 * y * x * z * y^-1 * z^-3 ] T12.2 : Triangle type {2,4,26} Group order 104 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-20 * x * y * z^-5 ] T12.3 : Triangle type {2,4,48} Group order 96 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-19 * x * y^-1 * z^-4 ] T12.4 : Triangle type {2,5,10} Group order 110 Action chiral Defining relators: [ x^2, x * y * z, y^-5, x * z * y^-2 * z^-1 * y * z^-1 ] T12.5 : Triangle type {2,5,10} Group order 110 Action chiral Defining relators: [ x^2, x * y * z, y^-5, y^2 * z^-1 * y^2 * z^-1 * x * z ] T12.6 : Triangle type {2,6,14} Group order 84 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-4 * x * z^4 * y^-1 * x * y^-1 * z^-4 ] T12.7 : Triangle type {2,8,10} Group order 80 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, x * z^4 * y^-1 * x * y^-1 * z^-4 ] T12.8 : Triangle type {2,10,30} Group order 60 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y^10 ] T12.9 : Triangle type {2,14,28} Group order 56 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y^-4 * z * y^-7 * z * y^-1 ] T12.10 : Triangle type {2,15,15} Group order 60 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-11 * z * y^-1 ] T12.11 : Triangle type {2,25,50} Group order 50 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^14 * y^-10 ] T12.12 : Triangle type {2,26,26} Group order 52 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^15 * y^-9 * z ] T12.13 : Triangle type {2,48,48} Group order 48 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^13 * y^-10 ] T12.14 : Triangle type {3,3,14} Group order 84 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, y^-1 * z^-2 * x^-1 * z^3 ] T12.15 : Triangle type {3,13,39} Group order 39 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-5 * z * y^-5 * z^2 ] T12.16 : Triangle type {3,14,14} Group order 42 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^4 * y^-9 ] T12.17 : Triangle type {3,36,36} Group order 36 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-4 * z * y^-1 * z * y^-3 * z^2 ] T12.18 : Triangle type {4,4,13} Group order 52 Action reflexible [n] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z * y * z^-1 * x * z^2 ] T12.19 : Triangle type {4,4,13} Group order 52 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^5 * y^-1 * x^-1 * z^7 ] T12.20 : Triangle type {4,4,24} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^5 * y^-1 * z^-3 * x * z^3 ] T12.21 : Triangle type {4,6,8} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^-2 * x^-1 * y * z^-1 ] T12.22 : Triangle type {4,6,8} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-1 * z^2, y^6 ] T12.23 : Triangle type {4,9,36} Group order 36 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y * z^-1 * y^4 * z^-3 ] T12.24 : Triangle type {4,10,10} Group order 40 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, (y^3 * z^-1 * y)^2 ] T12.25 : Triangle type {4,32,32} Group order 32 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^-2 * z * y^-3 * z^2 ] T12.26 : Triangle type {5,5,5} Group order 55 Action chiral Defining relators: [ x * y * z, x^-5, y * x^-2 * z * y, y^-1 * z * x^-1 * z * y^-1 ] T12.27 : Triangle type {5,5,5} Group order 55 Action chiral Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-1 * z * y, x * z^-1 * x^-1 * y^2 ] T12.28 : Triangle type {5,7,35} Group order 35 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z * y^-2 * x * y^-3 ] T12.29 : Triangle type {5,8,8} Group order 40 Action reflexible [n] Defining relators: [ x * y * z, z^-1 * x^2 * y^-1, x^-1 * y^-1 * x * z^-1, y^8 ] T12.30 : Triangle type {5,8,8} Group order 40 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^-5, y^6 * z^-2 ] T12.31 : Triangle type {5,30,30} Group order 30 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-5, z^-1 * y^3 * z^-2 ] T12.32 : Triangle type {5,30,30} Group order 30 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^4 * z^-2 ] T12.33 : Triangle type {6,6,7} Group order 42 Action reflexible [n] Defining relators: [ x * y * z, z * y * x * z, z * x^-2 * y^-2, x^6 ] T12.34 : Triangle type {6,6,7} Group order 42 Action reflexible [n] Defining relators: [ x * y * z, x * z^-1 * y * z^-1, z * y * x^-1 * y^-1 * x, x^6 ] T12.35 : Triangle type {6,6,7} Group order 42 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^3 * y^-1 * x^-1 * z^3 ] T12.36 : Triangle type {6,9,9} Group order 36 Action reflexible [m] Defining relators: [ x * y * z, z * y^-1 * x * z, y * x^-2 * y^2, x^-1 * z * x^-1 * y^-1 * z ] T12.37 : Triangle type {6,15,30} Group order 30 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, z * y^-2 * x^-1 * z^2 ] T12.38 : Triangle type {7,28,28} Group order 28 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-7 ] T12.39 : Triangle type {7,28,28} Group order 28 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-2 * x^2 * y^-2 ] T12.40 : Triangle type {7,28,28} Group order 28 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-7 ] T12.41 : Triangle type {9,27,27} Group order 27 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^9 ] T12.42 : Triangle type {9,27,27} Group order 27 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-3 * y * z^-2 ] T12.43 : Triangle type {9,27,27} Group order 27 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^3 * x^-1 * y^3 ] T12.44 : Triangle type {10,10,15} Group order 30 Action reflexible [m] Defining relators: [ x * y * z, z * y^-1 * x * z, (x * z^-1)^2 ] T12.45 : Triangle type {10,10,15} Group order 30 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^-2 * y * x * z^-2 ] T12.46 : Triangle type {13,26,26} Group order 26 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-5 * y^2 ] T12.47 : Triangle type {13,26,26} Group order 26 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-2 * y^2 * z^-2 ] T12.48 : Triangle type {13,26,26} Group order 26 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^3 ] T12.49 : Triangle type {13,26,26} Group order 26 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^4 * y^-2 ] T12.50 : Triangle type {13,26,26} Group order 26 Action reflexible [m] Defining relators: [ x * y * z, y * x^-1 * y, z^-2 * x * z^-2 * x^3 * z^-2 ] T12.51 : Triangle type {13,26,26} Group order 26 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^13, y * z^-1 ] T12.52 : Triangle type {14,14,14} Group order 28 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^-3 * x^2 * z^-3 ] T12.53 : Triangle type {14,14,14} Group order 28 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4 * z^-2, y^-2 * x^2 * y^-2 ] T12.54 : Triangle type {25,25,25} Group order 25 Action reflexible [m] Defining relators: [ x * y * z, y * x^-1 * y, z^-5 * x^2 * z^-2 ] T12.55 : Triangle type {25,25,25} Group order 25 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^9 * x^-1 * y^3, x * z^-1 ] T12.56 : Triangle type {25,25,25} Group order 25 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-6 * z ] Genus 13 T13.1 : Triangle type {2,3,10} Group order 360 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^10, x * z * y * x * z * y * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 ] T13.2 : Triangle type {2,3,12} Group order 288 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, z^-12 ] T13.3 : Triangle type {2,4,12} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z * y * x * y^-1 * z^-1 * x, y * z^-3 * y * z^-1 * y * z^-1 * y * z^-3 ] T13.4 : Triangle type {2,4,16} Group order 128 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-5 * x * z^5 * y^-1 * x * z * y^-1 * z^-3 ] T13.5 : Triangle type {2,4,16} Group order 128 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-1 * x * z * y * x * y^-1 * z^-4 ] T13.6 : Triangle type {2,4,28} Group order 112 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-22 * x * y * z^-5 ] T13.7 : Triangle type {2,4,52} Group order 104 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-20 * x * y^-1 * z^-5 ] T13.8 : Triangle type {2,5,10} Group order 120 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^-5, z * y * z^-1 * y^2 * z^-1 * x * y^-1 ] T13.9 : Triangle type {2,6,6} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^6, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1 ] T13.10 : Triangle type {2,6,12} Group order 96 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, (y * z^-2)^2 ] T13.11 : Triangle type {2,6,12} Group order 96 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, x * z^2 * y^-1 * z^-3 ] T13.12 : Triangle type {2,6,15} Group order 90 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, x * z^9 * y * z^-5 ] T13.13 : Triangle type {2,6,39} Group order 78 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-3 * x * z^4 * y^-1 * z^-5 ] T13.14 : Triangle type {2,9,18} Group order 72 Action reflexible [m] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^-9 ] T13.15 : Triangle type {2,12,12} Group order 72 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T13.16 : Triangle type {2,12,12} Group order 72 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y^-3 * z^2 * y^-5 * z^2 ] T13.17 : Triangle type {2,16,16} Group order 64 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-1 * y^4 * z^-3 ] T13.18 : Triangle type {2,16,16} Group order 64 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^5 * z^-1 * y * z^-1 ] T13.19 : Triangle type {2,16,16} Group order 64 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-1 * y^8 * z^-2 * y^2 * z^-1 * y ] T13.20 : Triangle type {2,27,54} Group order 54 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^16 * y^-10 ] T13.21 : Triangle type {2,28,28} Group order 56 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^17 * y^-9 * z ] T13.22 : Triangle type {2,52,52} Group order 52 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^15 * y^-10 ] T13.23 : Triangle type {3,3,5} Group order 180 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^2 * y^-1 * x^-1 * z^2, (x * z^2 * y)^2 ] T13.24 : Triangle type {3,3,6} Group order 144 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, (x * z * y)^2, z^6 ] T13.25 : Triangle type {3,4,6} Group order 96 Action chiral Defining relators: [ x^3, x * y * z, y^4, x * z * y^-1 * x * z * y, (z^-1 * y)^3 ] T13.26 : Triangle type {3,4,6} Group order 96 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * x^-1 * y^-1 * x * z * y, (z^-1 * y)^3 ] T13.27 : Triangle type {3,4,6} Group order 96 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z * x^-1 * y^-1 * x * y^-1 * x, z * y^-1 * z^-1 * x * z * y^-1 ] T13.28 : Triangle type {3,4,6} Group order 96 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y^-1 * x * z^2, (x * z * y)^2, (z^-1 * y)^3 ] T13.29 : Triangle type {3,4,12} Group order 72 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-2 * x^-1 * z * y ] T13.30 : Triangle type {3,6,6} Group order 72 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^6 ] T13.31 : Triangle type {3,6,6} Group order 72 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, (x * z * y)^2 ] T13.32 : Triangle type {3,6,6} Group order 72 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, (y * z^-2 * y)^2 ] T13.33 : Triangle type {3,12,12} Group order 48 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, (y * z^-1)^2, y^2 * x^-1 * z^2 ] T13.34 : Triangle type {3,12,12} Group order 48 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^3 * z^-2 ] T13.35 : Triangle type {3,14,42} Group order 42 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-6 * z * y^-5 * z^2 ] T13.36 : Triangle type {3,15,15} Group order 45 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-7 * z * y^-5 * z^2 ] T13.37 : Triangle type {3,39,39} Group order 39 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-5 * z * y^-6 * z ] T13.38 : Triangle type {4,4,6} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^6, z^-3 * x^-1 * z^2 * y^-1 ] T13.39 : Triangle type {4,4,8} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^8 ] T13.40 : Triangle type {4,4,8} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1 ] T13.41 : Triangle type {4,4,8} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^-1 * x^-1 * y^-1 * x * z * y ] T13.42 : Triangle type {4,4,8} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y ] T13.43 : Triangle type {4,4,8} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^8 ] T13.44 : Triangle type {4,4,8} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * z * y, z * y * x^2 * z * y^-1 ] T13.45 : Triangle type {4,4,8} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, y * x * y^-1 * x * z^2 ] T13.46 : Triangle type {4,4,8} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y^-1 ] T13.47 : Triangle type {4,4,8} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y ] T13.48 : Triangle type {4,4,14} Group order 56 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^6 * y^-1 * x^-1 * z^7 ] T13.49 : Triangle type {4,4,26} Group order 52 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^5 * y * x^-1 * z^7 ] T13.50 : Triangle type {4,6,12} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, x^-1 * z * y * x * y^-1 * z^-1 ] T13.51 : Triangle type {4,6,12} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^6 ] T13.52 : Triangle type {4,10,20} Group order 40 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y * z^-3 * y^4 * z^-1 * y ] T13.53 : Triangle type {4,18,36} Group order 36 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y * z^-1 * y^5 * z^-1 * y ] T13.54 : Triangle type {5,5,5} Group order 60 Action reflexible [m,n] Defining relators: [ x * y * z, x^-5, z * y * x^-1 * y^-1 * x, x * z^-1 * x^-1 * z * y ] T13.55 : Triangle type {6,6,6} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, y^2 * x^-1 * z^2 ] T13.56 : Triangle type {6,6,6} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, (y * z^-1)^2, x^6 ] T13.57 : Triangle type {6,12,12} Group order 36 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^6, z^-1 * y^3 * z^-2 ] T13.58 : Triangle type {6,12,12} Group order 36 Action reflexible [m,n] Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^2 * z^-1, x^6 ] T13.59 : Triangle type {6,12,12} Group order 36 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^6, (z^-1 * y)^3 ] T13.60 : Triangle type {8,16,16} Group order 32 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^8 ] T13.61 : Triangle type {8,16,16} Group order 32 Action reflexible [m,n] Defining relators: [ x * y * z, (y * z^-1)^2, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x ] T13.62 : Triangle type {8,16,16} Group order 32 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, z^-2 * x^2 * z^-2 ] T13.63 : Triangle type {8,16,16} Group order 32 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^-3 * z * y ] T13.64 : Triangle type {9,9,9} Group order 36 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y * x * y^-1, (x * z^-1)^2, y^-1 * x^3 * y^-2 ] T13.65 : Triangle type {10,15,30} Group order 30 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-3 * x^2 * y^-3 ] T13.66 : Triangle type {10,15,30} Group order 30 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^4 * z^-2 ] T13.67 : Triangle type {10,15,30} Group order 30 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^-1 * z * x^-7 * y * x^-1 ] T13.68 : Triangle type {14,28,28} Group order 28 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^14, y * z^-1 ] T13.69 : Triangle type {14,28,28} Group order 28 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-5 * x^2 * y^-3 ] T13.70 : Triangle type {14,28,28} Group order 28 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^5 * z^-1 ] T13.71 : Triangle type {27,27,27} Group order 27 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^-1 * x^3 * z^-2 ] T13.72 : Triangle type {27,27,27} Group order 27 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^10 * x^-1 * y^3, x * z^-1 ] Genus 14 T14.1 : Triangle type {2,3,7} Group order 1092 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^-3 * x * y * z^-3, x * z * y * x * z * y * x * z * y * x * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 ] T14.2 : Triangle type {2,3,7} Group order 1092 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^-3 * x * y * z^-3, z * y * x * z * y * x * z^2 * y * x * z * y * x * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z ] T14.3 : Triangle type {2,3,7} Group order 1092 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^-3 * x * y * z^-3, x * z * y * x * z * y * x * z * y * x * z * y * x * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 ] T14.4 : Triangle type {2,4,30} Group order 120 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-24 * x * y * z^-5 ] T14.5 : Triangle type {2,4,56} Group order 112 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-22 * x * y^-1 * z^-5 ] T14.6 : Triangle type {2,6,6} Group order 156 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^6, y^-1 * z^-1 * x * y^-1 * z * y^2 * x * y^-1 * z^-1 * x ] T14.7 : Triangle type {2,6,16} Group order 96 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^5 * y * x * z * y * x * y^-1 * z^-3 * x * z^4 ] T14.8 : Triangle type {2,6,42} Group order 84 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^5 * y * z^-1 * x * z * y^-1 * z^-2 * x * z^3 ] T14.9 : Triangle type {2,8,20} Group order 80 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-1 * x * z * y * x * z * y * z^-5 ] T14.10 : Triangle type {2,10,35} Group order 70 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-3 * x * y^-1 * z^-3 ] T14.11 : Triangle type {2,29,58} Group order 58 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^18 * y^-10 ] T14.12 : Triangle type {2,30,30} Group order 60 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^18 * y^-11 ] T14.13 : Triangle type {2,56,56} Group order 56 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^17 * y^-10 ] T14.14 : Triangle type {3,4,5} Group order 120 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y^-1 * x^-1 * z^2 ] T14.15 : Triangle type {3,6,6} Group order 78 Action chiral Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y * z^-2 * y^2 * z^-1 * y * z^-1 ] T14.16 : Triangle type {3,6,6} Group order 78 Action chiral Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, y * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 ] T14.17 : Triangle type {3,16,16} Group order 48 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^6 * y^-9 ] T14.18 : Triangle type {3,42,42} Group order 42 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-6 * z * y^-7 ] T14.19 : Triangle type {4,4,15} Group order 60 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^-1 * z ] T14.20 : Triangle type {4,4,15} Group order 60 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-15 ] T14.21 : Triangle type {4,4,28} Group order 56 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^6 * y^-1 * x * z^7 ] T14.22 : Triangle type {4,6,24} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, y^6 ] T14.23 : Triangle type {4,8,12} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z * y * z^-1 * x^-1 * z^3 ] T14.24 : Triangle type {4,20,20} Group order 40 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^3 * z^-1 * y^5 * z^-1 ] T14.25 : Triangle type {5,8,40} Group order 40 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^8 ] T14.26 : Triangle type {5,35,35} Group order 35 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z * y^-2 * z^3 ] T14.27 : Triangle type {5,35,35} Group order 35 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z * y^-5 ] T14.28 : Triangle type {6,6,8} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^4 * y * x * z^3 ] T14.29 : Triangle type {6,6,21} Group order 42 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^3 * y^-1 * x * z^3 ] T14.30 : Triangle type {6,18,18} Group order 36 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^4 * z^-2 ] T14.31 : Triangle type {8,8,10} Group order 40 Action reflexible [n] Defining relators: [ x * y * z, y * x^-2 * y * z^-1, z * x^-2 * y^-1 * x ] T14.32 : Triangle type {8,8,10} Group order 40 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, y * x^-1 * y * x^-1 * z^3 ] T14.33 : Triangle type {8,32,32} Group order 32 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z * x^-3 * z^3 ] T14.34 : Triangle type {8,32,32} Group order 32 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^8 ] T14.35 : Triangle type {15,30,30} Group order 30 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^15, y * z^-1 ] T14.36 : Triangle type {15,30,30} Group order 30 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^3 * x^-3 * z^3 ] T14.37 : Triangle type {29,29,29} Group order 29 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^11 * x^-1 * y^3, x * z^-1 ] T14.38 : Triangle type {29,29,29} Group order 29 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-6 * x * y^-3 ] T14.39 : Triangle type {29,29,29} Group order 29 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-2 * x^3 * y^-3 ] T14.40 : Triangle type {29,29,29} Group order 29 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-3 * x * y^-2 ] T14.41 : Triangle type {29,29,29} Group order 29 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-5 * y^2 ] Genus 15 T15.1 : Triangle type {2,3,9} Group order 504 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^-4 * x * y * z^-4, z^-2 * x * z * y * x * z * y * z^-2 * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T15.2 : Triangle type {2,3,12} Group order 336 Action chiral Defining relators: [ x^2, y^3, x * y * z, z^-3 * x * z * y * x * y * z^-2 * x * y^-1 * z^-1, y * z^-1 * x * z^2 * y * x * z * y * x * y^-1 * z^-2 * x * z^2 ] T15.3 : Triangle type {2,3,14} Group order 294 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^9 * y * x * z^-1 * x * z^4 ] T15.4 : Triangle type {2,3,20} Group order 240 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^-4 * x * z * y^2 * x * z^2 * y^-1 * z^-1, z^2 * y * x * z * y * x * z * y^2 * z^-1 * x * y^-1 * z^-1 * x ] T15.5 : Triangle type {2,4,6} Group order 336 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^6, (z * y^-1 * z)^3 ] T15.6 : Triangle type {2,4,18} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-5 * x * z^5 * y * z^-1 * x * y * x * y^-1 * z^-4 ] T15.7 : Triangle type {2,4,32} Group order 128 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-5 * x * z^5 * y^-1 * z^-5 ] T15.8 : Triangle type {2,4,32} Group order 128 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-18 * x * z^7 * y^-1 * z^-6 ] T15.9 : Triangle type {2,4,60} Group order 120 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-24 * x * y^-1 * z^-5 ] T15.10 : Triangle type {2,6,10} Group order 120 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^-1 * x * y^-2 * z^-3 ] T15.11 : Triangle type {2,7,14} Group order 98 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^-7 ] T15.12 : Triangle type {2,8,12} Group order 96 Action reflexible [m] Defining relators: [ x^2, x * y * z, z^-1 * x * y^-2 * z^-2 * y, x * z^2 * y^-1 * z^-3 ] T15.13 : Triangle type {2,8,12} Group order 96 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, z * y * z^-1 * x * y^-1 * z^-2 * x ] T15.14 : Triangle type {2,8,12} Group order 96 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^6 * y * x * y^-1 * x * y^-1 * z^-3 * x ] T15.15 : Triangle type {2,8,12} Group order 96 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-2 * x * z^2 * y * z^-2 * x * z * y^-1 * z^-3 ] T15.16 : Triangle type {2,8,40} Group order 80 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-5 * x * z^2 * y^-1 * z^-2 ] T15.17 : Triangle type {2,8,40} Group order 80 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^5 * y^-1 * x * z^2 * y^-1 * z^-1 * x ] T15.18 : Triangle type {2,14,35} Group order 70 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^2 * y^-2 * z^3 ] T15.19 : Triangle type {2,18,18} Group order 72 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-14 * z * y^-1 ] T15.20 : Triangle type {2,22,33} Group order 66 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y^-2 * z^2 * y^-6 * z ] T15.21 : Triangle type {2,31,62} Group order 62 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^19 * y^-10 * z ] T15.22 : Triangle type {2,32,32} Group order 64 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^20 * y^-11 ] T15.23 : Triangle type {2,32,32} Group order 64 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-1 * y^8 * z^-2 * y^3 * z^-1 ] T15.24 : Triangle type {2,60,60} Group order 60 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^18 * y^-10 * z ] T15.25 : Triangle type {3,3,6} Group order 168 Action chiral Defining relators: [ x^3, x * y * z, y^3, z^6, z * y * z^-1 * x^-1 * y * x * z ] T15.26 : Triangle type {3,3,6} Group order 168 Action chiral Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, y * x * z * x^-1 * y^-1 * x * z * y * x * z ] T15.27 : Triangle type {3,3,7} Group order 147 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^3 * y^-1 * x^-1 * z^3 ] T15.28 : Triangle type {3,3,10} Group order 120 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-2 * x * z^2, z * y * x^-1 * y * x^-1 * y^-1 * x * y^-1 * x ] T15.29 : Triangle type {3,3,31} Group order 93 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z * y^-1 * z^-1 * x^-1 * z^3 ] T15.30 : Triangle type {3,4,4} Group order 168 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^4, z^4, z * x^-1 * y^-1 * x * y^-1 * x ] T15.31 : Triangle type {3,4,8} Group order 96 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * x * y^-1 * x * y^-1 * z^-1, (z^-1 * y)^3 ] T15.32 : Triangle type {3,4,8} Group order 96 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * z * y^-1 * x * z^2 * y^-1 ] T15.33 : Triangle type {3,4,8} Group order 96 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-2 * x^-1 * z * y^-1, z * y * x^-1 * y^-1 * x * y^-1 * z * y^-1 ] T15.34 : Triangle type {3,4,12} Group order 84 Action chiral Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, z^-1 * x^-1 * z * y^-1 * x * z * y * z^-1 ] T15.35 : Triangle type {3,16,48} Group order 48 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-8 * z * y^-5 * z^2 ] T15.36 : Triangle type {3,45,45} Group order 45 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-7 * z * y^-6 * z ] T15.37 : Triangle type {4,4,9} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^2, z^-5 * x * y * z^-3 ] T15.38 : Triangle type {4,4,16} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^3 * y * x^-1 * z^4 ] T15.39 : Triangle type {4,4,16} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^3 * y * x^-1 * z^4 ] T15.40 : Triangle type {4,4,16} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-16 ] T15.41 : Triangle type {4,4,16} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T15.42 : Triangle type {4,4,30} Group order 60 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-8 * x * y^-1 * z^-6 ] T15.43 : Triangle type {4,8,24} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^2 * y * x^-1 * z^3 ] T15.44 : Triangle type {4,8,24} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z * y^-1 * z^-1 * x^-1 * z^3 ] T15.45 : Triangle type {4,11,44} Group order 44 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^2 * z^-4 * y^5 ] T15.46 : Triangle type {4,12,12} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, (y * z^-1 * y)^2 ] T15.47 : Triangle type {4,12,12} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * z * y^-1, z^-1 * y^3 * z^-2 ] T15.48 : Triangle type {4,12,12} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * y * z^-2 ] T15.49 : Triangle type {4,12,12} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y * z^-1 * y * z^-4 * y^2 * z^-3 ] T15.50 : Triangle type {4,12,12} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^5 * z^-1 * y^4 * z^-1 * y ] T15.51 : Triangle type {4,40,40} Group order 40 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y * z^-3 * y^4 * z^-2 ] T15.52 : Triangle type {4,40,40} Group order 40 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y * z^-3 * y^6 ] T15.53 : Triangle type {5,5,11} Group order 55 Action reflexible [n] Defining relators: [ x * y * z, x^-5, z^-1 * x^-2 * y^-2, z^-2 * x^-1 * y^-1 * z^-1 ] T15.54 : Triangle type {5,5,11} Group order 55 Action reflexible [n] Defining relators: [ x * y * z, x * z^-1 * y * z^-1, x^-5, y^-1 * z^-1 * x^2 * y^-2 ] T15.55 : Triangle type {6,7,42} Group order 42 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z * y^-2 * x * y^-3 ] T15.56 : Triangle type {6,8,8} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, y * z^-1 * x^-1 * y^-1 * z ] T15.57 : Triangle type {6,8,8} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z * y * x^-1 * y^-2 ] T15.58 : Triangle type {6,8,8} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^6, y^8 ] T15.59 : Triangle type {6,8,8} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, y * x^-2 * z * x^-1, x^6 ] T15.60 : Triangle type {6,36,36} Group order 36 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, z^-3 * y * z^-2 ] T15.61 : Triangle type {7,7,7} Group order 49 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-7, y^-7 ] T15.62 : Triangle type {7,35,35} Group order 35 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^-7 ] T15.63 : Triangle type {7,35,35} Group order 35 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^-7 ] T15.64 : Triangle type {7,35,35} Group order 35 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y^-3 * x * y^-2, z^-3 * x * z^-2 ] T15.65 : Triangle type {8,8,20} Group order 40 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^2 * y^-1 * x * z^2 ] T15.66 : Triangle type {8,8,20} Group order 40 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z * y^-1 * z^-1 * x * z^2 ] T15.67 : Triangle type {9,12,36} Group order 36 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-9 ] T15.68 : Triangle type {9,12,36} Group order 36 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y * x^-3 * y^3 ] T15.69 : Triangle type {11,33,33} Group order 33 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^5 * z^-1 ] T15.70 : Triangle type {11,33,33} Group order 33 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x * y^-1, x^-1 * z^3 * x^-2 * z^3 ] T15.71 : Triangle type {11,33,33} Group order 33 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * z, x * z^-1 * x^7 * y^-1 * x^2 ] T15.72 : Triangle type {11,33,33} Group order 33 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^3 * x^-1 * z^3 ] T15.73 : Triangle type {11,33,33} Group order 33 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^-1 * y^3 * z^-2 ] T15.74 : Triangle type {16,32,32} Group order 32 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^16, y * z^-1 ] T15.75 : Triangle type {16,32,32} Group order 32 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x * y^-2 * x^6 ] T15.76 : Triangle type {16,32,32} Group order 32 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^3 * x^-1 * y^3 ] T15.77 : Triangle type {16,32,32} Group order 32 Action reflexible [m] Defining relators: [ x * y * z, y * x^-1 * y, z^-8 * x * z^-2 ] T15.78 : Triangle type {16,32,32} Group order 32 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, z^-3 * y * z^-2 ] T15.79 : Triangle type {31,31,31} Group order 31 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^12 * x^-1 * y^3, x * z^-1 ] T15.80 : Triangle type {31,31,31} Group order 31 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^4 * x^-1 * y^3 * x^-1 * y^2 ] T15.81 : Triangle type {31,31,31} Group order 31 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-4 * x * y^-3 ] T15.82 : Triangle type {31,31,31} Group order 31 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-4 * y^3 ] T15.83 : Triangle type {31,31,31} Group order 31 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^5 * y^-1, y^5 * z^-1 ] T15.84 : Triangle type {31,31,31} Group order 31 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^-2 * x^3 * y^-3 ] Genus 16 T16.1 : Triangle type {2,3,8} Group order 720 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^8, x * z * y * x * z * y * x * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1, y * x * z^2 * y * z^-1 * x * z^3 * y * x * z * y^-1 * z^-2 * x * z^3 ] T16.2 : Triangle type {2,4,5} Group order 600 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^-2 * x * y * z^-2, (y * z^-1)^6, y^-1 * z^2 * y * x * z * y * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x * z ] T16.3 : Triangle type {2,4,10} Group order 200 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z * y * x * y^-1 * z^-1 * x, z^10 ] T16.4 : Triangle type {2,4,34} Group order 136 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-27 * x * y * z^-6 ] T16.5 : Triangle type {2,4,64} Group order 128 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-25 * x * y^-1 * z^-6 ] T16.6 : Triangle type {2,5,5} Group order 300 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^-5, z^-2 * x * y * z^-2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z * y^-1 * z * y^-2 * z^-2 * y * z^-1 * y ] T16.7 : Triangle type {2,6,8} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z^2 * y^-2 * z^-1 * x * y^-1, z^8 ] T16.8 : Triangle type {2,6,18} Group order 108 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z * y * z^-1 * x * y^-1 * z^-1 * x * z ] T16.9 : Triangle type {2,6,18} Group order 108 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^6 * y * x * z^3 * y * x * y * x * y^-1 * z^-3 * x * z^2 ] T16.10 : Triangle type {2,6,18} Group order 108 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, x * z^11 * y * x * y^-1 * z^-5 ] T16.11 : Triangle type {2,6,48} Group order 96 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, x * z^10 * y * x * y^-1 * z^-4 ] T16.12 : Triangle type {2,10,10} Group order 100 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^10, (y * z^-1 * y^3)^2 ] T16.13 : Triangle type {2,10,10} Group order 100 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, x * z^4 * y^-1 * x * y^-1 * z^-4 ] T16.14 : Triangle type {2,10,40} Group order 80 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^10 ] T16.15 : Triangle type {2,18,36} Group order 72 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-2 * y^8 * z^-2 * y^6 ] T16.16 : Triangle type {2,33,66} Group order 66 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^21 * y^-10 * z ] T16.17 : Triangle type {2,34,34} Group order 68 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^22 * y^-11 ] T16.18 : Triangle type {2,64,64} Group order 64 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^20 * y^-10 * z ] T16.19 : Triangle type {3,3,4} Group order 360 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^4, z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x, x^-1 * z * y * z^-1 * x^-1 * y * x^-1 * y^-1 * x * z * y^-1 * z^-1 ] T16.20 : Triangle type {3,4,6} Group order 120 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, (x * z * y)^2, (y * z^-2)^2 ] T16.21 : Triangle type {3,4,6} Group order 120 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, (y * z^-1)^2, z^6 ] T16.22 : Triangle type {3,6,12} Group order 72 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, z * x^-1 * y^-1 * x * y^-1 * x ] T16.23 : Triangle type {3,6,12} Group order 72 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6 ] T16.24 : Triangle type {3,6,12} Group order 72 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, y^6 ] T16.25 : Triangle type {3,8,8} Group order 72 Action reflexible [n] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * z * y^-1, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, y^8 ] T16.26 : Triangle type {3,8,8} Group order 72 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y^8 ] T16.27 : Triangle type {3,10,15} Group order 60 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^-3 * x^-1 * z^2 ] T16.28 : Triangle type {3,17,51} Group order 51 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-9 * z * y^-5 * z^2 ] T16.29 : Triangle type {3,18,18} Group order 54 Action chiral Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, z^-2 * y^2 * z^-1 * y ] T16.30 : Triangle type {3,18,18} Group order 54 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-10 * z * y^-5 * z^2 ] T16.31 : Triangle type {3,18,18} Group order 54 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^2 * z^-2 ] T16.32 : Triangle type {3,18,18} Group order 54 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^8 * y^-9 ] T16.33 : Triangle type {3,48,48} Group order 48 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-8 * z * y^-6 * z ] T16.34 : Triangle type {4,4,5} Group order 100 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, z^2 * y^-1 * x^-1 * z^2, y^-1 * z^-1 * y * x * z * x^-1 ] T16.35 : Triangle type {4,4,5} Group order 100 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^2 * y^-1 * x^-1 * z^2 ] T16.36 : Triangle type {4,4,17} Group order 68 Action reflexible [n] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-2 * y * x * z^-2 ] T16.37 : Triangle type {4,4,17} Group order 68 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^9 * y * x * z^7 ] T16.38 : Triangle type {4,4,32} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-9 * x * y^-1 * z^-6 ] T16.39 : Triangle type {4,6,6} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^6, z * y^2 * x * z^-1 * x ] T16.40 : Triangle type {4,6,6} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^6 ] T16.41 : Triangle type {4,6,6} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^6, (y * z^-1 * y)^2 ] T16.42 : Triangle type {4,6,12} Group order 60 Action chiral Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, x * z^-1 * x^-1 * y * z^-1 ] T16.43 : Triangle type {4,12,24} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, z^-1 * y^3 * z^-1 * y ] T16.44 : Triangle type {4,22,44} Group order 44 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^2 * z^-4 * y^3 * z^-2 ] T16.45 : Triangle type {5,9,45} Group order 45 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y * z^-3 * y^3 * z^-2 ] T16.46 : Triangle type {5,10,10} Group order 50 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-5, y * z^-4 * y^4 * z^-1 ] T16.47 : Triangle type {5,10,10} Group order 50 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, x^-5, z^-1 * y * x^-1 * y^-2 ] T16.48 : Triangle type {5,10,10} Group order 50 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^-5, (y^-3 * z * y^-1)^2 ] T16.49 : Triangle type {5,10,10} Group order 50 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^-5, x^-1 * y^-1 * x^2 * z * x^-1 ] T16.50 : Triangle type {5,40,40} Group order 40 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^6 * z^-1 * y ] T16.51 : Triangle type {5,40,40} Group order 40 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-5, z^-1 * y^4 * z^-3 ] T16.52 : Triangle type {6,6,9} Group order 54 Action chiral Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^-1 * y * x^-1 * y^-1 * z^-1 ] T16.53 : Triangle type {6,6,9} Group order 54 Action reflexible [n] Defining relators: [ x * y * z, z * y * x * z, x^6, (x * y^-1 * x)^2 ] T16.54 : Triangle type {6,6,9} Group order 54 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^9 ] T16.55 : Triangle type {6,6,9} Group order 54 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^9 ] T16.56 : Triangle type {6,6,24} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^3 * y^-1 * z^-1 * x^-1 * z^3 ] T16.57 : Triangle type {6,8,12} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^2 * x^-1 * y^-1 * z^-1, x^6 ] T16.58 : Triangle type {6,14,21} Group order 42 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z * y^-3 * z^2 ] T16.59 : Triangle type {8,10,40} Group order 40 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^8 ] T16.60 : Triangle type {9,36,36} Group order 36 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-9 ] T16.61 : Triangle type {9,36,36} Group order 36 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-1 * x^4 * y^-3 ] T16.62 : Triangle type {10,10,20} Group order 40 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * x^-1 * z^2, y^-2 * x^2 * y^-2 ] T16.63 : Triangle type {10,10,20} Group order 40 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-2 * x^-1 * z * y^-1, z^-2 * x^2 * z^-2 ] T16.64 : Triangle type {12,18,36} Group order 36 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^-12 ] T16.65 : Triangle type {12,18,36} Group order 36 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-3 * x^2 * z^-3 ] T16.66 : Triangle type {17,34,34} Group order 34 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-1 * y^2 * x^-6 ] T16.67 : Triangle type {17,34,34} Group order 34 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^-5 * z^2 ] T16.68 : Triangle type {17,34,34} Group order 34 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-3 * x^2 * z^-3 ] T16.69 : Triangle type {17,34,34} Group order 34 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^3 * x^-1 * z^3 ] T16.70 : Triangle type {17,34,34} Group order 34 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^4 * x^-1 * y^4 ] T16.71 : Triangle type {17,34,34} Group order 34 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4 * z^-2, y^5 * z^-1 ] T16.72 : Triangle type {17,34,34} Group order 34 Action reflexible [m] Defining relators: [ x * y * z, y * x^-1 * y, z^-8 * x^2 * z^-2 ] T16.73 : Triangle type {17,34,34} Group order 34 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^17, y * z^-1 ] T16.74 : Triangle type {18,18,18} Group order 36 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, (x^-1 * y^4)^2 ] T16.75 : Triangle type {33,33,33} Group order 33 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^12 * x^-1 * y^4, x * z^-1 ] T16.76 : Triangle type {33,33,33} Group order 33 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-4 * y, y^-1 * z * y^-2 * x^-1 * z^3 ] Genus 17 T17.1 : Triangle type {2,3,7} Group order 1344 Action chiral Defining relators: [ x^2, y^3, x * y * z, z^-3 * x * y * z^-3, x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1, z * y * x * z * y * z^-1 * x * z * y^-1 * z^-1 * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x * y^-1 * z^-2 * x * z ] T17.2 : Triangle type {2,3,8} Group order 768 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^8, z^2 * y * x * z^2 * y * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x ] T17.3 : Triangle type {2,3,14} Group order 336 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, y * z^-4 * x * z * y * x * y * z^-3 * x * z ] T17.4 : Triangle type {2,4,6} Group order 384 Action chiral Defining relators: [ x^2, x * y * z, y^4, z^6, z * y * x * z * y^2 * z^-1 * x * z * y^-1, x * z * y * z^-1 * y * z^-1 * x * y^-1 * z * y^-1 * z * y^-1 * z^-1 * y ] T17.5 : Triangle type {2,4,6} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^6, x * z^2 * y^-1 * z * y^2 * z^-2 * x * y^-1 * z^-1, z * y * z^-2 * y * x * y^-1 * z^2 * y^-1 * z^-1 * x ] T17.6 : Triangle type {2,4,6} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^6, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (y * z^-2)^4 ] T17.7 : Triangle type {2,4,6} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^6, (y * z^-1)^4, (y^-1 * z^2)^4 ] T17.8 : Triangle type {2,4,8} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T17.9 : Triangle type {2,4,8} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^8, z * y * z^-2 * x * y^-1 * z^-3 * x ] T17.10 : Triangle type {2,4,8} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^8, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z * y * z^-2 * x * y^-1 * z^-3 * x ] T17.11 : Triangle type {2,4,8} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y * x * z * y * x * y^-1 * z * y^-1 * z^-1 * y * z^-1 * x ] T17.12 : Triangle type {2,4,12} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^2 * y^-2 * z^-3 * y, z^-4 * x * z^5 * y^-1 * z^-2 ] T17.13 : Triangle type {2,4,12} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z * y * z^-1 * x * y^-1 * z^-2 * x ] T17.14 : Triangle type {2,4,12} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-12 ] T17.15 : Triangle type {2,4,20} Group order 160 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-14 * x * y * z^-5 ] T17.16 : Triangle type {2,4,36} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-29 * x * y * z^-6 ] T17.17 : Triangle type {2,4,68} Group order 136 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-27 * x * y^-1 * z^-6 ] T17.18 : Triangle type {2,5,6} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^-5, z^6, y^-1 * z * y^-1 * z * y^2 * z^-1 * x * z^2 ] T17.19 : Triangle type {2,5,10} Group order 160 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^-5, y * x * z * y^2 * z^-3 ] T17.20 : Triangle type {2,5,10} Group order 160 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^-5, z * y * x * y^-1 * z^-1 * x, z * y^2 * z^-1 * y^2 * z^-1 * y * x * y^-1 ] T17.21 : Triangle type {2,6,6} Group order 192 Action chiral Defining relators: [ x^2, x * y * z, y^6, z^6, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, y * z^-1 * x * z * y^2 * x * z * y^-1 * z ] T17.22 : Triangle type {2,6,6} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^6, y^-1 * z * y * x * y^-1 * z * y^-2 * z^-1 * x * y^-1 * z ] T17.23 : Triangle type {2,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, z^6, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1 ] T17.24 : Triangle type {2,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^6, z^6, y^-1 * z * y^-3 * z^-1 * x * z^2, z^-1 * y * x * y^-2 * z * y^-1 * z^-2 ] T17.25 : Triangle type {2,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^6, (z^-1 * y)^3, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1 ] T17.26 : Triangle type {2,6,15} Group order 120 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z * y * z^-1 * y^2 * z^-1 * x * z ] T17.27 : Triangle type {2,6,51} Group order 102 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-1 * x * z^9 * y * x * y^-1 * z^-5 ] T17.28 : Triangle type {2,7,14} Group order 112 Action chiral Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^-7, z^2 * y^-2 * z * y^-1 * z ] T17.29 : Triangle type {2,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^8 ] T17.30 : Triangle type {2,8,8} Group order 128 Action reflexible [m] Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, (y * z^-1 * y^2)^2, z^8 ] T17.31 : Triangle type {2,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y ] T17.32 : Triangle type {2,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, (y * z^-1)^4 ] T17.33 : Triangle type {2,8,8} Group order 128 Action reflexible [m] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, (y * z^-2 * y)^2, (y * z^-3)^2, y^-1 * z * y^-3 * z^-1 * y * x * z ] T17.34 : Triangle type {2,8,8} Group order 128 Action reflexible [m] Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, z^8, y^-1 * z * y^-3 * z^-2 * x * y^-1 ] T17.35 : Triangle type {2,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4 ] T17.36 : Triangle type {2,8,24} Group order 96 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-2 * x * z^3 * y * x * y^-1 * z^-5 ] T17.37 : Triangle type {2,8,24} Group order 96 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-2 * x * z^2 * y * z^-7 ] T17.38 : Triangle type {2,12,12} Group order 96 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^-12 ] T17.39 : Triangle type {2,12,12} Group order 96 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, (y * z^-2)^2 ] T17.40 : Triangle type {2,12,12} Group order 96 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^-12 ] T17.41 : Triangle type {2,20,20} Group order 80 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, (y * z^-1 * y^8)^2 ] T17.42 : Triangle type {2,35,70} Group order 70 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^23 * y^-10 * z ] T17.43 : Triangle type {2,36,36} Group order 72 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^24 * y^-11 ] T17.44 : Triangle type {2,68,68} Group order 68 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^22 * y^-10 * z ] T17.45 : Triangle type {3,3,4} Group order 384 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * z * y * x^-1 * y^-1 * x * z * y * x^-1 * z ] T17.46 : Triangle type {3,3,7} Group order 168 Action chiral Defining relators: [ x^3, x * y * z, y^3, x^-1 * y * x^-1 * y^-1 * x * z * y^-1 * z^-1 ] T17.47 : Triangle type {3,3,7} Group order 168 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, x^-1 * z^2 * y^-1 * x * z^3 ] T17.48 : Triangle type {3,4,4} Group order 192 Action chiral Defining relators: [ x^3, x * y * z, y^4, z^4, z * y * x^-1 * y^-1 * x * y^-1 * z * y^-1 ] T17.49 : Triangle type {3,4,4} Group order 192 Action chiral Defining relators: [ x^3, x * y * z, y^4, z^4, y^-2 * z^-1 * x^-1 * z * y^-1 * z, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T17.50 : Triangle type {3,4,4} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^4, z^4, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y^-1, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T17.51 : Triangle type {3,4,4} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^4, z^4, (x^-1 * z * y)^2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T17.52 : Triangle type {3,4,4} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^4, z^4, (z^-1 * y)^3, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T17.53 : Triangle type {3,4,12} Group order 96 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^-3 * x^-1 * z^2 * y^-1 ] T17.54 : Triangle type {3,5,5} Group order 120 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^-5, z^2 * y^-1 * x^-1 * z^2, z^-1 * x^-1 * y * x^-1 * z * y^-2 ] T17.55 : Triangle type {3,6,6} Group order 96 Action chiral Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-1 * z^-1, y^2 * z^-1 * x^-1 * y^-2 * z^-1 ] T17.56 : Triangle type {3,6,6} Group order 96 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, y * z^-1 * x^-1 * y^-1 * x * z * y * z^-1 ] T17.57 : Triangle type {3,6,6} Group order 96 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, (y^-1 * z)^4 ] T17.58 : Triangle type {3,6,6} Group order 96 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, (y * z^-1)^2, y^6, (x * z * y)^2 ] T17.59 : Triangle type {3,15,15} Group order 60 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z * y^-2 * x * y^-1 * z ] T17.60 : Triangle type {3,51,51} Group order 51 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-9 * z * y^-7 ] T17.61 : Triangle type {4,4,4} Group order 128 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, x^-1 * z * y * x^-1 * y^-1 * z^-1 ] T17.62 : Triangle type {4,4,4} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, z^-2 * x^-1 * z * y^-1, (x * y^-1)^4 ] T17.63 : Triangle type {4,4,4} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, z^-2 * x^-1 * z * y^-1, y * x^-1 * y * x^-2 * y^-1 * x * z^-1 * x^-1 ] T17.64 : Triangle type {4,4,4} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, (x^-1 * z * y)^2 ] T17.65 : Triangle type {4,4,4} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1 ] T17.66 : Triangle type {4,4,6} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^6, y^-1 * z * y * x^-1 * y^-1 * z^2 ] T17.67 : Triangle type {4,4,6} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, (x * z^-1 * y)^2, z^6 ] T17.68 : Triangle type {4,4,6} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z * y * x^-1 * y^-1 * x ] T17.69 : Triangle type {4,4,6} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, (y * z^-2)^2, z^6 ] T17.70 : Triangle type {4,4,6} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^6, y^-1 * z^-1 * y * x^-1 * z * y^-1 * z ] T17.71 : Triangle type {4,4,6} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z^6 ] T17.72 : Triangle type {4,4,10} Group order 80 Action reflexible [n] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, y^-1 * z^-2 * x^-1 * z^3 ] T17.73 : Triangle type {4,4,10} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^10 ] T17.74 : Triangle type {4,4,18} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^9 * y^-1 * x^-1 * z^8 ] T17.75 : Triangle type {4,4,34} Group order 68 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^9 * y * x^-1 * z^7 ] T17.76 : Triangle type {4,8,8} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^-1 * z * y * x * y^-1 * z^-1 ] T17.77 : Triangle type {4,8,8} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x * z^-1 * x ] T17.78 : Triangle type {4,8,8} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^8 ] T17.79 : Triangle type {4,8,8} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^8 ] T17.80 : Triangle type {4,8,8} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * y^-1 * z^-1 ] T17.81 : Triangle type {4,8,8} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-2 * x^-1 * y * z^-1 ] T17.82 : Triangle type {4,8,8} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y^8 ] T17.83 : Triangle type {4,8,8} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * z * y ] T17.84 : Triangle type {4,8,8} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y ] T17.85 : Triangle type {4,8,8} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^8 ] T17.86 : Triangle type {4,8,8} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, y^8 ] T17.87 : Triangle type {4,8,8} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1 ] T17.88 : Triangle type {4,8,8} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^-1 * z * y * x * z * y ] T17.89 : Triangle type {4,8,8} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1 ] T17.90 : Triangle type {4,8,8} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, z^-1 * y^2 * x * z^-1 * x ] T17.91 : Triangle type {4,8,8} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, z * x^-1 * y^-1 * x * y^-1 * z ] T17.92 : Triangle type {4,24,24} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, (y^5 * z^-1)^2 ] T17.93 : Triangle type {4,24,24} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y * z^-1 * y * z^-4 * y^4 * z^-1 ] T17.94 : Triangle type {5,5,5} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, (x * z^-1)^2, x^-5, (x * y^-2)^2, y^-5 ] T17.95 : Triangle type {6,8,24} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^2 * x^-1 * y * z^-1, x^6 ] T17.96 : Triangle type {6,8,24} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^8 ] T17.97 : Triangle type {6,12,12} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, y^2 * x^-1 * z^2 ] T17.98 : Triangle type {6,12,12} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, (y * z^-1)^2, x^6 ] T17.99 : Triangle type {6,12,12} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^6 ] T17.100 : Triangle type {6,21,42} Group order 42 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z * y^-4 * z ] T17.101 : Triangle type {7,7,7} Group order 56 Action chiral Defining relators: [ x * y * z, (x * z^-1)^2, y * x^-2 * y * z^-1, z^-2 * x^-1 * y^2 ] T17.102 : Triangle type {7,7,7} Group order 56 Action chiral Defining relators: [ x * y * z, z^-1 * y * x^-1 * y * x, z * y * x^-1 * z * y^-1 ] T17.103 : Triangle type {8,8,12} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z * y^-1 * z^-1 * x^-1 * z^3 ] T17.104 : Triangle type {8,8,12} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z * y^-1 * x * y^-1 * x * z^3 ] T17.105 : Triangle type {8,20,40} Group order 40 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^8 ] T17.106 : Triangle type {8,20,40} Group order 40 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^2 * x^-2 * y^3 ] T17.107 : Triangle type {10,20,20} Group order 40 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, z^-1 * x^4 * z^-3 ] T17.108 : Triangle type {10,20,20} Group order 40 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-1 * y * x^-6 * z * x^-2 ] T17.109 : Triangle type {18,36,36} Group order 36 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-18, y * z^-1 ] T17.110 : Triangle type {18,36,36} Group order 36 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-5 * z^2 ] T17.111 : Triangle type {35,35,35} Group order 35 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^-14 * x * y^-3, x * z^-1 ] T17.112 : Triangle type {35,35,35} Group order 35 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-1 * z^2 * x^-5 * y * x^-1 ] T17.113 : Triangle type {35,35,35} Group order 35 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-11 * z ] Genus 18 T18.1 : Triangle type {2,4,21} Group order 168 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-8 * x * z^5 * y * z^-1 * x * y * x * y^-1 * z^-4 ] T18.2 : Triangle type {2,4,38} Group order 152 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-31 * x * y * z^-6 ] T18.3 : Triangle type {2,4,72} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-29 * x * y^-1 * z^-6 ] T18.4 : Triangle type {2,6,20} Group order 120 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^7 * y^-1 * x * z^12 ] T18.5 : Triangle type {2,8,8} Group order 136 Action chiral Defining relators: [ x^2, x * y * z, z^-1 * y * x * y^-1 * z^-3 ] T18.6 : Triangle type {2,8,14} Group order 112 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-4 * x * z^3 * y * x * y * x * y^-1 * z^-4 ] T18.7 : Triangle type {2,10,45} Group order 90 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y * z^-3 * x * y^-1 * z^-3 ] T18.8 : Triangle type {2,12,16} Group order 96 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, z^3 * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T18.9 : Triangle type {2,14,42} Group order 84 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y^-4 * z * y^-7 * z * y^-1 ] T18.10 : Triangle type {2,20,40} Group order 80 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^6 * z^-4 ] T18.11 : Triangle type {2,21,21} Group order 84 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^2 * z^-10 * y^8 * z^-1 ] T18.12 : Triangle type {2,26,39} Group order 78 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y^-3 * z^2 * y^-6 * z * y^-1 ] T18.13 : Triangle type {2,37,74} Group order 74 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^25 * y^-10 * z ] T18.14 : Triangle type {2,38,38} Group order 76 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^38 ] T18.15 : Triangle type {2,72,72} Group order 72 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^24 * y^-10 * z ] T18.16 : Triangle type {3,3,37} Group order 111 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, y^-1 * z^-3 * x^-1 * z^3 ] T18.17 : Triangle type {3,19,57} Group order 57 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-11 * z * y^-5 * z^2 ] T18.18 : Triangle type {3,20,20} Group order 60 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^10 * y^-9 ] T18.19 : Triangle type {3,54,54} Group order 54 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-10 * z * y^-7 ] T18.20 : Triangle type {4,4,19} Group order 76 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^10 * y^-1 * x * y^-1 * z^-3 * x * z^4 ] T18.21 : Triangle type {4,4,36} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^9 * y^-1 * x * z^8 ] T18.22 : Triangle type {4,13,52} Group order 52 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^-2 * z * y^-1 * z^4 * y^-2 * z^3 ] T18.23 : Triangle type {4,14,14} Group order 56 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, y * z^-3 * y * z^-1 * y^2 * z^-1 * y * z^-3 * y ] T18.24 : Triangle type {4,48,48} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y * z^-1 * y * z^-4 * y^3 * z^-2 ] T18.25 : Triangle type {5,45,45} Group order 45 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y * z^-3 * y^5 ] T18.26 : Triangle type {5,45,45} Group order 45 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-5, z^-4 * y^2 * z^-3 ] T18.27 : Triangle type {6,6,10} Group order 60 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-4 * x^-1 * y * x^-1 * y * x^-1 * y * z^-3 ] T18.28 : Triangle type {6,12,24} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2 ] T18.29 : Triangle type {6,16,16} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^6, y * z^-1 * y^3 * z^-1 * y * z^-1 ] T18.30 : Triangle type {7,8,8} Group order 56 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^-7, y^8 ] T18.31 : Triangle type {7,42,42} Group order 42 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^-7 ] T18.32 : Triangle type {7,42,42} Group order 42 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-7 ] T18.33 : Triangle type {7,42,42} Group order 42 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-7 ] T18.34 : Triangle type {8,12,12} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, z^-1 * y * z^-1 * x^-1 * y * z^-1 * y ] T18.35 : Triangle type {10,40,40} Group order 40 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-10 ] T18.36 : Triangle type {10,40,40} Group order 40 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z * x^-3 * z^3 ] T18.37 : Triangle type {13,39,39} Group order 39 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^-1 * y^9 ] T18.38 : Triangle type {13,39,39} Group order 39 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * x^3 * y^-2, z^3 * x^-1 * z^3 ] T18.39 : Triangle type {13,39,39} Group order 39 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, x * z^-3 * x^2 * z^-3 ] T18.40 : Triangle type {13,39,39} Group order 39 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-13 ] T18.41 : Triangle type {13,39,39} Group order 39 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^5 * y^-3 ] T18.42 : Triangle type {13,39,39} Group order 39 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-4 * z^3 ] T18.43 : Triangle type {14,14,21} Group order 42 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, x^-1 * y * x^-1 * y * z^-1 ] T18.44 : Triangle type {14,14,21} Group order 42 Action reflexible [m] Defining relators: [ x * y * z, z * y^-1 * x * z, z^-1 * y * x^-1 * y^-2, x^4 * y^-2 ] T18.45 : Triangle type {14,14,21} Group order 42 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^-3 * x^2 * z^-3 ] T18.46 : Triangle type {19,38,38} Group order 38 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^2 * z^-1 * y^7 ] T18.47 : Triangle type {19,38,38} Group order 38 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-11 * x * y^-1 ] T18.48 : Triangle type {19,38,38} Group order 38 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^-3 * x^2 * z^-3 ] T18.49 : Triangle type {19,38,38} Group order 38 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-1 * y * x^-6 * y * x^-2 ] T18.50 : Triangle type {19,38,38} Group order 38 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4 * y^-2, z^3 * x^-1 * z^3 ] T18.51 : Triangle type {19,38,38} Group order 38 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^6 * z^-1 * y ] T18.52 : Triangle type {19,38,38} Group order 38 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-5 * z^2 ] T18.53 : Triangle type {19,38,38} Group order 38 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, y * x^-3 * y^3 ] T18.54 : Triangle type {19,38,38} Group order 38 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-19, y * z^-1 ] T18.55 : Triangle type {20,20,20} Group order 40 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, z^-1 * y * x^-1 * y^-2, y^-1 * x * y^-1 * x * y^-2 ] T18.56 : Triangle type {37,37,37} Group order 37 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^-15 * x * y^-3, x * z^-1 ] T18.57 : Triangle type {37,37,37} Group order 37 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-4 * x^2 * y^-7 ] T18.58 : Triangle type {37,37,37} Group order 37 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^-1 * y^4 * x^-2 * y^3 ] T18.59 : Triangle type {37,37,37} Group order 37 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-2 * x^3 * y^-3 ] T18.60 : Triangle type {37,37,37} Group order 37 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-5 * y^2 ] T18.61 : Triangle type {37,37,37} Group order 37 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-3 * x^2 * y * z^-3 ] T18.62 : Triangle type {37,37,37} Group order 37 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y * x^-3 * y^3 ] Genus 19 T19.1 : Triangle type {2,3,12} Group order 432 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z * y * z^-3 * x * y^-1 * z^-4 * x, x * z * y * x * z * y * x * z * y * x * z * y * z^-1 * x * z^2 * y^-1 * z^-2 ] T19.2 : Triangle type {2,3,24} Group order 288 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-1 * x * z^8 * y * x * y * z^-5 ] T19.3 : Triangle type {2,4,5} Group order 720 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^-2 * x * y * z^-2, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T19.4 : Triangle type {2,4,7} Group order 336 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^-3 * x * y * z^-3, x * z * y^-1 * z * y^-2 * z^-2 * y * z^-1 * y ] T19.5 : Triangle type {2,4,8} Group order 288 Action chiral Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z^3 * y * x * y^-1 * z^-3 * x ] T19.6 : Triangle type {2,4,8} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, (y^-1 * z)^6 ] T19.7 : Triangle type {2,4,8} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, x * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^-2 ] T19.8 : Triangle type {2,4,10} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (y * z^-2 * y * z^-1)^2 ] T19.9 : Triangle type {2,4,12} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^3 * y^-1 * z^-4 ] T19.10 : Triangle type {2,4,12} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T19.11 : Triangle type {2,4,40} Group order 160 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-33 * x * y * z^-6 ] T19.12 : Triangle type {2,4,40} Group order 160 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-14 * x * z * y^-1 * z^-4 ] T19.13 : Triangle type {2,4,76} Group order 152 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-31 * x * y^-1 * z^-6 ] T19.14 : Triangle type {2,5,5} Group order 360 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^-5, z^-2 * x * y * z^-2, (y * z^-1)^4 ] T19.15 : Triangle type {2,6,9} Group order 162 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, z^-4 * x * y * z^-4 ] T19.16 : Triangle type {2,6,9} Group order 162 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, (y^-2 * z)^3 ] T19.17 : Triangle type {2,6,9} Group order 162 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, x * y^-1 * z * y^-2 * z^-1 * x * y^-1 * z^-1 ] T19.18 : Triangle type {2,6,9} Group order 162 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, x * z^2 * y^-1 * z^-3, (y^-2 * z)^3 ] T19.19 : Triangle type {2,6,12} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^3 * y^-1 * z^-4 ] T19.20 : Triangle type {2,6,12} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, z * y * z^-1 * x * y^-1 * z^-2 * x, (y * z^-1)^4 ] T19.21 : Triangle type {2,6,12} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^3 * y^2 * x * z^2, x * z^2 * y^-1 * z * y * x * z * y^-1 * z^-2 ] T19.22 : Triangle type {2,6,21} Group order 126 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, x * z^5 * y * z^-1 * x * y^-1 * z^-13 ] T19.23 : Triangle type {2,6,57} Group order 114 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-1 * x * z^4 * y^-1 * z^-13 ] T19.24 : Triangle type {2,7,7} Group order 168 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^-7, z^-1 * x * z * y^2 * x * y^-1 * z^-1 ] T19.25 : Triangle type {2,8,8} Group order 144 Action chiral Defining relators: [ x^2, x * y * z, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, y^8, z^-2 * y^3 * z^-1 * y * z^-1 ] T19.26 : Triangle type {2,8,8} Group order 144 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, x * z * y * z^-1 * y^2 * z^-1 * x * y^-1 * z^-1 ] T19.27 : Triangle type {2,8,8} Group order 144 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T19.28 : Triangle type {2,10,10} Group order 120 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, (y * z^-2 * y)^2, y * x * z * y^2 * x * y^-1 * z^-1 ] T19.29 : Triangle type {2,12,12} Group order 108 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, x * y^-3 * z^-3 ] T19.30 : Triangle type {2,12,12} Group order 108 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, z^-1 * y^4 * z^-3 ] T19.31 : Triangle type {2,12,24} Group order 96 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^-2 * z^2 * y^-5 * z^2 * y^-1 ] T19.32 : Triangle type {2,12,24} Group order 96 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-4 * z^-1 * y^3, y^12 ] T19.33 : Triangle type {2,15,30} Group order 90 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-3 * z^-1 * y^2, y^-1 * z^3 * y^-1 * z * y^-9 ] T19.34 : Triangle type {2,39,78} Group order 78 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^39 ] T19.35 : Triangle type {2,40,40} Group order 80 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-1 * y^10 * z^-1 * y^8 ] T19.36 : Triangle type {2,40,40} Group order 80 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^40 ] T19.37 : Triangle type {2,76,76} Group order 76 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^37 * z^-1 ] T19.38 : Triangle type {3,3,6} Group order 216 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, x^-1 * z * y^-1 * z^-1 * x * z * y * z^-1 ] T19.39 : Triangle type {3,3,6} Group order 216 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^3, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, z^-1 * x * z * y^-1 * x * z * y^-1 * z^-1 ] T19.40 : Triangle type {3,3,6} Group order 216 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, y * x^-1 * y * x^-1 * y * x^-1 * y * x * z * y^-1 * z^-1 * x^-1 ] T19.41 : Triangle type {3,3,12} Group order 144 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-4 * x^-1 * z^3 * y^-1 ] T19.42 : Triangle type {3,3,39} Group order 117 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z * y^-1 * z^-2 * x^-1 * z^3 ] T19.43 : Triangle type {3,4,6} Group order 144 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^6, x^-1 * y^-1 * z^-2 * x^-1 * y^-1 * x * z^2 * y * z^-1 ] T19.44 : Triangle type {3,4,12} Group order 108 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, y * z^-1 * x^-1 * z^2 ] T19.45 : Triangle type {3,4,12} Group order 108 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, (y * z^-1)^2, y^-1 * z^-1 * x^-1 * y * x^-1 * y * x * z^2 ] T19.46 : Triangle type {3,4,12} Group order 108 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y^-1 * x * z^2, x^-1 * z * y * x * y^-1 * z^-1 ] T19.47 : Triangle type {3,4,12} Group order 108 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T19.48 : Triangle type {3,5,6} Group order 120 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^-5, y * z^-1 * y * x^-1 * z * y ] T19.49 : Triangle type {3,6,26} Group order 78 Action chiral Defining relators: [ x^3, x * y * z, y^-1 * z^-1 * x^-1 * z^2 ] T19.50 : Triangle type {3,8,24} Group order 72 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^8 ] T19.51 : Triangle type {3,9,9} Group order 81 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, (z * y^-2)^3 ] T19.52 : Triangle type {3,9,9} Group order 81 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, z^-1 * y^3 * z^-2 ] T19.53 : Triangle type {3,9,9} Group order 81 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y * z^-1 * y * x * y^-1 * z^-1 ] T19.54 : Triangle type {3,9,9} Group order 81 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z * x^-1 * y^-1 * x * y^-1 * x ] T19.55 : Triangle type {3,9,9} Group order 81 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * y^3 * z^-2, y * z^-1 * y * x * y^-1 * z^-1 ] T19.56 : Triangle type {3,12,12} Group order 72 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (y * z^-1 * y)^2, (x^-1 * z * y)^2 ] T19.57 : Triangle type {3,12,12} Group order 72 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, (z^-1 * y)^3, z^-1 * y^4 * z^-3 ] T19.58 : Triangle type {3,20,60} Group order 60 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-12 * z * y^-5 * z^2 ] T19.59 : Triangle type {3,21,21} Group order 63 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-13 * z * y^-5 * z^2 ] T19.60 : Triangle type {3,57,57} Group order 57 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-11 * z * y^-6 * z ] T19.61 : Triangle type {4,4,4} Group order 144 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^4, z^4, z^-1 * y * x^2 * z * y^-1 ] T19.62 : Triangle type {4,4,4} Group order 144 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, y^-1 * z * y^-1 * x * z * x^-1 ] T19.63 : Triangle type {4,4,4} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T19.64 : Triangle type {4,4,4} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T19.65 : Triangle type {4,4,5} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (y^-1 * x)^3, z^2 * y^-1 * x^-1 * z^2, (x * z * y)^2 ] T19.66 : Triangle type {4,4,6} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (y^-1 * x)^3 ] T19.67 : Triangle type {4,4,6} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * z * y^-1, (y^-1 * x)^3 ] T19.68 : Triangle type {4,4,20} Group order 80 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * y^-1 * z ] T19.69 : Triangle type {4,4,20} Group order 80 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^-1 * z^2, y * x^-1 * y^-1 * x * z^-2 ] T19.70 : Triangle type {4,4,20} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^-1 * z^4 * y * z^-1 * x^-1 * y^-1 * z^-3 ] T19.71 : Triangle type {4,4,20} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^-1 * z^4 * y * z^-1 * x^-1 * z * y * z^-2 ] T19.72 : Triangle type {4,4,20} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-10 * x * y^-1 * x * y^-1 * z^-8 ] T19.73 : Triangle type {4,4,38} Group order 76 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^10 * y^-1 * x * z^8 ] T19.74 : Triangle type {4,6,12} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z * y * z^-1 * x^-1 * z^3 ] T19.75 : Triangle type {4,6,12} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^-3 * x^-1 * y * z^-2 ] T19.76 : Triangle type {4,6,12} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^6, z^-1 * y * z^-1 * y * z^-2 ] T19.77 : Triangle type {4,8,8} Group order 72 Action reflexible [n] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y^2 * x^2 * y^-1 * z^-1 ] T19.78 : Triangle type {4,8,8} Group order 72 Action chiral Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * x^-1 * z * y^-1, z * y * x^2 * z^2 ] T19.79 : Triangle type {4,8,8} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, (z^-1 * y)^3 ] T19.80 : Triangle type {4,8,8} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z * y^2 * x^-1 * y^-1 * z * y^-1 ] T19.81 : Triangle type {4,8,16} Group order 64 Action chiral Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y^-1 * z^-1 * x^-1 * z^2 ] T19.82 : Triangle type {4,8,16} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^2 * y * z^-1 * x^-1 * z^4 ] T19.83 : Triangle type {4,8,16} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-3 * x^-1 * z^4 ] T19.84 : Triangle type {4,12,15} Group order 60 Action chiral Defining relators: [ x * y * z, x^4, z^-1 * y * x * z^-1 ] T19.85 : Triangle type {4,12,15} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^2 * y * x * z^2 ] T19.86 : Triangle type {4,14,28} Group order 56 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y * z^-3 * y^2 * z^-4 * y * z^-1 * y^2 ] T19.87 : Triangle type {4,26,52} Group order 52 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^-2 * z * y^-1 * z^4 * y^-4 * z ] T19.88 : Triangle type {6,6,6} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y * z^-1, z * x^-2 * y^-2, y^2 * x^-1 * z^2, z * y * x^-2 * z * y * x ] T19.89 : Triangle type {6,6,6} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-2 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, z * x^-1 * y^-1 * x * z * x^-1 ] T19.90 : Triangle type {6,6,6} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, y * z^-1 * x^-1 * y^-1 * z, x^6, y^6 ] T19.91 : Triangle type {6,9,18} Group order 54 Action chiral Defining relators: [ x * y * z, y^-2 * x * z, x^6, x^-1 * y^-1 * x^2 * y^-1 * z ] T19.92 : Triangle type {6,9,18} Group order 54 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z^3 * y^-2 * z^3 ] T19.93 : Triangle type {6,9,18} Group order 54 Action reflexible [m] Defining relators: [ x * y * z, y * x^-2 * y^2, z^-2 * x^-1 * z * y^-1, x^-1 * z * x^-1 * y^-1 * z ] T19.94 : Triangle type {6,9,18} Group order 54 Action reflexible [m] Defining relators: [ x * y * z, y^2 * x * z^-1, z^-2 * x^-1 * z * y^-1, x^6 ] T19.95 : Triangle type {6,16,48} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^5 * z^-3 ] T19.96 : Triangle type {6,24,24} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^6, z^-1 * y^4 * z^-3 ] T19.97 : Triangle type {6,24,24} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^6 ] T19.98 : Triangle type {8,12,24} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^8 ] T19.99 : Triangle type {8,12,24} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, z^-2 * y^2 * z^-2 ] T19.100 : Triangle type {9,15,45} Group order 45 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^9 ] T19.101 : Triangle type {9,15,45} Group order 45 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^-2 * x^3 * y^-3 ] T19.102 : Triangle type {12,12,12} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y^-1 * x^4 * y^-3, z^-1 * x^4 * z^-3 ] T19.103 : Triangle type {12,12,12} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, z^-1 * y * x^-1 * y^-2, y^3 * x^-1 * y * z^-1 * y ] T19.104 : Triangle type {14,21,42} Group order 42 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-3 * x^2 * y^-3 ] T19.105 : Triangle type {14,21,42} Group order 42 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^5 * z^-3 ] T19.106 : Triangle type {14,21,42} Group order 42 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^-1 * y^5 * x^-1 * y^4 ] T19.107 : Triangle type {14,21,42} Group order 42 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^-2 * y * x^-2 * z * x^-9 ] T19.108 : Triangle type {14,21,42} Group order 42 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-5 * y * z^-3 ] T19.109 : Triangle type {15,15,15} Group order 45 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^2 * x^-3 * y^4 ] T19.110 : Triangle type {20,40,40} Group order 40 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, z^3 * x^-1 * z^3 ] T19.111 : Triangle type {20,40,40} Group order 40 Action reflexible [m] Defining relators: [ x * y * z, y * x^-1 * y, z^-10 * x^2 * z^-2 ] T19.112 : Triangle type {20,40,40} Group order 40 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-20, y * z^-1 ] T19.113 : Triangle type {20,40,40} Group order 40 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-1 * y * x^-6 * y * x^-2 ] T19.114 : Triangle type {39,39,39} Group order 39 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^-15 * x * y^-4, x * z^-1 ] T19.115 : Triangle type {39,39,39} Group order 39 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^7 * y^-1 ] T19.116 : Triangle type {39,39,39} Group order 39 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^2 * x^-2 * y^3 ] Genus 20 T20.1 : Triangle type {2,4,42} Group order 168 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-35 * x * y * z^-6 ] T20.2 : Triangle type {2,4,80} Group order 160 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-33 * x * y^-1 * z^-6 ] T20.3 : Triangle type {2,6,6} Group order 228 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, z^2 * y * x * z * y * x * y * x * z * y^-1 * z^-2 * x ] T20.4 : Triangle type {2,6,22} Group order 132 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-8 * x * y * z^-13 ] T20.5 : Triangle type {2,6,60} Group order 120 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^6 * y * x * y^-1 * z^-12 * x ] T20.6 : Triangle type {2,8,9} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, z^-4 * x * y * z^-4 ] T20.7 : Triangle type {2,8,28} Group order 112 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-4 * x * z^3 * y * x * y^-1 * z^-5 ] T20.8 : Triangle type {2,10,12} Group order 120 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^-6 * x * y * z^-5 ] T20.9 : Triangle type {2,12,48} Group order 96 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-3 * x * y^-1 * z^-4 ] T20.10 : Triangle type {2,18,45} Group order 90 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z * y^-4 * z^4 ] T20.11 : Triangle type {2,22,44} Group order 88 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-5 * y^9 * z^-2 * y^5 * z^-1 ] T20.12 : Triangle type {2,41,82} Group order 82 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^41 ] T20.13 : Triangle type {2,42,42} Group order 84 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^42 ] T20.14 : Triangle type {2,80,80} Group order 80 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^39 * z^-1 ] T20.15 : Triangle type {3,4,10} Group order 120 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^2 ] T20.16 : Triangle type {3,6,6} Group order 114 Action chiral Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y * z^-1 * y * z^-1 * y * z^-2 * y * z^-1 * y ] T20.17 : Triangle type {3,6,6} Group order 114 Action chiral Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, y * x * z * y * x * z * y^-1 * z ] T20.18 : Triangle type {3,22,22} Group order 66 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^12 * y^-9 ] T20.19 : Triangle type {3,60,60} Group order 60 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-12 * z * y^-7 ] T20.20 : Triangle type {4,4,21} Group order 84 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-14 * x * y * z^-6 ] T20.21 : Triangle type {4,4,40} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-10 * x * y^-1 * z^-9 ] T20.22 : Triangle type {4,9,9} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, z * y^-1 * z^2 * y^-2 * z^2 * y^-1 ] T20.23 : Triangle type {4,12,30} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^2 * y * x^-1 * z^2 ] T20.24 : Triangle type {4,15,20} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^-3 * x * z * y^-1 ] T20.25 : Triangle type {4,28,28} Group order 56 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, z^-1 * y * z^-2 * y * z^-1 * y^2 * z^-1 * y * z^-3 * y ] T20.26 : Triangle type {5,11,55} Group order 55 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^-2 * z^4 * y^-4 * z ] T20.27 : Triangle type {5,12,12} Group order 60 Action reflexible [n] Defining relators: [ x * y * z, y * x^2 * z, x * y^-1 * x * z^-1, y^-2 * z * y^-1 * z * y^-1 * z * y^-2 * z^2 * y^-1 ] T20.28 : Triangle type {5,12,12} Group order 60 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^-5, y^-1 * z * y^-3 * z * y^-1 * z * y^-1 * z * y^-1 * z ] T20.29 : Triangle type {5,50,50} Group order 50 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y * z^-4 * y^2 * z^-3 ] T20.30 : Triangle type {5,50,50} Group order 50 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y * z^-4 * y^3 * z^-2 ] T20.31 : Triangle type {6,6,11} Group order 66 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^6 * y^-1 * x * y * x^-1 * z^3 ] T20.32 : Triangle type {6,6,30} Group order 60 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^4 * y * x^-1 * z^5 ] T20.33 : Triangle type {6,10,10} Group order 60 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^6, (z^-2 * y * z^-1 * y)^2 ] T20.34 : Triangle type {6,48,48} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^6, y^7 * z^-1 ] T20.35 : Triangle type {8,8,14} Group order 56 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, y^-1 * z^-3 * x * y^-1 * x * z^2 ] T20.36 : Triangle type {9,45,45} Group order 45 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-4 * z, x^2 * z^-3 * x^3 * z^-2 ] T20.37 : Triangle type {9,45,45} Group order 45 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^2 * x^-2 * z^3 ] T20.38 : Triangle type {11,44,44} Group order 44 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^-1 * x^4 * z^-3 ] T20.39 : Triangle type {11,44,44} Group order 44 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^7 * z^-1 ] T20.40 : Triangle type {11,44,44} Group order 44 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-1 * y^8 ] T20.41 : Triangle type {11,44,44} Group order 44 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^2 * z^-1 * x * y^-1 * x^7 ] T20.42 : Triangle type {11,44,44} Group order 44 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-11 ] T20.43 : Triangle type {12,12,24} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z * y * x^-1 * z^2 ] T20.44 : Triangle type {12,16,16} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-1 * z ] T20.45 : Triangle type {21,42,42} Group order 42 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^6 * x^-1 * y^4 ] T20.46 : Triangle type {21,42,42} Group order 42 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, x * z^-3 * x^2 * z^-3 ] T20.47 : Triangle type {21,42,42} Group order 42 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-21, y * z^-1 ] T20.48 : Triangle type {22,22,22} Group order 44 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^6 * x^-2 * y^4 ] T20.49 : Triangle type {22,22,22} Group order 44 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-3 * x^2 * y^-3 ] T20.50 : Triangle type {41,41,41} Group order 41 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^-16 * x * y^-4, x * z^-1 ] T20.51 : Triangle type {41,41,41} Group order 41 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-8 * x * y^-5 ] T20.52 : Triangle type {41,41,41} Group order 41 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-5 * x^3 * y^-3 ] T20.53 : Triangle type {41,41,41} Group order 41 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y * x^-4 * y^4 ] T20.54 : Triangle type {41,41,41} Group order 41 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^3 * x^-1 * y^3 ] T20.55 : Triangle type {41,41,41} Group order 41 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, x^-4 * z^3 ] T20.56 : Triangle type {41,41,41} Group order 41 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x * z^-2 * x^6 ] Genus 21 T21.1 : Triangle type {2,3,16} Group order 384 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-10 * x * y * z^-5 ] T21.2 : Triangle type {2,3,16} Group order 384 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, x * z^2 * y * z^-2 * x * z * y^-1 * z^-3, z^-1 * x * z * y * z^-5 * x * y^-1 * z^-5 ] T21.3 : Triangle type {2,4,6} Group order 480 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^6, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T21.4 : Triangle type {2,4,8} Group order 320 Action chiral Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * x * z * y^2 * z^-1 * x * z * y^-1, (z^-1 * y)^5 ] T21.5 : Triangle type {2,4,8} Group order 320 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z * y^-1 * z^-2 ] T21.6 : Triangle type {2,4,8} Group order 320 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, y * z^-1 * y * z^-1 * y * x * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-2 ] T21.7 : Triangle type {2,4,12} Group order 240 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z^-12 ] T21.8 : Triangle type {2,4,12} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-4 ] T21.9 : Triangle type {2,4,12} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (z^-1 * y)^3, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T21.10 : Triangle type {2,4,20} Group order 200 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^2 * y * z^-1 * x * z * y^-1 * z^-3 * x * z ] T21.11 : Triangle type {2,4,24} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^2 * y^-2 * z^-3 * y, x * z * y * z^-4 * x * z^3 * y^-1 * z^-2 ] T21.12 : Triangle type {2,4,24} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-11 * x * z^5 * y * z^-1 * x * y * x * y^-1 * z^-4 ] T21.13 : Triangle type {2,4,24} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y^-1 * z^-3 ] T21.14 : Triangle type {2,4,24} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y^-2 * z^-3 * y, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T21.15 : Triangle type {2,4,24} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-18 * x * y * z^-5 ] T21.16 : Triangle type {2,4,24} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^5 * y * x * y^-1 * z^-5 * x ] T21.17 : Triangle type {2,4,44} Group order 176 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-37 * x * y * z^-6 ] T21.18 : Triangle type {2,4,84} Group order 168 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-35 * x * y^-1 * z^-6 ] T21.19 : Triangle type {2,6,6} Group order 240 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^6, z^6, (y * z^-2 * y)^2 ] T21.20 : Triangle type {2,6,8} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, z * y * z^-1 * x * y^-1 * z^-2 * x, z^8 ] T21.21 : Triangle type {2,6,8} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T21.22 : Triangle type {2,6,8} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, x * z * y^-3 * z^-2 * y^2 ] T21.23 : Triangle type {2,6,8} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-1)^4, z^8 ] T21.24 : Triangle type {2,6,8} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^8, x * z * y * x * y^-1 * z^-2 * y * z^-1 ] T21.25 : Triangle type {2,8,8} Group order 160 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z * y * z^-1 * y * x * y^-1 * z * y^-1 * z^-1 * x ] T21.26 : Triangle type {2,8,8} Group order 160 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T21.27 : Triangle type {2,8,16} Group order 128 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-10 * x * y * z^-5 ] T21.28 : Triangle type {2,8,16} Group order 128 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-1 * x * z^11 * y^-1 * z^-3 ] T21.29 : Triangle type {2,8,16} Group order 128 Action reflexible [m] Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, (y * z^-1 * y^2)^2, z^2 * y * z^-1 * x * y^-1 * z^-2 * x * z ] T21.30 : Triangle type {2,8,16} Group order 128 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-1 * x * z * y * x * y^-1 * z^-4 ] T21.31 : Triangle type {2,8,16} Group order 128 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^3 * y * x * y^-1 * z^-3 * x ] T21.32 : Triangle type {2,8,16} Group order 128 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-2 * x * z * y^-1 * z^-4 ] T21.33 : Triangle type {2,8,16} Group order 128 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, y^2 * z^-1 * y^2 * z^-3 ] T21.34 : Triangle type {2,8,16} Group order 128 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^8 ] T21.35 : Triangle type {2,8,56} Group order 112 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-1 * x * z^8 * y^-1 * z^-4 ] T21.36 : Triangle type {2,8,56} Group order 112 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-1 * x * z^7 * y * z^-5 ] T21.37 : Triangle type {2,12,12} Group order 120 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, y * z^-1 * y^7 * z^-1 * y^2 ] T21.38 : Triangle type {2,14,14} Group order 112 Action reflexible [n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-2 * y, y^-3 * z * y^-8 * z^2 ] T21.39 : Triangle type {2,16,48} Group order 96 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-3 * y^2 * z^-3 ] T21.40 : Triangle type {2,16,48} Group order 96 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y^-6 * z^2 * y^-5 * z^2 * y^-1 ] T21.41 : Triangle type {2,20,20} Group order 100 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, y^6 * z^-1 * y * z^-2 ] T21.42 : Triangle type {2,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z^-1 * y^3 * z^-2 ] T21.43 : Triangle type {2,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, x * y^-3 * z^-1 * y^2 ] T21.44 : Triangle type {2,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^-9 * z^3 ] T21.45 : Triangle type {2,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^2 * z^-13 * y^8 * z^-1 ] T21.46 : Triangle type {2,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-5 * y^9 * z^-2 * y^5 * z^-1 * y ] T21.47 : Triangle type {2,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^-9 * z * y^-1 * z ] T21.48 : Triangle type {2,43,86} Group order 86 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^43 ] T21.49 : Triangle type {2,44,44} Group order 88 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^44 ] T21.50 : Triangle type {2,84,84} Group order 84 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^41 * z^-1 ] T21.51 : Triangle type {3,3,8} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^8 ] T21.52 : Triangle type {3,3,8} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z * y^-1 * z^-1 * x^-1 * z * y * x, z^8, z^3 * y * x^-1 * z^2 * y^-1 * x ] T21.53 : Triangle type {3,3,43} Group order 129 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^3 * y * x * z^3 ] T21.54 : Triangle type {3,4,4} Group order 240 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^4, z^4, (x * z * y)^2 ] T21.55 : Triangle type {3,6,6} Group order 120 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * y^-1 * z, x^-1 * z * y^-1 * x * z^2, y^6 ] T21.56 : Triangle type {3,8,8} Group order 96 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y * x^-1 * y^-1 * x * z * y, y^8 ] T21.57 : Triangle type {3,8,8} Group order 96 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, (z^-1 * y)^3, y^8 ] T21.58 : Triangle type {3,8,8} Group order 96 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (y * z^-1 * y)^2, y^2 * x^-1 * y^-1 * x * z * y^2 ] T21.59 : Triangle type {3,8,8} Group order 96 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^3 * x^-1 * z^3 ] T21.60 : Triangle type {3,8,8} Group order 96 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (x^-1 * z * y)^2, y^8 ] T21.61 : Triangle type {3,22,66} Group order 66 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-14 * z * y^-5 * z^2 ] T21.62 : Triangle type {3,63,63} Group order 63 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-13 * z * y^-7 ] T21.63 : Triangle type {4,4,4} Group order 160 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, z^-1 * x^-1 * z * y * z^-1 * y * x * y^-1 * z * y^-1 ] T21.64 : Triangle type {4,4,4} Group order 160 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, z^-1 * x^-1 * z * y * z^-1 * y * x^-1 * y^-1 * z * y^-1 ] T21.65 : Triangle type {4,4,6} Group order 120 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, x^-1 * y * x^-2 * y^-1 * z^-1 * y ] T21.66 : Triangle type {4,4,10} Group order 100 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z^-1 * x^-1 * y * x^-1 * y^-1 * z^-2 ] T21.67 : Triangle type {4,4,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^2, z^-5 * x * z^2 * y * z^-3 * x * y^-1 ] T21.68 : Triangle type {4,4,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, (x * z^-1 * y)^2, z * y * z^-1 * x^-1 * z^3 ] T21.69 : Triangle type {4,4,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (y * z^-1)^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z^-3 * x^-1 * z * y * z^-1 ] T21.70 : Triangle type {4,4,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, (y^-1 * x)^3 ] T21.71 : Triangle type {4,4,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x * z ] T21.72 : Triangle type {4,4,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-2 * z^2 * x^-1, z^2 * y * x^-1 * z^3 ] T21.73 : Triangle type {4,4,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, (x * z^-2)^2, z^2 * y * x^-1 * z^3 ] T21.74 : Triangle type {4,4,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-4 * x^-1 * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T21.75 : Triangle type {4,4,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, y * z^-1 * x^-1 * y^-1 * x * z^3 ] T21.76 : Triangle type {4,4,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^-5 * x * z^2 * y^-1 * z^-4 ] T21.77 : Triangle type {4,4,22} Group order 88 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-22 ] T21.78 : Triangle type {4,4,42} Group order 84 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-14 * x * y^-1 * z^-6 ] T21.79 : Triangle type {4,6,6} Group order 96 Action reflexible [n] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * z * y^-1, y * x * y^-1 * x * z * y, y^6 ] T21.80 : Triangle type {4,6,6} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^2 * x^-1 * z^2, (y^-1 * x)^3 ] T21.81 : Triangle type {4,6,6} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^2 * x^-1 * z^2, y * x * y^-1 * x * y^-1 * z^-1, y^6 ] T21.82 : Triangle type {4,6,6} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * z * y, z^6, z^-1 * y^2 * x^-1 * y^3 ] T21.83 : Triangle type {4,6,6} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1 ] T21.84 : Triangle type {4,6,6} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * y^-1 * z, y * x^-1 * y^-1 * x * z * y, y^6 ] T21.85 : Triangle type {4,8,8} Group order 80 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y^-1 * z * y * x^-1 * z * y^-1 * z ] T21.86 : Triangle type {4,8,8} Group order 80 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y^-2 * z^-1 * x^-1 * z * y^-1 * z ] T21.87 : Triangle type {4,15,60} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^3 * z^-1 * y^7 * z^-2 * y ] T21.88 : Triangle type {4,16,16} Group order 64 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * z^2 ] T21.89 : Triangle type {4,16,16} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^6 * z^-2 ] T21.90 : Triangle type {4,16,16} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, y * z^-2 * y * z^-1 * y^4 * z^-1 * y * z^-4 * y ] T21.91 : Triangle type {4,16,16} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, z^-1 * y^2 * z^-1 ] T21.92 : Triangle type {4,16,16} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z * x^-1 * y^-1 * x * z * y^-1 ] T21.93 : Triangle type {4,16,16} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^5 * z^-1 * y * z^-1 ] T21.94 : Triangle type {4,16,16} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, (y * z^-1 * y^2)^2 ] T21.95 : Triangle type {4,16,16} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-2 * x^-1 * z * y^-1, z^-1 * y^4 * z^-3 ] T21.96 : Triangle type {4,16,16} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y^3 * z^-2 * y^6 * z^-1 * y * z^-1 * y^2 ] T21.97 : Triangle type {4,16,16} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-1 * y^3 * z^-3 ] T21.98 : Triangle type {4,20,30} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2 ] T21.99 : Triangle type {4,56,56} Group order 56 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y^6 * z^-4 * y * z^-1 * y^2 ] T21.100 : Triangle type {4,56,56} Group order 56 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^5 * z^-4 * y * z^-1 * y * z^-1 ] T21.101 : Triangle type {6,12,12} Group order 60 Action chiral Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-1 * z^-1, x^6 ] T21.102 : Triangle type {7,8,56} Group order 56 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, y^8 ] T21.103 : Triangle type {7,9,9} Group order 63 Action reflexible [n] Defining relators: [ x * y * z, x^-1 * y^-1 * x * z^-1, x^-3 * z * y, y^-1 * z * y^-4 * z * y^-1 * z ] T21.104 : Triangle type {7,49,49} Group order 49 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, y^-6 * z ] T21.105 : Triangle type {7,49,49} Group order 49 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, y^-4 * x^-1 * z^3 ] T21.106 : Triangle type {7,49,49} Group order 49 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, z * y^-3 * x^-1 * z^3 ] T21.107 : Triangle type {8,8,8} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x * z^-1 * x ] T21.108 : Triangle type {8,8,8} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y, (x * z^-1 * y)^2 ] T21.109 : Triangle type {8,8,8} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z * x^-1 * y^-1 * x * z * y^-1 ] T21.110 : Triangle type {8,8,8} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, y * x^-2 * z * x^-1, z^-2 * y * z^-1 * y^2 * z^-1 * y ] T21.111 : Triangle type {8,8,8} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, y^8, x^8 ] T21.112 : Triangle type {8,8,8} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, y * x^-2 * z * x^-1, x^8 ] T21.113 : Triangle type {8,8,8} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^8 ] T21.114 : Triangle type {8,8,8} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y^8, x^8 ] T21.115 : Triangle type {8,8,28} Group order 56 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^3 * y^-1 * x * z^3 ] T21.116 : Triangle type {8,8,28} Group order 56 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^2 * y^-1 * z^-1 * x * z^3 ] T21.117 : Triangle type {8,48,48} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^8 ] T21.118 : Triangle type {8,48,48} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^8 ] T21.119 : Triangle type {8,48,48} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, z^3 * x^-1 * z^3 ] T21.120 : Triangle type {12,16,48} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^12 ] T21.121 : Triangle type {12,16,48} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^-3 * y^2 * z^-3 ] T21.122 : Triangle type {12,24,24} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-2 * y * x^-6 * z * x^-3 ] T21.123 : Triangle type {12,24,24} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^-5 * z * y ] T21.124 : Triangle type {15,45,45} Group order 45 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-5 * y * x^-7 * z * x^-2 ] T21.125 : Triangle type {15,45,45} Group order 45 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, x^-4 * z^3 ] T21.126 : Triangle type {15,45,45} Group order 45 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^4 * x^-3 * y^5 ] T21.127 : Triangle type {16,16,24} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, z * y * x^-1 * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^3 * z^-1 * y ] T21.128 : Triangle type {16,16,24} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z * x^-2 * z^2 ] T21.129 : Triangle type {16,16,24} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^-4 * y * x * z^-3 ] T21.130 : Triangle type {22,44,44} Group order 44 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, z^-1 * x^4 * z^-3 ] T21.131 : Triangle type {22,44,44} Group order 44 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^10 * x^-1 * y^4 ] T21.132 : Triangle type {22,44,44} Group order 44 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-5 * x^2 * z^-3 ] T21.133 : Triangle type {22,44,44} Group order 44 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-5 * y, z^3 * x^-1 * z^3 ] T21.134 : Triangle type {22,44,44} Group order 44 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-22, y * z^-1 ] T21.135 : Triangle type {43,43,43} Group order 43 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^-17 * x * y^-4, x * z^-1 ] T21.136 : Triangle type {43,43,43} Group order 43 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^9 * x^-2 * y^4 ] T21.137 : Triangle type {43,43,43} Group order 43 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^-1 * y^10 ] T21.138 : Triangle type {43,43,43} Group order 43 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^2 * x^-7 * y ] T21.139 : Triangle type {43,43,43} Group order 43 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^5 * y^-3 ] T21.140 : Triangle type {43,43,43} Group order 43 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-6, z^3 * x^-1 * z^3 ] T21.141 : Triangle type {43,43,43} Group order 43 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-5 * x * z^-3 ] T21.142 : Triangle type {43,43,43} Group order 43 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^5 * z^-2, y^-1 * z * y^-3 * z^2 ] Genus 22 T22.1 : Triangle type {2,3,8} Group order 1008 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^8, x * z^2 * y * z^-1 * x * z^2 * y * x * z * x * z^2 * y^-1 * z^-2 ] T22.2 : Triangle type {2,3,8} Group order 1008 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^8, x * z^2 * y * z^-1 * x * z^2 * y * x * z * y^-1 * z^-2 * x * z * y^-1 * z^-1 ] T22.3 : Triangle type {2,3,12} Group order 504 Action chiral Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * z^2 * y * z^-2 * x * z^2 * y^-1 * z^-2 ] T22.4 : Triangle type {2,4,8} Group order 336 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^8, (y * z^-2 * y * z^-1)^2, z^-1 * x * z * y * x * y^-1 * z^-3 * y * z^-1 ] T22.5 : Triangle type {2,4,8} Group order 336 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (z * y^-1 * z)^3 ] T22.6 : Triangle type {2,4,46} Group order 184 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-39 * x * y * z^-6 ] T22.7 : Triangle type {2,4,88} Group order 176 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-37 * x * y^-1 * z^-6 ] T22.8 : Triangle type {2,5,8} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^-5, (y * z^-3)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T22.9 : Triangle type {2,6,6} Group order 252 Action chiral Defining relators: [ x^2, x * y * z, y^6, z^6, z * y * z^-1 * x * y^-1 * z^-1 * x * z ] T22.10 : Triangle type {2,6,6} Group order 252 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, z * y * x * z * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x ] T22.11 : Triangle type {2,6,12} Group order 168 Action chiral Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, x * y^-1 * z * y^-2 * z^-4, x * z^2 * y^-2 * z^-1 * y * z^-2 ] T22.12 : Triangle type {2,6,12} Group order 168 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-1 * z * y^-3 * z^-1 * x * z * y^-1 ] T22.13 : Triangle type {2,6,24} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-10 * x * y * z^-13 ] T22.14 : Triangle type {2,6,24} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, x * z * y^-2 * z^-2 * y, x * z^3 * y^-1 * z^-4 ] T22.15 : Triangle type {2,6,24} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-2 * x * z^4 * y * z^-1 * x * z * y^-1 * z^-14 ] T22.16 : Triangle type {2,6,24} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, x * z * y * x * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-1 * z^-4 ] T22.17 : Triangle type {2,6,66} Group order 132 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^6 * y * x * z * y^-1 * z^-13 * x ] T22.18 : Triangle type {2,8,12} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z * y^-1 * z^-1, y^8, z^-1 * x * y^-3 * z^-4 ] T22.19 : Triangle type {2,9,18} Group order 126 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z * y * z^-1 * x * y^-1 * z^-1 * x * z, y^-9 ] T22.20 : Triangle type {2,10,55} Group order 110 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^-4 * x * z^2 * y^-1 * z^-4 ] T22.21 : Triangle type {2,18,18} Group order 108 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-3 * z^-1 * y^2, z^7 * y^-8 * z * y^-2 ] T22.22 : Triangle type {2,45,90} Group order 90 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^45 ] T22.23 : Triangle type {2,46,46} Group order 92 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^46 ] T22.24 : Triangle type {2,88,88} Group order 88 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^43 * z^-1 ] T22.25 : Triangle type {3,3,4} Group order 504 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^4, z * y * x * z * y * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x ] T22.26 : Triangle type {3,3,4} Group order 504 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^4, (z^-1 * x^-1 * y^-1)^3 ] T22.27 : Triangle type {3,3,6} Group order 252 Action chiral Defining relators: [ x^3, x * y * z, y^3, z^6, (y * x^-1 * z)^3, z^-1 * x * z * y * x^-1 * y * x * z * y^-1 ] T22.28 : Triangle type {3,6,6} Group order 126 Action chiral Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z^-1 ] T22.29 : Triangle type {3,6,6} Group order 126 Action chiral Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, x^-1 * y * x^-1 * y * x^-1 * y^-1 * z * y^-1 * z^-1 ] T22.30 : Triangle type {3,6,6} Group order 126 Action chiral Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^6, z^-2 * x^-1 * y^-1 * x * z^2 * y ] T22.31 : Triangle type {3,6,6} Group order 126 Action chiral Defining relators: [ x^3, x * y * z, y^6, z^-2 * y^2 * z^-1 * y ] T22.32 : Triangle type {3,6,6} Group order 126 Action chiral Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y * z^-1 * y * z^-1 * y^2 * z^-2 * y * z^-1 ] T22.33 : Triangle type {3,12,12} Group order 84 Action chiral Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z * x^-1 * y^-1 * x * y^-1 * z ] T22.34 : Triangle type {3,12,12} Group order 84 Action chiral Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^3 * x^-1 * y^-1 * z^2 ] T22.35 : Triangle type {3,23,69} Group order 69 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-15 * z * y^-5 * z^2 ] T22.36 : Triangle type {3,24,24} Group order 72 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^4 * z^-3 ] T22.37 : Triangle type {3,24,24} Group order 72 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^14 * y^-9 ] T22.38 : Triangle type {3,24,24} Group order 72 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-16 * z * y^-5 * z^2 ] T22.39 : Triangle type {3,66,66} Group order 66 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-14 * z * y^-6 * z ] T22.40 : Triangle type {4,4,4} Group order 168 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-1 * y * x^-1 * z * x^-1 * z, z^-1 * x^-1 * y * x^-1 * y * z^-1 * y ] T22.41 : Triangle type {4,4,4} Group order 168 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, (y^-1 * x)^3, (z^-1 * x)^3 ] T22.42 : Triangle type {4,4,23} Group order 92 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-15 * x * y * z^-7 ] T22.43 : Triangle type {4,4,44} Group order 88 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-15 * x * y^-1 * z^-6 ] T22.44 : Triangle type {4,5,5} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, z^2 * y^-1 * x^-1 * z^2, (z^-1 * y)^3 ] T22.45 : Triangle type {4,6,12} Group order 84 Action chiral Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^-3 * x^-1 * y * z^-2, z^-1 * x^-1 * z * y * x * z * y^-1 * z^-1 ] T22.46 : Triangle type {4,8,10} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^4 * y * x^-1 * z * y * z^-2 * x * z ] T22.47 : Triangle type {4,9,18} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * z * y^-1, y^-3 * z * y^-1 * z * y^-1 * z * y^-1 ] T22.48 : Triangle type {4,12,12} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * y * z^-2, y^3 * x^-1 * y^-2 * z ] T22.49 : Triangle type {4,12,12} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^3 * x^-1 * y^-1 * z * y, z * y * z^-1 * x^-1 * z^3 ] T22.50 : Triangle type {4,30,60} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y * z^-4 * y^7 * z^-2 * y ] T22.51 : Triangle type {5,12,60} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^2 * z^-1 * y^5 * z^-4 ] T22.52 : Triangle type {5,55,55} Group order 55 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^-2 * z^4 * y^-2 * z^3 ] T22.53 : Triangle type {5,55,55} Group order 55 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-5, y^-2 * z^4 * y^-1 * z^4 ] T22.54 : Triangle type {6,6,6} Group order 84 Action chiral Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, y^-1 * z^-1 * x^2 * y^-1 * z ] T22.55 : Triangle type {6,6,6} Group order 84 Action chiral Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, x^6, y^6, z^-1 * y^2 * x^-1 * y^-1 * z^-2 ] T22.56 : Triangle type {6,6,12} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^6 ] T22.57 : Triangle type {6,6,12} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^12 ] T22.58 : Triangle type {6,6,12} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^6 ] T22.59 : Triangle type {6,6,12} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, x^6 ] T22.60 : Triangle type {6,6,12} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^4 * y * x * y^-1 * z^-5 * x^-1 * z ] T22.61 : Triangle type {6,6,12} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-2 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, z * x^-1 * y^-1 * x * y^-1 * x ] T22.62 : Triangle type {6,6,33} Group order 66 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z * y^-1 * z^-5 * x * z^4 ] T22.63 : Triangle type {6,8,8} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, x^6, y^-2 * x^2 * y^-1 * z ] T22.64 : Triangle type {6,10,30} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^10 ] T22.65 : Triangle type {6,27,54} Group order 54 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z^3 * y^-4 * z ] T22.66 : Triangle type {6,27,54} Group order 54 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, z^4 * y^-1 * z^4 ] T22.67 : Triangle type {9,9,9} Group order 63 Action chiral Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * z * x^-1, y^-1 * x^3 * y^-2 ] T22.68 : Triangle type {9,18,18} Group order 54 Action reflexible [n] Defining relators: [ x * y * z, z^-1 * x^2 * y^-1, y^-1 * x^3 * z^-1 * x^-1, z^-1 * y^3 * z^-2 ] T22.69 : Triangle type {9,18,18} Group order 54 Action reflexible [m] Defining relators: [ x * y * z, (x * y^-1)^2, y^2 * x^-1 * z * y, z^-1 * y * x^2 * z^-2 ] T22.70 : Triangle type {9,18,18} Group order 54 Action reflexible [m,n] Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^2 * z^-1, x^-2 * y * x^-6 * z ] T22.71 : Triangle type {9,18,18} Group order 54 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-9 ] T22.72 : Triangle type {10,25,50} Group order 50 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^5 * y^-3 * z * y^-1 ] T22.73 : Triangle type {10,25,50} Group order 50 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^-2 * x^3 * z^-3 ] T22.74 : Triangle type {10,25,50} Group order 50 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^2 * z^-1 * x * y^-2 * x^5 * z^-1 ] T22.75 : Triangle type {10,25,50} Group order 50 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^10 ] T22.76 : Triangle type {12,48,48} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^2 * x^-7 * y^2 ] T22.77 : Triangle type {16,24,48} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^8 * z^-1 * x^6 * y^-1 * x ] T22.78 : Triangle type {16,24,48} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x * y^-3 * x^5 ] T22.79 : Triangle type {16,24,48} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y * z^-2 * y^6 ] T22.80 : Triangle type {16,24,48} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-2 * x * z^-3 * x * y * z^-3 ] T22.81 : Triangle type {23,46,46} Group order 46 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-5 * x^3 * y^-5 ] T22.82 : Triangle type {23,46,46} Group order 46 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-8 * x^2 * y^-6 ] T22.83 : Triangle type {23,46,46} Group order 46 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-5 * y, z^-3 * x^2 * z^-3 ] T22.84 : Triangle type {23,46,46} Group order 46 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^5 * x^-4 * y ] T22.85 : Triangle type {23,46,46} Group order 46 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^3 * x^-1 * z^3 ] T22.86 : Triangle type {23,46,46} Group order 46 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^6 * z^-2 ] T22.87 : Triangle type {23,46,46} Group order 46 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x * z^-3 * x^4 * z^-1 ] T22.88 : Triangle type {23,46,46} Group order 46 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4 * z^-2, y^7 * z^-1 ] T22.89 : Triangle type {23,46,46} Group order 46 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-7 * z^2 * x^-3 ] T22.90 : Triangle type {23,46,46} Group order 46 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^2 * z^-2 * y^6 ] T22.91 : Triangle type {23,46,46} Group order 46 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-23, y * z^-1 ] T22.92 : Triangle type {45,45,45} Group order 45 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^-18 * x * y^-4, x * z^-1 ] T22.93 : Triangle type {45,45,45} Group order 45 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * x^3 * y^-2, z^-4 * y * z^-3 ] Genus 23 T23.1 : Triangle type {2,4,48} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-41 * x * y * z^-6 ] T23.2 : Triangle type {2,4,48} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-18 * x * z * y^-1 * z^-4 ] T23.3 : Triangle type {2,4,92} Group order 184 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-39 * x * y^-1 * z^-6 ] T23.4 : Triangle type {2,6,69} Group order 138 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^9 * y^-1 * z^-13 * x ] T23.5 : Triangle type {2,8,32} Group order 128 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-1 * x * z^9 * y * x * y^-1 * z^-4 ] T23.6 : Triangle type {2,8,32} Group order 128 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-1 * x * z^9 * y^-1 * z^-5 ] T23.7 : Triangle type {2,12,20} Group order 120 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, x * z * y * x * z * y * x * y^-1 * z^-5 ] T23.8 : Triangle type {2,47,94} Group order 94 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^47 ] T23.9 : Triangle type {2,48,48} Group order 96 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-5 * y^9 * z^-2 * y^6 * z^-1 ] T23.10 : Triangle type {2,48,48} Group order 96 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^48 ] T23.11 : Triangle type {2,92,92} Group order 92 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^45 * z^-1 ] T23.12 : Triangle type {3,5,10} Group order 120 Action reflexible [m] Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^-5 ] T23.13 : Triangle type {3,69,69} Group order 69 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-15 * z * y^-7 ] T23.14 : Triangle type {4,4,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-18 * x^-1 * y^-1 * z^-5 ] T23.15 : Triangle type {4,4,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-3 * x * z^3 * y * z^-5 ] T23.16 : Triangle type {4,4,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^-5 * x * z^2 * y * z^-4 ] T23.17 : Triangle type {4,4,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-3 * x * z^3 * y * z^-1 * x * z * y^-1 * z^-2 ] T23.18 : Triangle type {4,4,46} Group order 92 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-15 * x * y^-1 * z^-7 ] T23.19 : Triangle type {4,6,8} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^6, (y * z^-1 * y)^2 ] T23.20 : Triangle type {4,6,8} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^6, z^-1 * y^2 * x^-1 * y^3 ] T23.21 : Triangle type {4,6,8} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, x^-1 * z * y * z^-1 * x^-1 * y^-1 * z^-2 ] T23.22 : Triangle type {4,6,8} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z * y^2 * x * z^2 ] T23.23 : Triangle type {4,6,8} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z * y^2 * x^-1 * z^2 ] T23.24 : Triangle type {4,6,8} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, z * y * x^-1 * z * x^-1 ] T23.25 : Triangle type {4,6,8} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^8 ] T23.26 : Triangle type {4,6,8} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, y^6 ] T23.27 : Triangle type {4,32,32} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, y * z^-2 * y * z^-1 * y^4 * z^-1 * y * z^-3 * y * z^-1 ] T23.28 : Triangle type {4,32,32} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y^2 * z^-3 * y^6 * z^-1 * y * z^-1 * y * z^-1 ] T23.29 : Triangle type {6,20,20} Group order 60 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^6, y * z^-1 * y * z^-1 * y * z^-1 * y^4 ] T23.30 : Triangle type {8,8,16} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, y * z^-2 * x * z^5 ] T23.31 : Triangle type {8,8,16} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, y^-1 * x^6 * y^-1, z^2 * y * x^-1 * y * x^-1 * z^4 ] T23.32 : Triangle type {8,14,56} Group order 56 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, y^-4 * x^-1 * z^3 ] T23.33 : Triangle type {10,12,12} Group order 60 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, y * z^-1 * y * x^2 * z^-1 * y * z^-1 ] T23.34 : Triangle type {24,48,48} Group order 48 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-24, y * z^-1 ] T23.35 : Triangle type {24,48,48} Group order 48 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-2 * y * x^-6 * y * x^-3 ] T23.36 : Triangle type {24,48,48} Group order 48 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, z^-1 * y^4 * z^-3 ] T23.37 : Triangle type {47,47,47} Group order 47 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^-19 * x * y^-4, x * z^-1 ] T23.38 : Triangle type {47,47,47} Group order 47 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-9 * x * y^-6 ] T23.39 : Triangle type {47,47,47} Group order 47 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-5 * x * y^-6 ] T23.40 : Triangle type {47,47,47} Group order 47 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-2 * x^3 * y^-5 ] T23.41 : Triangle type {47,47,47} Group order 47 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^-4 * x * y^-3 ] T23.42 : Triangle type {47,47,47} Group order 47 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^3 * x^-1 * z^3 ] T23.43 : Triangle type {47,47,47} Group order 47 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-2 * x * z^-3 * x * y * z^-3 ] T23.44 : Triangle type {47,47,47} Group order 47 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x^5, y^-4 * z^3 ] Genus 24 T24.1 : Triangle type {2,4,27} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-14 * x * z^5 * y * z^-1 * x * y * x * y^-1 * z^-4 ] T24.2 : Triangle type {2,4,50} Group order 200 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-43 * x * y * z^-6 ] T24.3 : Triangle type {2,4,96} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-41 * x * y^-1 * z^-6 ] T24.4 : Triangle type {2,6,26} Group order 156 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-7 * x * z^5 * y * z^-5 * x * y^-1 * z^-7 ] T24.5 : Triangle type {2,8,18} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, z^5 * y * x * z * y^-1 * z^-1 * x ] T24.6 : Triangle type {2,8,18} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-18 ] T24.7 : Triangle type {2,10,14} Group order 140 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^-14 ] T24.8 : Triangle type {2,10,60} Group order 120 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^-5 * x * z * y * z^-5 ] T24.9 : Triangle type {2,12,30} Group order 120 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^5 * y^-1 * x * z * y^-1 * z^-2 * x ] T24.10 : Triangle type {2,14,56} Group order 112 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^-3 * z^3 * y^-5 * z^3 ] T24.11 : Triangle type {2,15,20} Group order 120 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y * x * z * y^2 * z^-1 * y * z^-1, y * z^-2 * x * y^-1 * z^-3 ] T24.12 : Triangle type {2,26,52} Group order 104 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-4 * y^11 * z^-1 * y^9 * z^-1 ] T24.13 : Triangle type {2,27,27} Group order 108 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-23 * z * y^-1 ] T24.14 : Triangle type {2,34,51} Group order 102 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y^-5 * z^3 * y^-9 ] T24.15 : Triangle type {2,49,98} Group order 98 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^49 ] T24.16 : Triangle type {2,50,50} Group order 100 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^50 ] T24.17 : Triangle type {2,96,96} Group order 96 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^47 * z^-1 ] T24.18 : Triangle type {3,3,26} Group order 156 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-4 * x^-1 * z * y^-1 * z^-2 ] T24.19 : Triangle type {3,3,49} Group order 147 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-4 * x^-1 * z^2 * y^-1 * z^-1 ] T24.20 : Triangle type {3,4,7} Group order 168 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z * x^-1 * y^-1 * x * y^-1 * x, (y * z^-2)^2 ] T24.21 : Triangle type {3,4,7} Group order 168 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, (y * z^-1)^2, z^3 * y^-1 * x^-1 * z^3 ] T24.22 : Triangle type {3,12,28} Group order 84 Action chiral Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y * z^-1 ] T24.23 : Triangle type {3,14,21} Group order 84 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^-4 * z^3 ] T24.24 : Triangle type {3,25,75} Group order 75 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-17 * z * y^-5 * z^2 ] T24.25 : Triangle type {3,26,26} Group order 78 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^16 * y^-9 ] T24.26 : Triangle type {3,72,72} Group order 72 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-16 * z * y^-7 ] T24.27 : Triangle type {4,4,25} Group order 100 Action reflexible [n] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-1 * y * z^-2 * x * z^-3 ] T24.28 : Triangle type {4,4,25} Group order 100 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-19 * x^-1 * y^-1 * z^-5 ] T24.29 : Triangle type {4,4,48} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-18 * x^-1 * y * z^-5 ] T24.30 : Triangle type {4,5,6} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x^4, z * y^-1 * x * z, y^-5 ] T24.31 : Triangle type {4,5,6} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y^-5, (x * z * y)^2 ] T24.32 : Triangle type {4,5,6} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^-5, (y * z^-2)^2 ] T24.33 : Triangle type {4,8,20} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^4 * y * x^-1 * z * y * z^-2 * x^-1 * z ] T24.34 : Triangle type {4,17,68} Group order 68 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^5 * z^-1 * y^7 * z^-2 * y ] T24.35 : Triangle type {4,18,18} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, z^-1 * y^8 * z^-1 * y * z^-1 * y^4 * z^-1 * y ] T24.36 : Triangle type {4,18,18} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, z * y^-1 * z^2 * y^-4 * z ] T24.37 : Triangle type {4,64,64} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y * z^-3 * y^6 * z^-1 * y * z^-1 * y * z^-1 ] T24.38 : Triangle type {5,13,65} Group order 65 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^-2 * z * y^-1 * z^9 ] T24.39 : Triangle type {5,14,14} Group order 70 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^-5, y^7 * z^-1 * y * z^-2 * y * z^-1 * y ] T24.40 : Triangle type {5,60,60} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^2 * z^-1 * y^6 * z^-3 ] T24.41 : Triangle type {5,60,60} Group order 60 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-5, y^2 * z^-1 * y^9 ] T24.42 : Triangle type {6,6,13} Group order 78 Action reflexible [n] Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, y^-1 * z * x^-1 * z^2, x^6 ] T24.43 : Triangle type {6,6,13} Group order 78 Action reflexible [n] Defining relators: [ x * y * z, z * x^-2 * y^-2, y^-1 * z^-1 * x^-1 * z^2, x^6 ] T24.44 : Triangle type {6,6,13} Group order 78 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^13 ] T24.45 : Triangle type {6,20,60} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^7 * z^-3 ] T24.46 : Triangle type {6,30,30} Group order 60 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^6, y^8 * z^-2 ] T24.47 : Triangle type {7,9,63} Group order 63 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z^4 * y^-1 * z^3 ] T24.48 : Triangle type {7,10,10} Group order 70 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^-7, y^3 * z^-1 * y * z^-2 * y * z^-1 * y ] T24.49 : Triangle type {7,56,56} Group order 56 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, y^6 * z^-2 ] T24.50 : Triangle type {7,56,56} Group order 56 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, z^-2 * y^3 * z^-3 ] T24.51 : Triangle type {7,56,56} Group order 56 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-7, z^-1 * y^4 * z^-3 ] T24.52 : Triangle type {8,8,9} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^9 ] T24.53 : Triangle type {8,28,56} Group order 56 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, z^2 * y^-2 * x^-1 * z^3 ] T24.54 : Triangle type {8,28,56} Group order 56 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, y^-5 * z^2 ] T24.55 : Triangle type {9,9,21} Group order 63 Action chiral Defining relators: [ x * y * z, z * x^-2 * y^-2, x^-1 * y * x^-1 * z^2 ] T24.56 : Triangle type {9,54,54} Group order 54 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^-9 ] T24.57 : Triangle type {9,54,54} Group order 54 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-3 * x^2 * y^-3 ] T24.58 : Triangle type {9,54,54} Group order 54 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z^4 * x^-3 * z^2 ] T24.59 : Triangle type {10,10,30} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-2 * x^2 * y^-2, z * y * z^-1 * x^-1 * z^3 ] T24.60 : Triangle type {10,10,30} Group order 60 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-2)^2, z^2 * y * x^-1 * z^3 ] T24.61 : Triangle type {10,15,15} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, z * y^-1 * x * z, y * z^-1 * y * x * z * y, (z^-1 * x)^3 ] T24.62 : Triangle type {10,15,15} Group order 60 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * y * x^-1 * y * z^-1, x^-1 * z * x^-1 * y^-1 * z, y * z^-1 * y * x^-1 * z * y ] T24.63 : Triangle type {12,12,15} Group order 60 Action reflexible [n] Defining relators: [ x * y * z, (x * y^-1)^2, x * z^-1 * y * z^-1 ] T24.64 : Triangle type {12,12,15} Group order 60 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * y * x * z^2 ] T24.65 : Triangle type {13,52,52} Group order 52 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, z^-1 * x^4 * z^-3 ] T24.66 : Triangle type {13,52,52} Group order 52 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, x * y^-8 ] T24.67 : Triangle type {13,52,52} Group order 52 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^2 * z^-2 * x^7 * z^-1 * x * z^-1 ] T24.68 : Triangle type {13,52,52} Group order 52 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-6 * x^3 * y^-2 ] T24.69 : Triangle type {13,52,52} Group order 52 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^-4 * y * z^-3 ] T24.70 : Triangle type {13,52,52} Group order 52 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^4 * y^-2 * x^4 * y^-2 * x^3 ] T24.71 : Triangle type {14,14,28} Group order 56 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * x^-1 * z^2, y^-3 * x^2 * y^-3 ] T24.72 : Triangle type {14,14,28} Group order 56 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^4 * y^-2, z^-2 * x^2 * z^-2 ] T24.73 : Triangle type {14,14,28} Group order 56 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-2 * x^-1 * z * y^-1, z^-2 * x * z^-1 * x * z^-3 ] T24.74 : Triangle type {17,51,51} Group order 51 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-1 * z * y^-7 ] T24.75 : Triangle type {17,51,51} Group order 51 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, y^-1 * z^3 * y^-3 * z^2 ] T24.76 : Triangle type {17,51,51} Group order 51 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-2 * x * y^-10 ] T24.77 : Triangle type {17,51,51} Group order 51 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, x^5 * z^-3 ] T24.78 : Triangle type {17,51,51} Group order 51 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^17 ] T24.79 : Triangle type {17,51,51} Group order 51 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z^3 * x^-5 ] T24.80 : Triangle type {17,51,51} Group order 51 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-2 * z^2, y * z^-1 * y^3 * x^-3 * y^4 ] T24.81 : Triangle type {17,51,51} Group order 51 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-2 * y^3 * x^-5 ] T24.82 : Triangle type {25,50,50} Group order 50 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-3 * z * y^-3 * x^2 * y^-5 ] T24.83 : Triangle type {25,50,50} Group order 50 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6 * y^-2, z^3 * x^-1 * z^3 ] T24.84 : Triangle type {25,50,50} Group order 50 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x * z^-2 * x^6 ] T24.85 : Triangle type {25,50,50} Group order 50 Action reflexible [m] Defining relators: [ x * y * z, y * x^-1 * y, z^-14 * x * z^-2 ] T24.86 : Triangle type {25,50,50} Group order 50 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^2 * y^-1 * x^8 * y^-1 * x ] T24.87 : Triangle type {25,50,50} Group order 50 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-25, y * z^-1 ] T24.88 : Triangle type {25,50,50} Group order 50 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^3 * z^-2, y^-3 * x^2 * y^-3 ] T24.89 : Triangle type {25,50,50} Group order 50 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4 * y^-2, z^-5 * x * z^-3 ] T24.90 : Triangle type {26,26,26} Group order 52 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, (y^3 * z^-1 * y^3)^2 ] T24.91 : Triangle type {26,26,26} Group order 52 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-2 * x^4 * y^-4 ] T24.92 : Triangle type {26,26,26} Group order 52 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6 * y^-2, z^-3 * x^2 * z^-3 ] T24.93 : Triangle type {49,49,49} Group order 49 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^-20 * x * y^-4, x * z^-1 ] T24.94 : Triangle type {49,49,49} Group order 49 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^3 * z^-2 * x^6 ] T24.95 : Triangle type {49,49,49} Group order 49 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^5 * y^-1, y * z^-3 * y^4 * z^-1 ] T24.96 : Triangle type {49,49,49} Group order 49 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x * y^-1, z^2 * x^-4 * z^3 * x^-1 * z * x^-1 * z * x^-1 ] T24.97 : Triangle type {49,49,49} Group order 49 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-9 * x^2 * y^-6 ] T24.98 : Triangle type {49,49,49} Group order 49 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^2 * y^-3 * x^2 * y^-3 * x ] T24.99 : Triangle type {49,49,49} Group order 49 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, x^5 * z^-3 ] Genus 25 T25.1 : Triangle type {2,3,10} Group order 720 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^10, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, y * z^-2 * x * z * y * z^-3 * x * z * y * z^-2 * x * z^4 ] T25.2 : Triangle type {2,3,12} Group order 576 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z * y * z^-3 * x * y^-1 * z^-4 * x, z^-1 * x * z * y * x * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-1 * x * z * y^-1 * z^-1 ] T25.3 : Triangle type {2,3,12} Group order 576 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, y * z^-1 * x * z^3 * y * x * z * y^-1 * z^-3 * x * z, z^-1 * x * z * y * x * z * y * x * z * y * x * z^3 * y^-1 * z^-3 ] T25.4 : Triangle type {2,3,24} Group order 384 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^3 * y * z^-3 * x * y * z^-1 * x * z^3, z * y * x * z^2 * y * z^-2 * x * z^-3 * x * z ] T25.5 : Triangle type {2,3,30} Group order 360 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, x * z^4 * y^-1 * z^-5, z^-1 * x * z * y * x * z^2 * y * z^-1 * x * y^-1 * z^-1 * x * z * y^-1 * z^-1 ] T25.6 : Triangle type {2,4,10} Group order 320 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^-1 * y * z^-1 * y * z^-1 * x * z^2 * y^-1 * z^-1 ] T25.7 : Triangle type {2,4,10} Group order 320 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-4)^2, z^10 ] T25.8 : Triangle type {2,4,12} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z * y * x * y^-1 * z^-1 * x, z^12 ] T25.9 : Triangle type {2,4,16} Group order 256 Action chiral Defining relators: [ x^2, x * y * z, y^4, z^-2 * y * x * y^-1 * z^2 * y^-1 * z^-1 ] T25.10 : Triangle type {2,4,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-3 * x * z^7 * y^-1 * z^-5 ] T25.11 : Triangle type {2,4,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^3 * y^-1 * z^-4 ] T25.12 : Triangle type {2,4,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-1 * z^-4 ] T25.13 : Triangle type {2,4,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T25.14 : Triangle type {2,4,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z * y * z^-2 * x * y^-1 * z^-3 * x, z^-1 * y * x * z * y^-2 * z^-5 ] T25.15 : Triangle type {2,4,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z * y * x * y^-1 * z^-1 * x, y * x * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^2 * z^-1 * y * z^-1 * y * z^-1 ] T25.16 : Triangle type {2,4,28} Group order 224 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-22 * x * y * z^-5 ] T25.17 : Triangle type {2,4,52} Group order 208 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-45 * x * y * z^-6 ] T25.18 : Triangle type {2,4,100} Group order 200 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-43 * x * y^-1 * z^-6 ] T25.19 : Triangle type {2,6,6} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z^6, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (z * y^-1 * z)^3 ] T25.20 : Triangle type {2,6,6} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z^6, x * z * y^-3 * z^-2 * y^2, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T25.21 : Triangle type {2,6,9} Group order 216 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-4 * x * y * z^-4, z^-1 * y^2 * x * y^-2 * z^-1 * y * x * y^-1 * z^-1 ] T25.22 : Triangle type {2,6,9} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, z^-4 * x * y * z^-4 ] T25.23 : Triangle type {2,6,12} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, z * y^-1 * z * y^-2 * z^-1 * x * z^2 ] T25.24 : Triangle type {2,6,12} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^3 * y^2 * x * z^2, y * z^-1 * x * z * y * x * y^-1 * z^-2 * y * z^-2 ] T25.25 : Triangle type {2,6,21} Group order 168 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, x * z * y * x * y^-1 * z^-4 ] T25.26 : Triangle type {2,6,27} Group order 162 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, x * z * y * z^-1 * x * z * y^-1 * z^-4 ] T25.27 : Triangle type {2,6,27} Group order 162 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^27 ] T25.28 : Triangle type {2,6,75} Group order 150 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^10 * y^-1 * z^-14 * x ] T25.29 : Triangle type {2,10,10} Group order 160 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-4, y^10 ] T25.30 : Triangle type {2,10,10} Group order 160 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y * z^-1 * y^3 * z^-1 * x * z, y * x * z * y^2 * z^-3 ] T25.31 : Triangle type {2,12,12} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y * z^-3 * y^5 * z^-3, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x ] T25.32 : Triangle type {2,12,12} Group order 144 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^-12 ] T25.33 : Triangle type {2,12,60} Group order 120 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^4 * y^-1 * z^-5, y^12 ] T25.34 : Triangle type {2,15,30} Group order 120 Action reflexible [m] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^-15 ] T25.35 : Triangle type {2,16,16} Group order 128 Action chiral Defining relators: [ x^2, x * y * z, y * x * y^-2 * z^3 ] T25.36 : Triangle type {2,16,16} Group order 128 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^5 * z^-1 * y * z^-1, x * z^3 * y^-1 * z^-4 ] T25.37 : Triangle type {2,16,16} Group order 128 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, (y^-5 * z^3)^2 ] T25.38 : Triangle type {2,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, z * y * x * z * y^3 * x * y^-1 * z^-3 * x ] T25.39 : Triangle type {2,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^-6 * z^-1 * y * x, z^-2 * x * z * y^-1 * z^-4 ] T25.40 : Triangle type {2,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, z^-1 * y^4 * z^-3 ] T25.41 : Triangle type {2,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T25.42 : Triangle type {2,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^-1 * z^5 * y^-7 * z * y^-2 ] T25.43 : Triangle type {2,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, z^-1 * y^4 * z^-3 ] T25.44 : Triangle type {2,22,55} Group order 110 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z * y^-6 * z^4 ] T25.45 : Triangle type {2,28,28} Group order 112 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-5 * y^11 * z^-1 * y^10 ] T25.46 : Triangle type {2,51,102} Group order 102 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^37 * y^-12 * z ] T25.47 : Triangle type {2,52,52} Group order 104 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^38 * y^-13 ] T25.48 : Triangle type {2,100,100} Group order 100 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^49 * z^-1 ] T25.49 : Triangle type {3,3,5} Group order 360 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^2 * y^-1 * x^-1 * z^2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (x * z^2 * y * z^-1)^2 ] T25.50 : Triangle type {3,3,6} Group order 288 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, (x^-1 * y^-1 * z^-1)^4 ] T25.51 : Triangle type {3,3,6} Group order 288 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^6, z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * y^-1, x^-1 * z * y^-1 * z^-1 * x^-1 * y * z^-1 * x^-1 * z ] T25.52 : Triangle type {3,3,12} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^-3 * x^-1 * z^2 * y^-1, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x ] T25.53 : Triangle type {3,3,15} Group order 180 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^3, (x^-1 * z * y)^2 ] T25.54 : Triangle type {3,3,15} Group order 180 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-2 * x * z^2, (z^-1 * x^-1 * y^-1)^3 ] T25.55 : Triangle type {3,4,6} Group order 192 Action chiral Defining relators: [ x^3, x * y * z, y^4, x * z * y^-1 * x * z * y ] T25.56 : Triangle type {3,4,6} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^6, y * z^-2 * x^-1 * y * z^-2, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y ] T25.57 : Triangle type {3,4,6} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^6, y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y * x * z ] T25.58 : Triangle type {3,4,6} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^6, z * y * z^-1 * x^-1 * z * y^-1 * z, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, z^-1 * y * x * y^-1 * x * z * y * z^-1 ] T25.59 : Triangle type {3,4,6} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, (x * z * y)^2, z^6, z * y * z^-1 * x^-1 * z * y^-1 * z ] T25.60 : Triangle type {3,4,6} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y^-1 * x * z^2, (z^-1 * y)^3 ] T25.61 : Triangle type {3,4,12} Group order 144 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * z * y^2 ] T25.62 : Triangle type {3,4,12} Group order 144 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * z^-1, z^-4 * x^-1 * z^3 * y^-1 ] T25.63 : Triangle type {3,4,12} Group order 144 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-2 * x^-1 * z * y^-1, z^-1 * y * x^-1 * y * x^-1 * y^2 * x * y^-1 ] T25.64 : Triangle type {3,4,12} Group order 144 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, x^-1 * y^-1 * z^-2 * x^-1 * y^-1 * x * z^2 * y * z^-1 ] T25.65 : Triangle type {3,6,6} Group order 144 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^6, (x * z * y)^2 ] T25.66 : Triangle type {3,6,6} Group order 144 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^3 ] T25.67 : Triangle type {3,6,6} Group order 144 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^6, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T25.68 : Triangle type {3,6,10} Group order 120 Action reflexible [m] Defining relators: [ x^3, x * y * z, x^-1 * z * y^-1 * x * z^2, y^6, (x^-1 * z * y)^2 ] T25.69 : Triangle type {3,8,24} Group order 96 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^-8 ] T25.70 : Triangle type {3,8,24} Group order 96 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, x^-1 * z * y^-1 * x * z^2 ] T25.71 : Triangle type {3,9,9} Group order 108 Action chiral Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y * x^-1 * y^-1 * z^-1 * y ] T25.72 : Triangle type {3,9,9} Group order 108 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, y^-1 * z * y^-3 * z^2 * y^-2 ] T25.73 : Triangle type {3,10,30} Group order 90 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z^5 * y^-2 * z * y^-1 ] T25.74 : Triangle type {3,12,12} Group order 96 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^3 * x^-1 * z * y * z^-1 ] T25.75 : Triangle type {3,21,21} Group order 84 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, y^-4 * z * y^-1 * z ] T25.76 : Triangle type {3,26,78} Group order 78 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-18 * z * y^-5 * z^2 ] T25.77 : Triangle type {3,27,27} Group order 81 Action chiral Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, z * y^-2 * z * y^-3 * z * y^-1 ] T25.78 : Triangle type {3,27,27} Group order 81 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-19 * z * y^-5 * z^2 ] T25.79 : Triangle type {3,75,75} Group order 75 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-17 * z * y^-6 * z ] T25.80 : Triangle type {4,4,5} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^2 * y^-1 * x^-1 * z^2 ] T25.81 : Triangle type {4,4,5} Group order 160 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, (x * z^-1 * y)^2, (x * z^-2)^2 ] T25.82 : Triangle type {4,4,6} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y, z^6 ] T25.83 : Triangle type {4,4,6} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^6 ] T25.84 : Triangle type {4,4,8} Group order 128 Action chiral Defining relators: [ x * y * z, x^4, y^4, y^-1 * x * y^-1 * x * z^2, (x * z^-1 * y)^2, x^-1 * z * y * x * z * y ] T25.85 : Triangle type {4,4,8} Group order 128 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^-1 * x^-1 * y^-1 * x * z^-1 * y ] T25.86 : Triangle type {4,4,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z^8 ] T25.87 : Triangle type {4,4,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1 ] T25.88 : Triangle type {4,4,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * z * y^-1, (x * z^-1 * y)^2 ] T25.89 : Triangle type {4,4,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z * y)^2 ] T25.90 : Triangle type {4,4,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-4 * x^-1 * z^3 * y^-1 ] T25.91 : Triangle type {4,4,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, x^-1 * y * x^-2 * z^3 ] T25.92 : Triangle type {4,4,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^2, z^-2 * x^-1 * z * y^-1 * x * z^2 * y * z^-1 ] T25.93 : Triangle type {4,4,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y^-1 * x * y^-1 * x * z^2, (x * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1 ] T25.94 : Triangle type {4,4,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-1)^4 ] T25.95 : Triangle type {4,4,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y^-1 * x * y^-1 * x * z^2, (x * z^-1 * y)^2, (x^-1 * z * y)^2 ] T25.96 : Triangle type {4,4,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x * y^-1 * x * z^2, x^-1 * z * y^-1 * x * y^-1 * z^-1 ] T25.97 : Triangle type {4,4,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * z * y, (x * z^-1 * y)^2 ] T25.98 : Triangle type {4,4,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z * y * x^2 * z * y^-1, z^4 * y^-1 * x^-1 * z^3 ] T25.99 : Triangle type {4,4,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-2)^2, z^-3 * x^-1 * y^-1 * x * z * y * z^-2 ] T25.100 : Triangle type {4,4,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-1 * z^2, (x * z^-1)^4 ] T25.101 : Triangle type {4,4,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y^-1, (x * z^-1)^4 ] T25.102 : Triangle type {4,4,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y, (x * z^-3)^2 ] T25.103 : Triangle type {4,4,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y^-1, (x * z^-3)^2 ] T25.104 : Triangle type {4,4,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-1 * z^2, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1 ] T25.105 : Triangle type {4,4,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y^-1 * z^-1 * x^-2 * z^2 * x^-1, z^8 ] T25.106 : Triangle type {4,4,14} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^5 * y * x^-1 * z * y * z^-6 * x^-1 ] T25.107 : Triangle type {4,4,26} Group order 104 Action reflexible [n] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-3 * x^-1 * y^-1 * z^-2 ] T25.108 : Triangle type {4,4,26} Group order 104 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-15 * x * y * z^-10 ] T25.109 : Triangle type {4,4,50} Group order 100 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-19 * x^-1 * y * z^-5 ] T25.110 : Triangle type {4,6,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^2 * y * x * z * y^-1 ] T25.111 : Triangle type {4,6,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-2)^2, z^-1 * y^2 * x^-1 * y^3 ] T25.112 : Triangle type {4,6,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-1 * y)^2, x^-1 * z * y * x * z * y ] T25.113 : Triangle type {4,6,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^2 * y * x^-1 * z * y^-1 ] T25.114 : Triangle type {4,6,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^-3 * x^-1 * z^2 * y^-1 ] T25.115 : Triangle type {4,6,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6 ] T25.116 : Triangle type {4,8,40} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^-1 * z^-5 * x * z^4 ] T25.117 : Triangle type {4,8,40} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^4 * y^-1 * z^-1 * x^-1 * z^4 ] T25.118 : Triangle type {4,10,20} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z^2 * y^-1 * z * y^-4 * z ] T25.119 : Triangle type {4,18,36} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^-1 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z * y^-5 * z^3 * y^-1 ] T25.120 : Triangle type {4,34,68} Group order 68 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^6 * z^-1 * y^8 * z^-1 * y ] T25.121 : Triangle type {6,6,6} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y * z^-1, z * x^-2 * y^-2, y^2 * x^-1 * z^2, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x ] T25.122 : Triangle type {6,6,6} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^6, z^-1 * y * x^2 * y^-1 * z^-1, y^-1 * z^-1 * x^2 * z * y^-1, z^-1 * x * y^-1 * x * z^-1 * y ] T25.123 : Triangle type {6,8,24} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-1 * z, x^6 ] T25.124 : Triangle type {6,9,18} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, y * x^-2 * y^2, x^-1 * z * x^-1 * y^-1 * z, x^-1 * z * y * x * y^-1 * z^-1 ] T25.125 : Triangle type {6,9,18} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, y^2 * x * z^-1, x^6, x^-1 * z * y * x * y^-1 * z^-1 ] T25.126 : Triangle type {6,11,66} Group order 66 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, z^-2 * y^5 * z^-4 ] T25.127 : Triangle type {6,12,12} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, z * y^-1 * z^-1 * x^-1 * z^3 ] T25.128 : Triangle type {6,12,12} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z * y^-1 * z^5 * y^-4 ] T25.129 : Triangle type {6,12,12} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^6, y^5 * z^-1 * y * z^-2 * y * z^-1 * y ] T25.130 : Triangle type {6,12,12} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^6, y * x^-3 * z * x^-2 ] T25.131 : Triangle type {6,12,12} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-3 * x^-1 * z * y * z^-1 ] T25.132 : Triangle type {6,60,60} Group order 60 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^6, z^-1 * y^5 * z^-4 ] T25.133 : Triangle type {8,16,16} Group order 64 Action chiral Defining relators: [ x * y * z, y * x^-2 * z * x^-1, y^2 * x^-1 * y * z^-1 ] T25.134 : Triangle type {8,16,16} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, y * x^-2 * z * x^-1, (y * z^-1)^4 ] T25.135 : Triangle type {8,16,16} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, (y * z^-1)^4 ] T25.136 : Triangle type {8,16,16} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x * y^-1 * x * y^-2, z^-1 * x * z^-1 * x * z^-2 ] T25.137 : Triangle type {8,16,16} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^8 ] T25.138 : Triangle type {8,16,16} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-2 * x^2 * y^-2 ] T25.139 : Triangle type {8,16,16} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^8 ] T25.140 : Triangle type {8,16,16} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, z^-2 * x^2 * z^-2 ] T25.141 : Triangle type {8,16,16} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * y^-2, z^-2 * x^2 * z^-2 ] T25.142 : Triangle type {8,16,16} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-2, z^-2 * x^2 * z^-2 ] T25.143 : Triangle type {8,16,16} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1 ] T25.144 : Triangle type {8,16,16} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, z^-1 * y^4 * z^-3 ] T25.145 : Triangle type {8,16,16} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^8 ] T25.146 : Triangle type {10,12,60} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^-1 * y^3 * x^-4 * y^3 ] T25.147 : Triangle type {11,55,55} Group order 55 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-5 * y^5 ] T25.148 : Triangle type {11,55,55} Group order 55 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, x^-1 * z^3 * x^-3 * z^2 ] T25.149 : Triangle type {11,55,55} Group order 55 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, z^-2 * x^3 * z^-3 ] T25.150 : Triangle type {11,55,55} Group order 55 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^11 ] T25.151 : Triangle type {11,55,55} Group order 55 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-4 * z, x^-1 * z * x^-1 * z^4 * x^-5 ] T25.152 : Triangle type {12,12,30} Group order 60 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-2 * x * z^2, z^2 * x^-2 * z^3 ] T25.153 : Triangle type {12,15,20} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^3 * z^-3, y * x^-4 * y^4 ] T25.154 : Triangle type {14,28,28} Group order 56 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^6 * z^-2 ] T25.155 : Triangle type {14,28,28} Group order 56 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^2 * x^-3 * y^3 * z^-1 * y^2 ] T25.156 : Triangle type {14,28,28} Group order 56 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-6 * z * x^-6 * y * x^-1 ] T25.157 : Triangle type {15,15,15} Group order 60 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y * x * y^-1, (x * z^-1)^2, y^3 * x^-3 * y^3 ] T25.158 : Triangle type {18,27,54} Group order 54 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^2 * y^-1 * z^4 * y^-1 * z^4 ] T25.159 : Triangle type {18,27,54} Group order 54 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-2 * z^3 * x^-5 ] T25.160 : Triangle type {18,27,54} Group order 54 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^2 * x^-1 * y^9 * x^-1 * y ] T25.161 : Triangle type {18,27,54} Group order 54 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^-8 * y * x^-7 * z * x^-2 ] T25.162 : Triangle type {18,27,54} Group order 54 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^-3 * x^2 * y^-3 ] T25.163 : Triangle type {18,27,54} Group order 54 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, y^-1 * z^3 * y^-2 * z^3 ] T25.164 : Triangle type {26,52,52} Group order 52 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, z^-1 * x^4 * z^-3 ] T25.165 : Triangle type {26,52,52} Group order 52 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^10 * x^-2 * y^6 ] T25.166 : Triangle type {26,52,52} Group order 52 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^6 * z^-2 ] T25.167 : Triangle type {26,52,52} Group order 52 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z^2 * x^-6 ] T25.168 : Triangle type {26,52,52} Group order 52 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^-6 * x * y^-4 ] T25.169 : Triangle type {26,52,52} Group order 52 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-26, y * z^-1 ] T25.170 : Triangle type {51,51,51} Group order 51 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^-21 * x * y^-4, x * z^-1 ] T25.171 : Triangle type {51,51,51} Group order 51 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^7 * y^-1, y^-5 * z^2 ] T25.172 : Triangle type {51,51,51} Group order 51 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-4 * z, x^-2 * z^4 * x^-5 ] Genus 26 T26.1 : Triangle type {2,3,10} Group order 750 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^10, y * x * z * y * x * z^2 * y * x * z * y^-1 * z * y^-1 * z^-2 * x * z ] T26.2 : Triangle type {2,3,11} Group order 660 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^-5 * x * y * z^-5, y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z, y * z^-2 * x * z^3 * y * x * y^-2 * z^-1 * x * z^3 ] T26.3 : Triangle type {2,4,54} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-47 * x * y * z^-6 ] T26.4 : Triangle type {2,4,104} Group order 208 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-45 * x * y^-1 * z^-6 ] T26.5 : Triangle type {2,5,10} Group order 250 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^-5, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z^-2 * y * z^-1 * y^2 * z^-1 * y * z^-2 ] T26.6 : Triangle type {2,6,6} Group order 300 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^6, y * x * y^-1 * z * y^2 * z^-1 * y^2 * z^-1 * y * x * y^-2 * z^-1 * y ] T26.7 : Triangle type {2,6,28} Group order 168 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^14 * y * x * z^5 * y^-1 * z^-5 * x * z^2 ] T26.8 : Triangle type {2,6,78} Group order 156 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^11 * y^-1 * x * y^-1 * z^-13 * x ] T26.9 : Triangle type {2,8,8} Group order 200 Action reflexible [n] Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, (y * z^-1)^4, z * y^-4 * z^-1 * y * x * y^-1 ] T26.10 : Triangle type {2,8,36} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^3 * y * x * z^8 * y^-1 * z^-5 * x ] T26.11 : Triangle type {2,10,15} Group order 150 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^6 * y * z^-3 * x * z^3 * y^-1 * z^-1 * x ] T26.12 : Triangle type {2,10,65} Group order 130 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^-1 * x * z^6 * y^-1 * x * z * y^-1 * z^-3 ] T26.13 : Triangle type {2,20,30} Group order 120 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-2 * y^4 * z^-4 ] T26.14 : Triangle type {2,28,56} Group order 112 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^-3 * z^3 * y^-6 * z * y^-1 ] T26.15 : Triangle type {2,53,106} Group order 106 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^39 * y^-12 * z ] T26.16 : Triangle type {2,54,54} Group order 108 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^40 * y^-13 ] T26.17 : Triangle type {2,104,104} Group order 104 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^38 * y^-12 * z ] T26.18 : Triangle type {3,3,4} Group order 600 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * y * x^-1 * y * x^-1 * y * x * z^-1 * x * z^-1 * x * z^-1, x * z * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 * x * y^-1 * z^-1 ] T26.19 : Triangle type {3,3,4} Group order 600 Action chiral Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * y * x^-1 * y * x^-1 * y * x * z^-1 * x * z^-1 * x * z^-1, z^2 * x^-1 * z * y * x^-1 * y * z^-1 * x^-1 * y^-1 * z^-1 * x ] T26.20 : Triangle type {3,3,5} Group order 375 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^2 * y^-1 * x^-1 * z^2, z^2 * y * z^-1 * x^-1 * z * y^-1 * z^-1 * x ] T26.21 : Triangle type {3,3,28} Group order 168 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-1 * x * y^-1 * x * z * y^-1 * x, y * x * z * y * x * z^3 ] T26.22 : Triangle type {3,4,4} Group order 300 Action chiral Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y^-1 * z^-1 * x * y^-1 * x * y^-1 * z * y^-1 ] T26.23 : Triangle type {3,4,4} Group order 300 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, x * y^-1 * z^-1 * y * x * z * y^-1 * z^-1 ] T26.24 : Triangle type {3,6,6} Group order 150 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, z * y * z^-1 * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x ] T26.25 : Triangle type {3,6,6} Group order 150 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y * z^-1 * y * z^-1 * y * x^-1 * y^-1 * z^-2 * y * z^-1 ] T26.26 : Triangle type {3,28,28} Group order 84 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^18 * y^-9 ] T26.27 : Triangle type {3,78,78} Group order 78 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-18 * z * y^-7 ] T26.28 : Triangle type {4,4,4} Group order 200 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, z * x^-1 * y * x^2 * y^-1 * z * x^-1, y^-1 * z^-1 * x * y^-1 * x * y^-1 * z * y^-1 ] T26.29 : Triangle type {4,4,4} Group order 200 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, z * x^-1 * y * x^2 * y^-1 * z^-1 * x, z^-1 * y * x^-1 * y^-1 * x * z * y^2 ] T26.30 : Triangle type {4,4,27} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^17 * y^-1 * z^-3 * x * y^-1 * x * z^5 ] T26.31 : Triangle type {4,4,52} Group order 104 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-15 * x * y^-1 * z^-10 ] T26.32 : Triangle type {4,5,20} Group order 100 Action chiral Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, x * y^-2 * x * z^-2, y^-5 ] T26.33 : Triangle type {4,5,20} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^-5 ] T26.34 : Triangle type {4,6,16} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^2 * y * z^-1 * x^-1 * z^4 ] T26.35 : Triangle type {4,10,40} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, y^-1 * z^2 * y^-1 * z * y^-4 * z ] T26.36 : Triangle type {4,36,36} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^9 * z^-1 * y * z^-1 * y^6 ] T26.37 : Triangle type {5,5,5} Group order 125 Action reflexible [m,n] Defining relators: [ x * y * z, x^-5, z^-1 * x^-1 * y^-1 * x * z * y, y^-5, z^2 * y^-1 * x^-1 * z^2, y^-1 * z^-1 * y * x * z * x^-1 ] T26.38 : Triangle type {5,14,70} Group order 70 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y * z^-9 * y * z^-1 * y^2 ] T26.39 : Triangle type {5,15,15} Group order 75 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-5, y^-3 * z * y^-1 * z^9 * y^-1 ] T26.40 : Triangle type {5,65,65} Group order 65 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^-2 * z * y^-1 * z^5 * y^-4 ] T26.41 : Triangle type {5,65,65} Group order 65 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-5, y^-2 * z * y^-1 * z^5 * y^-1 * z^3 ] T26.42 : Triangle type {6,6,14} Group order 84 Action reflexible [n] Defining relators: [ x * y * z, z^2 * x^-1 * y^-1 * z, x^6, y * z^-1 * x^2 * z * y ] T26.43 : Triangle type {6,6,14} Group order 84 Action reflexible [n] Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * z^2, x^6, (x * y^-1 * x)^2, y^2 * x^2 * z^2 ] T26.44 : Triangle type {6,6,14} Group order 84 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-6 * x^-1 * y * x^-1 * y * x^-1 * y * z^-5 ] T26.45 : Triangle type {6,6,39} Group order 78 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^-5 * x * y^-1 * z^-7 ] T26.46 : Triangle type {6,22,33} Group order 66 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y * z^-1 * y^7 * z^-2 ] T26.47 : Triangle type {8,8,18} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, y * z^-3 * x^-1 * y * x^-1 * z^4 ] T26.48 : Triangle type {9,9,12} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, z * x^-2 * y^-2, z * y * x^-1 * z * x^-1 ] T26.49 : Triangle type {10,30,30} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-10 ] T26.50 : Triangle type {10,30,30} Group order 60 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^-3 * x^2 * y^-3 ] T26.51 : Triangle type {12,15,60} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^-1 * y * x^-1 * y^3 * x^-6 * y ] T26.52 : Triangle type {12,20,30} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^-2 * y * x^-1 * y^3 * x^-6 * y ] T26.53 : Triangle type {14,56,56} Group order 56 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-1 * z^3 * x^-1 * z * x^-9 ] T26.54 : Triangle type {14,56,56} Group order 56 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, x^-1 * z * x^-1 * z^4 * x^-2 * z^3 ] T26.55 : Triangle type {14,56,56} Group order 56 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-1 * z^3 * x^-4 * z ] T26.56 : Triangle type {15,20,20} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-1 * z, x^4 * y^-1 * z^-1 ] T26.57 : Triangle type {15,20,20} Group order 60 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^4 * y^-1 * z^-1 ] T26.58 : Triangle type {27,54,54} Group order 54 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-27, y * z^-1 ] T26.59 : Triangle type {27,54,54} Group order 54 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-2 * y^2 * x^-6 ] T26.60 : Triangle type {27,54,54} Group order 54 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-1 * y * x^-4 * y^5 * x^-1 ] T26.61 : Triangle type {27,54,54} Group order 54 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^7 * z^-1 ] T26.62 : Triangle type {27,54,54} Group order 54 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^-5 * x^3 * z^-7 ] T26.63 : Triangle type {28,28,28} Group order 56 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, z^-1 * y * x^-1 * y^-2, y^-3 * x^2 * y^-3 ] T26.64 : Triangle type {28,28,28} Group order 56 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x^3 * y^-1 * x, z^-1 * y^3 * z^-1 * y ] T26.65 : Triangle type {53,53,53} Group order 53 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^-22 * x * y^-4, x * z^-1 ] T26.66 : Triangle type {53,53,53} Group order 53 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^11 * x^-1 * y^6 ] T26.67 : Triangle type {53,53,53} Group order 53 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^-1 * y^11 * x^-2 ] T26.68 : Triangle type {53,53,53} Group order 53 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-1 * y * x^-4 * y^4 * x^-2 ] T26.69 : Triangle type {53,53,53} Group order 53 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x * y^-8 ] T26.70 : Triangle type {53,53,53} Group order 53 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-2 * x^3 * y^-3 ] T26.71 : Triangle type {53,53,53} Group order 53 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^-4 * x * z^-3 ] T26.72 : Triangle type {53,53,53} Group order 53 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^6 * x^-1 * z^4 ] T26.73 : Triangle type {53,53,53} Group order 53 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-1 * z^3 * y^-3 * z^2 ] Genus 27 T27.1 : Triangle type {2,3,12} Group order 624 Action chiral Defining relators: [ x^2, y^3, x * y * z, z * y * z^-3 * x * y^-1 * z^-4 * x, z^2 * y * z^-1 * x * z^2 * y^-1 * z^-3 * x * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * x ] T27.2 : Triangle type {2,4,8} Group order 416 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, y * x * z * y * x * z * y * x * y^-1 * z * y^-1 * z * y^-1 * z^-1 * x * z ] T27.3 : Triangle type {2,4,8} Group order 416 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, y * x * z * y * x * z * y * x * y^-1 * z * y^-1 * z * y^-1 * z^-1 * y * z^-2 ] T27.4 : Triangle type {2,4,12} Group order 312 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^2 * y * z^-1 * x * z * y^-2 * z^-1 * y * z^-1 * x ] T27.5 : Triangle type {2,4,30} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-16 * x * z^7 * y^-1 * x * y^-1 * z^-5 ] T27.6 : Triangle type {2,4,56} Group order 224 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-49 * x * y * z^-6 ] T27.7 : Triangle type {2,4,56} Group order 224 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-22 * x * z * y^-1 * z^-4 ] T27.8 : Triangle type {2,4,108} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-47 * x * y^-1 * z^-6 ] T27.9 : Triangle type {2,5,12} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^-5, x * z^2 * y^-1 * z^-3, y * z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1 ] T27.10 : Triangle type {2,8,8} Group order 208 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, y^-1 * z * y^-1 * z * y^-2 * z^-1 * x * z * y^-1 * z ] T27.11 : Triangle type {2,8,8} Group order 208 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, y^-1 * z * y^-1 * z * y^-2 * z^-1 * y * z^-1 * x * z ] T27.12 : Triangle type {2,8,20} Group order 160 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^7 * y * z^-5 * x * z^7 ] T27.13 : Triangle type {2,8,20} Group order 160 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^20 ] T27.14 : Triangle type {2,8,72} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, x * z^11 * y * z^-6 ] T27.15 : Triangle type {2,8,72} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^12 * y * x * z^5 ] T27.16 : Triangle type {2,9,36} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z^2 * y^-1 * z^-3, y^-9 ] T27.17 : Triangle type {2,12,12} Group order 156 Action chiral Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, y * x * z * y^2 * x * y^-1 * z ] T27.18 : Triangle type {2,12,12} Group order 156 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y * x * z * y^-2 * z * y^-1 * z^2 ] T27.19 : Triangle type {2,14,63} Group order 126 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-4 * x * y^-1 * z^-4 ] T27.20 : Triangle type {2,20,60} Group order 120 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y^-8 * z^3 * y^-6 * z^3 ] T27.21 : Triangle type {2,30,30} Group order 120 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-26 * z * y^-1 ] T27.22 : Triangle type {2,38,57} Group order 114 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y^-7 * z^3 * y^-9 ] T27.23 : Triangle type {2,55,110} Group order 110 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^41 * y^-12 * z ] T27.24 : Triangle type {2,56,56} Group order 112 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-5 * y^11 * z^-1 * y^8 * z^-2 ] T27.25 : Triangle type {2,56,56} Group order 112 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^42 * y^-13 ] T27.26 : Triangle type {2,108,108} Group order 108 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^40 * y^-12 * z ] T27.27 : Triangle type {3,3,6} Group order 312 Action chiral Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, y * x^-1 * y * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 ] T27.28 : Triangle type {3,4,12} Group order 156 Action chiral Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y^-1 * x * z^2, z^-1 * y * z^-1 * x^-1 * z * y^2 ] T27.29 : Triangle type {3,4,12} Group order 156 Action chiral Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, x^-1 * z * y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * z^-2 ] T27.30 : Triangle type {3,4,12} Group order 156 Action chiral Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y^-1 * x * z^2, y * z^-1 * y * x^-1 * z^3 ] T27.31 : Triangle type {3,28,84} Group order 84 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-20 * z * y^-5 * z^2 ] T27.32 : Triangle type {3,81,81} Group order 81 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-19 * z * y^-7 ] T27.33 : Triangle type {4,4,4} Group order 208 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * z^-1 * y * z^-1 * y * x^-1 * y^-1 * z^2 * y * z^-1 ] T27.34 : Triangle type {4,4,4} Group order 208 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * z^-1 * y * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z^-2 ] T27.35 : Triangle type {4,4,6} Group order 156 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, y^-1 * z^-1 * y * x^2 * y^-1 * z^-1 * x^-1 ] T27.36 : Triangle type {4,4,15} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^2, z^-7 * x * z * y^-1 * z^-6 ] T27.37 : Triangle type {4,4,28} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^28 ] T27.38 : Triangle type {4,4,28} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^7 * y * z^-6 * x ] T27.39 : Triangle type {4,4,28} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^7 * y * z^-6 * x^-1 ] T27.40 : Triangle type {4,4,54} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^17 * y^-1 * z^-3 * x * y^-1 * x^-1 * z^5 ] T27.41 : Triangle type {4,6,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^6 ] T27.42 : Triangle type {4,6,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^3 * y * x^-1 * z^4 ] T27.43 : Triangle type {4,8,8} Group order 104 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z * y * z^-1 * y * x * y^-1 * z^-1 * x ] T27.44 : Triangle type {4,8,8} Group order 104 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z * y * z^-1 * y * x * y^-1 * z^-1 * x^-1 ] T27.45 : Triangle type {4,8,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z * y^2 * x^-1 * z * y^-1 * z, y * z^-2 * x^-1 * z^3 ] T27.46 : Triangle type {4,8,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, (y * z^-2)^2, z^-3 * x^-1 * y * z^-2 ] T27.47 : Triangle type {4,8,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, z * y * x^-1 * z ] T27.48 : Triangle type {4,8,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, (y^-1 * x)^3, y^-3 * x^-1 * z^2 ] T27.49 : Triangle type {4,8,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, y * x^-1 * z * y * x^-1 * z^3 ] T27.50 : Triangle type {4,8,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, z * y * x^-1 * y * x^-1 * z^3 ] T27.51 : Triangle type {4,8,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z * y * x * y^-1 * z^-3 * x^-1 * y^-1 * x^-1 * z^5 ] T27.52 : Triangle type {4,8,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * z^4 * y^-1 * z^-1 * x^-1 * z * y * z^-3 ] T27.53 : Triangle type {4,8,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, y * x^-1 * z * y * x * z^3 ] T27.54 : Triangle type {4,8,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z * y * z^-1 * x^-1 * z^3, y^8 ] T27.55 : Triangle type {4,12,21} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^2 * y * z^-1 * x * z^3 ] T27.56 : Triangle type {4,19,76} Group order 76 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^4 * z^-3 * y^5 * z^-1 * y * z^-1 * y * z^-2 ] T27.57 : Triangle type {4,20,20} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z^2 * y^-1 * z * y^-3 * z * y^-1 ] T27.58 : Triangle type {4,20,20} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y * z^-1 * y^3 * z^-2 * y^6 * z^-1 * y * z^-1 * y * z^-2 ] T27.59 : Triangle type {4,20,20} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-3 * z * y^-7 * z * y^-1 * z * y^-5 * z ] T27.60 : Triangle type {4,72,72} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y^-1 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z * y^-5 * z^4 ] T27.61 : Triangle type {4,72,72} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-5 * z^3 * y^-1 ] T27.62 : Triangle type {5,5,6} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * z^-1 * x * z, x^-5, z^6 ] T27.63 : Triangle type {6,18,18} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^2 * x^-1 * z^2, x^6, (y * z^-1 * y)^2 ] T27.64 : Triangle type {6,33,66} Group order 66 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y * z^-1 * y^6 * z^-3 ] T27.65 : Triangle type {7,10,70} Group order 70 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z^5 * y^-2 * z^2 ] T27.66 : Triangle type {7,63,63} Group order 63 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z^4 * y^-4 ] T27.67 : Triangle type {7,63,63} Group order 63 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, z^5 * x^-1 * z^4 ] T27.68 : Triangle type {7,63,63} Group order 63 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z^8 ] T27.69 : Triangle type {8,8,10} Group order 80 Action reflexible [n] Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, z^-2 * x^-1 * y^-1 * z^-1, x^8 ] T27.70 : Triangle type {8,8,10} Group order 80 Action reflexible [n] Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, y^-2 * x^2 * z^2 ] T27.71 : Triangle type {8,8,10} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, y * z^-1 * x^-1 * z^3 * y * x^-1 * z^4 ] T27.72 : Triangle type {8,8,10} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^10 ] T27.73 : Triangle type {8,8,36} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^4 * y * x^-1 * z^4 ] T27.74 : Triangle type {8,8,36} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, y^-1 * z^-3 * x * z^5 ] T27.75 : Triangle type {8,32,32} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^5 * z^-1 * y * z^-1 ] T27.76 : Triangle type {8,32,32} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-8, z^-3 * y^2 * z^-3 ] T27.77 : Triangle type {9,9,18} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * z * y^-1, z^-2 * x^-1 * y^-1 * x, y^-1 * x^3 * y^-2 ] T27.78 : Triangle type {9,9,18} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * z^-1 * x * z, y^-1 * x^3 * y^-2, x * z^-1 * y * x * z^-2 ] T27.79 : Triangle type {9,21,63} Group order 63 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * y^-1 * z^3, x^-9 ] T27.80 : Triangle type {9,21,63} Group order 63 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^-9 ] T27.81 : Triangle type {10,60,60} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^2 * x^-3 * y^4 ] T27.82 : Triangle type {10,60,60} Group order 60 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-10 ] T27.83 : Triangle type {12,30,60} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z * x^-5 * z^4 ] T27.84 : Triangle type {15,20,60} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^9 * y^-3 * x * y^-1 * x^2 ] T27.85 : Triangle type {15,20,60} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^4 * x^-3 * y^4 ] T27.86 : Triangle type {15,20,60} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^4 * y^-2 * x^-3 * z^2 ] T27.87 : Triangle type {19,57,57} Group order 57 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x * y^-2 * x * y^-9 * x * y^-1 ] T27.88 : Triangle type {19,57,57} Group order 57 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-1 * z * y^-7 ] T27.89 : Triangle type {19,57,57} Group order 57 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * x^3 * y^-2, z^5 * x^-1 * z^4 ] T27.90 : Triangle type {19,57,57} Group order 57 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^-1 * z^3 * y^-3 * z^2 ] T27.91 : Triangle type {19,57,57} Group order 57 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^-1 * z^2 * y^-6 ] T27.92 : Triangle type {19,57,57} Group order 57 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-11 * z * x^-6 * y * x^-1 ] T27.93 : Triangle type {19,57,57} Group order 57 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-2 * z^2, y^3 * x^-4 * y^6 ] T27.94 : Triangle type {19,57,57} Group order 57 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-2 * z^3 * x^-5 ] T27.95 : Triangle type {19,57,57} Group order 57 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-3 * y^3 * x^-5 ] T27.96 : Triangle type {20,20,30} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, z * y^-1 * x * z, z^-1 * y * x^-1 * y^-2, x^6 * y^-2 ] T27.97 : Triangle type {20,20,30} Group order 60 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, y^-1 * z * y^-1 * z^3 * x^-2 * z^4 ] T27.98 : Triangle type {28,56,56} Group order 56 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^-5 * y^4 * x^-1 ] T27.99 : Triangle type {28,56,56} Group order 56 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^2 * y^-1 * z^4 * y^-1 * z^4 ] T27.100 : Triangle type {28,56,56} Group order 56 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-12 * x^3 * y^-3 * x * y^-1 ] T27.101 : Triangle type {28,56,56} Group order 56 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-2 * z * y^-7 ] T27.102 : Triangle type {28,56,56} Group order 56 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-28, y * z^-1 ] T27.103 : Triangle type {28,56,56} Group order 56 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-6 * z * x^-6 * z * x^-1 ] T27.104 : Triangle type {55,55,55} Group order 55 Action reflexible [m] Defining relators: [ x * y * z, y * x^-1 * y, z^14 * x^-2 * z^3 ] T27.105 : Triangle type {55,55,55} Group order 55 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^-23 * x * y^-4, x * z^-1 ] T27.106 : Triangle type {55,55,55} Group order 55 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-2 * y * x^-1 * y * x^-7 * z * x^-2 ] T27.107 : Triangle type {55,55,55} Group order 55 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * y^-3 * z^3, x^-1 * z^2 * x^-6 ] T27.108 : Triangle type {55,55,55} Group order 55 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-4 * x * y^-3 ] Genus 28 T28.1 : Triangle type {2,3,8} Group order 1296 Action chiral Defining relators: [ x^2, y^3, x * y * z, z^8, x * z^2 * y * z^-2 * x * z * y * x * z * y * x * z^2 * y^-1 * z^-2 ] T28.2 : Triangle type {2,3,12} Group order 648 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, x * z^3 * y * z^-1 * x * z^2 * y^-1 * z^-2, z^12 ] T28.3 : Triangle type {2,3,12} Group order 648 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^12, z^2 * y * x * z^3 * y * x * y^-1 * x * z * y^-1 * z^-1 * x * z, z * y * x * z^2 * y * x * z * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 * x ] T28.4 : Triangle type {2,3,18} Group order 486 Action chiral Defining relators: [ x^2, y^3, x * y * z, z * y * z^-2 * x * z * y * z^-2 * x * y^-1 * z^-3 * x, z^-1 * x * z^4 * y * z^-3 * x * z * y^-1 * z^-1 ] T28.5 : Triangle type {2,3,18} Group order 486 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^5 * y * z^-5 * x * z, z * y * z^-2 * x * z * y * z^-2 * x * y^-1 * z^-3 * x, z^2 * y * z^-1 * x * z^2 * y * z^-2 * y * x * y^-1 * z^-2 * x ] T28.6 : Triangle type {2,3,18} Group order 486 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^8 * y^-1 * z^-2 * x * z^6 * y^-1 * z^-2 ] T28.7 : Triangle type {2,3,24} Group order 432 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, y * x * z^3 * y * z^-1 * y * z^-3 * x * z, z^4 * y * z^-1 * x * z * y * z^-1 * x * z^5 ] T28.8 : Triangle type {2,4,6} Group order 648 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^6, (y * z^-1)^6, y^-1 * z * y * x * z * y * z^-1 * y * x * y^-1 * z^-1 * x * z ] T28.9 : Triangle type {2,4,8} Group order 432 Action chiral Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z * y^-1 * z^2 * y^-2 * z^-2 * x * z^2 ] T28.10 : Triangle type {2,4,58} Group order 232 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-51 * x * y * z^-6 ] T28.11 : Triangle type {2,4,112} Group order 224 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-49 * x * y^-1 * z^-6 ] T28.12 : Triangle type {2,6,6} Group order 324 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z^6, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1 ] T28.13 : Triangle type {2,6,6} Group order 324 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^6, z^6, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1 ] T28.14 : Triangle type {2,6,6} Group order 324 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z^6, z * y * z^-1 * x * y^-1 * z^-2 * x ] T28.15 : Triangle type {2,6,6} Group order 324 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^6, x * y^-1 * z * y^2 * z^-1 * y^3 * z^-1 * y * x * y^-2 * z^-1 * y ] T28.16 : Triangle type {2,6,12} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y ] T28.17 : Triangle type {2,6,12} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z^2 * y^-2 * z^-1 * x * y^-1, x * z^4 * y * z^-7 ] T28.18 : Triangle type {2,6,12} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, (y * z^-3)^2 ] T28.19 : Triangle type {2,6,12} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2 * y)^2, (y * z^-3)^2 ] T28.20 : Triangle type {2,6,12} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, x * y^-1 * z * y^-2 * z^-4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1 ] T28.21 : Triangle type {2,6,12} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, x * z * y^-2 * z^-2 * y, z^-1 * x * z^2 * y * z^-3 * x * z^3 * y^-1 * z^-1 ] T28.22 : Triangle type {2,6,12} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, z^-4 * x * z^2 * y^-1 * z^-5 ] T28.23 : Triangle type {2,6,12} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, x * z^3 * y * x * z^2 * y^-1 * z^-1 * x * z^2 * y^-1 * z^-1 ] T28.24 : Triangle type {2,6,30} Group order 180 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, x * z * y^-2 * z^-2 * y, z^3 * y * z^-1 * x * z^5 ] T28.25 : Triangle type {2,6,30} Group order 180 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-6 * x * z * y * x * z^13 * y * x * y^-1 * z^-7 ] T28.26 : Triangle type {2,6,30} Group order 180 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-10 * x * z^5 * y * z^-1 * x * y^-1 * z^-12 ] T28.27 : Triangle type {2,6,84} Group order 168 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^20 * y * x * y * z^-6 * x ] T28.28 : Triangle type {2,8,8} Group order 216 Action chiral Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-1 * y * z^-1, y^8, z^-1 * x * y^-3 * z^2 * y^-1 * z^-1 ] T28.29 : Triangle type {2,9,18} Group order 162 Action chiral Defining relators: [ x^2, x * y * z, x * y^-1 * z * y^2 * x * y^-1 * z^-1, y^-9, x * y^-4 * z^-3 * y ] T28.30 : Triangle type {2,9,18} Group order 162 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^-9 ] T28.31 : Triangle type {2,9,18} Group order 162 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y^-9, z^2 * y^-3 * z^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T28.32 : Triangle type {2,9,18} Group order 162 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z^3 * y^2 * x * z^2, y^-9, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T28.33 : Triangle type {2,10,16} Group order 160 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^-4 * x * z^5 * y^-1 * z^-6 ] T28.34 : Triangle type {2,10,70} Group order 140 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, x * z^7 * y^-1 * x * z^3 * y^-1 * z^-2 ] T28.35 : Triangle type {2,12,24} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y * z^-3 * y^5 * z^-3, z^-1 * x * z * y * z^-4 * x * z * y^-1 * z^-3 ] T28.36 : Triangle type {2,12,24} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^7 * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T28.37 : Triangle type {2,12,24} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^-5 * z^-1 * x * z^2 ] T28.38 : Triangle type {2,18,63} Group order 126 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^3 * y^-2 * z^4 ] T28.39 : Triangle type {2,21,42} Group order 126 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-3 * z^-1 * y^2, y^-1 * z^3 * y^-1 * z^5 * y^-8 * z^2 * y^-1 ] T28.40 : Triangle type {2,30,60} Group order 120 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-7 * y^11 * z^-1 * y^8 * z^-2 ] T28.41 : Triangle type {2,57,114} Group order 114 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^43 * y^-12 * z ] T28.42 : Triangle type {2,58,58} Group order 116 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^44 * y^-13 ] T28.43 : Triangle type {2,112,112} Group order 112 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^42 * y^-12 * z ] T28.44 : Triangle type {3,3,4} Group order 648 Action chiral Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * z * y * x^-1 * y * x^-1 * y * z^-1 * x^-1 * y^-1 * z^-1 ] T28.45 : Triangle type {3,3,6} Group order 324 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^6, z * y^-1 * z^-1 * x^-1 * z * y * x ] T28.46 : Triangle type {3,3,6} Group order 324 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^6, (y * x^-1 * z)^3, z^2 * y^-1 * z^-1 * x^-1 * z^2 * y * x, z^-1 * x^-1 * y * x^-1 * y * x^-1 * y^-1 * x * y^-1 * x * y^-1 ] T28.47 : Triangle type {3,3,9} Group order 243 Action chiral Defining relators: [ x^3, x * y * z, y^3, x * z^2 * y * x * z * y * z^-1 ] T28.48 : Triangle type {3,3,9} Group order 243 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z^-3 * x^-1 * z^2 * y^-1, (y * x^-1 * z)^3, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 * z^-1 * x^-1 * y^-1 ] T28.49 : Triangle type {3,3,9} Group order 243 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^-3 * x^-1 * z^2 * y^-1, (y * x^-1 * z)^3, (z^-1 * x^-1 * y^-1)^3 ] T28.50 : Triangle type {3,3,9} Group order 243 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-9 ] T28.51 : Triangle type {3,3,12} Group order 216 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-1 * x * y^-1 * x * z * y^-1 * x, z^-1 * x * z * y * x^-1 * y^-1 * z^-3 ] T28.52 : Triangle type {3,3,21} Group order 189 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z * y^-1 * z^-3 * x^-1 * z^4 ] T28.53 : Triangle type {3,3,57} Group order 171 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T28.54 : Triangle type {3,4,4} Group order 324 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^4, z^4, z^-1 * y * x^-1 * y * x^-1 * y * z^-1 * x^-1 * y^-1, y * z^-1 * x^-1 * y * x^-1 * y^2 * x * z ] T28.55 : Triangle type {3,4,6} Group order 216 Action chiral Defining relators: [ x^3, x * y * z, y^4, z * x^-1 * y^-1 * x * y^-1 * x, z^6, z^-1 * y * z^-1 * y * x^-1 * y^-1 * z^-2 ] T28.56 : Triangle type {3,4,6} Group order 216 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z * x^-1 * y^-1 * x * y^-1 * x, z^6, z^-2 * y * x^-1 * z * y^2 ] T28.57 : Triangle type {3,4,6} Group order 216 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z * x^-1 * y^-1 * x * y^-1 * x, z^6, z * y * z^-1 * x^-1 * z * y^-1 * z ] T28.58 : Triangle type {3,4,6} Group order 216 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^6, z^-2 * y * x^-1 * z * y^2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y ] T28.59 : Triangle type {3,4,24} Group order 144 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * z * y^-1 * z^-1, z^-4 * x^-1 * z^3 * y^-1 ] T28.60 : Triangle type {3,5,6} Group order 180 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y^-5, (z^-1 * y)^3 ] T28.61 : Triangle type {3,6,6} Group order 162 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^6, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * y)^3, y * z^-2 * x^-1 * y^-2 * z ] T28.62 : Triangle type {3,6,6} Group order 162 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^6, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T28.63 : Triangle type {3,6,6} Group order 162 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^6, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^-2 ] T28.64 : Triangle type {3,6,6} Group order 162 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T28.65 : Triangle type {3,6,6} Group order 162 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^6, (y * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1 ] T28.66 : Triangle type {3,6,6} Group order 162 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, (y * z^-1 * y)^2 ] T28.67 : Triangle type {3,6,6} Group order 162 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, y^6 ] T28.68 : Triangle type {3,6,6} Group order 162 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y * z^-1 * y * z^-2 * y * x * y^3 * z^-2 * y ] T28.69 : Triangle type {3,6,6} Group order 162 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, (z^-1 * x^-1 * y^-1)^3 ] T28.70 : Triangle type {3,6,8} Group order 144 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^-1 * x^-1 * z * y^-1 * x * z^2 * y ] T28.71 : Triangle type {3,6,14} Group order 126 Action chiral Defining relators: [ x^3, x * y * z, x * y^-2 * x * z * y ] T28.72 : Triangle type {3,6,38} Group order 114 Action chiral Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^6, z^-2 * y * x^-1 * z^2 * y ] T28.73 : Triangle type {3,9,18} Group order 108 Action chiral Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, z^-2 * y * x^-1 * z * y ] T28.74 : Triangle type {3,9,18} Group order 108 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y * x * y^-1 * x * y^-1 * z^-1, y^-1 * z * y^-4 * z * y^-1 * z ] T28.75 : Triangle type {3,12,12} Group order 108 Action reflexible [m] Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * z^2, x^-1 * y^-2 * x * y^-1 * z ] T28.76 : Triangle type {3,12,12} Group order 108 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, (y * z^-1)^2, y * x^-1 * y * x^-1 * y^-1 * x * z ] T28.77 : Triangle type {3,12,12} Group order 108 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, (y * z^-1)^2, x^-1 * z * y * x * y^-1 * z^-1 ] T28.78 : Triangle type {3,12,12} Group order 108 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, (z * y^-3)^3 ] T28.79 : Triangle type {3,12,12} Group order 108 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * y^-1 * z, x^-1 * z * y^-1 * x * z^2, y^3 * x^-1 * z^3 ] T28.80 : Triangle type {3,12,12} Group order 108 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * z^3 * y^-4 * z^3 ] T28.81 : Triangle type {3,12,12} Group order 108 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, y^2 * z^-2 * y * z^-2 * y * z^-2 * y^2 ] T28.82 : Triangle type {3,12,12} Group order 108 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y * z^-1 * y * x^-1 * y^-1 * z^-2, y^-1 * z * y * x^-1 * y^-3 ] T28.83 : Triangle type {3,12,12} Group order 108 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, y * x^-1 * y^-1 * x * z * y, z^2 * y^-1 * z * y^-6 * z * y^-1 ] T28.84 : Triangle type {3,29,87} Group order 87 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, z * y^-19 * z * y^-7 * z ] T28.85 : Triangle type {3,30,30} Group order 90 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^19 * y^-8 * z * y^-1 ] T28.86 : Triangle type {3,30,30} Group order 90 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z * y^-1 * z * y^-1 * z * y^-2 * z^2 ] T28.87 : Triangle type {3,30,30} Group order 90 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-21 * z * y^-6 * z^2 ] T28.88 : Triangle type {3,84,84} Group order 84 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-20 * z * y^-6 * z ] T28.89 : Triangle type {4,4,4} Group order 216 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, x^-1 * y * x^-2 * y^-1 * z^-1 * y, y^-2 * z^-1 * x^-1 * z * y^-1 * z ] T28.90 : Triangle type {4,4,29} Group order 116 Action reflexible [n] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^2 * y * z^-1 * x * z^3 ] T28.91 : Triangle type {4,4,29} Group order 116 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^29 ] T28.92 : Triangle type {4,4,56} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^17 * y * x^-1 * z^10 ] T28.93 : Triangle type {4,5,10} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, z^2 * y^-1 * x * z^2, y * z^-1 * y * x^-1 * y^2 * z^-1 ] T28.94 : Triangle type {4,6,12} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, y^6, (z^-1 * x)^3 ] T28.95 : Triangle type {4,6,12} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, (z^-1 * x)^3 ] T28.96 : Triangle type {4,6,12} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^-3 * x^-1 * y * z^-2, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T28.97 : Triangle type {4,6,48} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T28.98 : Triangle type {4,12,42} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^2 * y * z^-1 * x^-1 * z^3 ] T28.99 : Triangle type {4,20,40} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, y^-1 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T28.100 : Triangle type {4,38,76} Group order 76 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^5 * z^-3 * y^5 * z^-1 * y * z^-1 * y * z^-1 * y ] T28.101 : Triangle type {5,16,16} Group order 80 Action reflexible [n] Defining relators: [ x * y * z, y * x^2 * z, x * y^-1 * x * z^-1, y * z^-7 * y * z^-1 * y^3 * z^-1 * y^2 ] T28.102 : Triangle type {5,16,16} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^-5, z * y^-1 * z * y^-3 * z * y^-1 * z * y^-5 * z * y^-1 ] T28.103 : Triangle type {5,70,70} Group order 70 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, z^-10 * y * z^-3 ] T28.104 : Triangle type {5,70,70} Group order 70 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-5, y * z^-9 * y * z^-3 ] T28.105 : Triangle type {6,6,6} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, (x * y^-1 * x)^2, z^6 ] T28.106 : Triangle type {6,6,6} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^6, z^6 ] T28.107 : Triangle type {6,6,6} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, z^-1 * y * x^2 * z^-1 * y, z^6 ] T28.108 : Triangle type {6,6,6} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, y^6 ] T28.109 : Triangle type {6,6,6} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, (x * y^-1)^2, z^-2 * x^-1 * z * y^-1, x^6, y^6 ] T28.110 : Triangle type {6,6,6} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, (x * y^-1)^2, (y * z^-1)^2, x^6, y^6, y^-1 * z^-1 * x^-2 * z * x^-1 * z ] T28.111 : Triangle type {6,6,6} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, (x * z^-1 * x)^2, y^6 ] T28.112 : Triangle type {6,6,6} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^6, y^6, z^6 ] T28.113 : Triangle type {6,6,6} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, (x * y^-1)^2, z^2 * x^-1 * z * y^-1, x^6, y^6 ] T28.114 : Triangle type {6,6,15} Group order 90 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^2 * y * x * z^2 ] T28.115 : Triangle type {6,6,15} Group order 90 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^2 * y * z^-5 * x^-1 * y * z^-3 * x^-1 * y * z^-1 * x^-1 * z ] T28.116 : Triangle type {6,6,15} Group order 90 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-7 * x^-1 * y * x * y^-1 * z^-6 ] T28.117 : Triangle type {6,6,42} Group order 84 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^2 * y * z^-2 * x * z^4 * y * x^-1 * y^-1 * z^-3 * x ] T28.118 : Triangle type {6,18,36} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, z^-2 * y^2 * z^-2 ] T28.119 : Triangle type {6,18,36} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y^3 * z^-1 * y ] T28.120 : Triangle type {6,24,24} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z * y^-1 * z^5 * y^-1 * z^3 ] T28.121 : Triangle type {6,24,24} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^-2 * x^2 * z * y^-1 ] T28.122 : Triangle type {6,24,24} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^6, y^5 * z^-1 * y * z^-1 * y^3 * z^-1 ] T28.123 : Triangle type {8,9,72} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z^8 ] T28.124 : Triangle type {8,10,10} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^8, y^3 * z^-1 * y * z^-2 * y * z^-1 * y ] T28.125 : Triangle type {8,12,24} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, y * x^-2 * y^2, z^-2 * x^-1 * z * y^-1, (z^-1 * x)^3 ] T28.126 : Triangle type {8,12,24} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, y^2 * x * z^-1, z^-2 * x^-1 * z * y^-1, x^8 ] T28.127 : Triangle type {8,64,64} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-8, z^-4 * y * z^-3 ] T28.128 : Triangle type {8,64,64} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^8 ] T28.129 : Triangle type {9,9,9} Group order 81 Action reflexible [n] Defining relators: [ x * y * z, z^-1 * y * x * z^-1, y * z^-1 * x^2 * z^-1 * x^-1, x^2 * y^-1 * x^4 * y^-2 ] T28.130 : Triangle type {9,9,9} Group order 81 Action chiral Defining relators: [ x * y * z, x * y^-1 * x^2 * y^-2, y^2 * x^2 * z^2, x * z^-1 * x^2 * z^-2 ] T28.131 : Triangle type {9,9,9} Group order 81 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-9, z^9 ] T28.132 : Triangle type {9,9,9} Group order 81 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y ] T28.133 : Triangle type {9,9,9} Group order 81 Action reflexible [m] Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, z * x^-1 * y^-1 * x * z * x^-1 ] T28.134 : Triangle type {9,9,9} Group order 81 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y * z^-1, z * x^-2 * y^-2, (y^-1 * x)^3 ] T28.135 : Triangle type {9,9,9} Group order 81 Action reflexible [m] Defining relators: [ x * y * z, z * x^-2 * y^-2, y^2 * x^-1 * z^2, z * x^-1 * y^-1 * x * y^-1 * x ] T28.136 : Triangle type {9,12,18} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x * z^-1 * x^2 * z * y^-1, z * x^-1 * y^-1 * x * y^-1 * x ] T28.137 : Triangle type {9,12,18} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, z * y * x^-1 * z, y^-1 * z * x^-1 * y^-1 * z ] T28.138 : Triangle type {9,63,63} Group order 63 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * z^3, x^-9 ] T28.139 : Triangle type {9,63,63} Group order 63 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y^-4 * x * y^-3, z^-4 * x * z^-3 ] T28.140 : Triangle type {10,10,35} Group order 70 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-2 * x^2 * y^-2, z^3 * y * x * z^3 ] T28.141 : Triangle type {10,10,35} Group order 70 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-2)^2, z^3 * y * x * z^3 ] T28.142 : Triangle type {12,12,12} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, y^-1 * z * x^-3 * y^-1 * z * y^-1 * z ] T28.143 : Triangle type {12,12,12} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^-4 * y * x * z^-1 ] T28.144 : Triangle type {12,12,12} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, y^3 * x^-1 * y * z^-1 * y ] T28.145 : Triangle type {15,60,60} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^7 * z^-1 ] T28.146 : Triangle type {15,60,60} Group order 60 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^15 ] T28.147 : Triangle type {20,30,60} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^5 * x^-2 * y^4 ] T28.148 : Triangle type {20,30,60} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^8 * z^-1 * x^9 * y^-1 * x^2 ] T28.149 : Triangle type {20,30,60} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, x^-6 * y^3 ] T28.150 : Triangle type {21,21,21} Group order 63 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-5 * x^3 * y^-4 ] T28.151 : Triangle type {21,21,21} Group order 63 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, z^2 * x^-3 * z^4 ] T28.152 : Triangle type {29,58,58} Group order 58 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^10 * y^-1 * x * y^-1 * x^2 ] T28.153 : Triangle type {29,58,58} Group order 58 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^-1 * z^2 * x^-8 ] T28.154 : Triangle type {29,58,58} Group order 58 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^6 * y^-2 ] T28.155 : Triangle type {29,58,58} Group order 58 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^4 * x^-1 * y^4 ] T28.156 : Triangle type {29,58,58} Group order 58 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4 * z^-2, y^-4 * x^2 * y^-1 * z^3 * y^-2 ] T28.157 : Triangle type {29,58,58} Group order 58 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-5 * y * z^-6 ] T28.158 : Triangle type {29,58,58} Group order 58 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-5 * y^4 ] T28.159 : Triangle type {29,58,58} Group order 58 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, x^-1 * z * x^-1 * z^2 * x^-5 * z^3 ] T28.160 : Triangle type {29,58,58} Group order 58 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-2 * z * y^-2 * z * y^-6 * z * y^-3 ] T28.161 : Triangle type {29,58,58} Group order 58 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, z^-4 * y * z^-3 ] T28.162 : Triangle type {29,58,58} Group order 58 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y^2 * x^-4 * y^4 ] T28.163 : Triangle type {29,58,58} Group order 58 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z * x^-7 * z ] T28.164 : Triangle type {29,58,58} Group order 58 Action reflexible [m] Defining relators: [ x * y * z, y * x^-1 * y, z^15 * x^-2 * z^3 ] T28.165 : Triangle type {29,58,58} Group order 58 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-29, y * z^-1 ] T28.166 : Triangle type {30,30,30} Group order 60 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-7 * x^2 * y^-7 ] T28.167 : Triangle type {57,57,57} Group order 57 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^-24 * x * y^-4, x * z^-1 ] T28.168 : Triangle type {57,57,57} Group order 57 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^2 * y^-3 * x^7 ] T28.169 : Triangle type {57,57,57} Group order 57 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * z^3, x * y^-4 * x^3 * z^-1 * x ] T28.170 : Triangle type {57,57,57} Group order 57 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^7 * y^-1, y^7 * z^-1 ] Genus 29 T29.1 : Triangle type {2,4,6} Group order 672 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^6, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^2 * y * z^-2 * y * x * z^2 * y^-1 * z * y^-1 * z^-1 * x ] T29.2 : Triangle type {2,4,18} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^2 * y^-2 * z^-3 * y, z^-3 * x * z * y * x * z^6 * y^-1 * z^-2 * x * z * y^-1 * z^-2 ] T29.3 : Triangle type {2,4,32} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-18 * x * z^5 * y * z^-2 * x * y^-1 * z^-5 ] T29.4 : Triangle type {2,4,32} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, x * z^7 * y * z^-1 * x * y^-1 * z^-6 ] T29.5 : Triangle type {2,4,60} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-60 ] T29.6 : Triangle type {2,4,116} Group order 232 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-51 * x * y^-1 * z^-6 ] T29.7 : Triangle type {2,5,8} Group order 320 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^-5, (y * z^-1)^4, (y * z^-3)^2 ] T29.8 : Triangle type {2,5,8} Group order 320 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^-5, (y * z^-3)^2, y^-1 * z * y^-1 * z * y^-1 * z^-2 * x * z ] T29.9 : Triangle type {2,6,6} Group order 336 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, z^2 * y * z^-1 * x * z * y * x * y^-1 * z^-1 * x * z * y^-1 * z^-2 * x ] T29.10 : Triangle type {2,6,6} Group order 336 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^6, z^6, (y * z^-1)^4, z^-1 * y^2 * z^-1 * y^2 * z^-2 * y * z^-1 ] T29.11 : Triangle type {2,6,10} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z * y * z^-2 * x * y^-1 * z^-3 * x ] T29.12 : Triangle type {2,6,10} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, (y * z^-1)^4, (y * z^-3 * y)^2 ] T29.13 : Triangle type {2,6,10} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * z^-3 ] T29.14 : Triangle type {2,6,15} Group order 210 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, x * z * y^-3 * z^-1 * x * y^-1 * z^-1 ] T29.15 : Triangle type {2,6,24} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T29.16 : Triangle type {2,6,24} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, x * y^-1 * z * y^-2 * z^-4 ] T29.17 : Triangle type {2,6,87} Group order 174 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-5 * x * z * y * x * z^13 * y * x * z^7 * y^-1 ] T29.18 : Triangle type {2,8,12} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, z^12 ] T29.19 : Triangle type {2,8,12} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z^2 * y^-1 * z^-3, y^8, (y * z^-1 * y^2)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y ] T29.20 : Triangle type {2,8,12} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, z^-1 * x * y^-2 * z^-2 * y, x * z^6 * y * z^-5 ] T29.21 : Triangle type {2,8,12} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^2 * y^-3 * z^-2 * x * z, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y ] T29.22 : Triangle type {2,8,12} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z * y * z^-1 * x * y^-1 * z^-2 * x, z^-1 * x * y^-3 * z^-4 ] T29.23 : Triangle type {2,8,12} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, z^-1 * x * y^-3 * z^-4, x * z^2 * y^-2 * z^2 * y^-1 * z^-1 ] T29.24 : Triangle type {2,8,12} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-12 ] T29.25 : Triangle type {2,8,12} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, (y * z^-1 * y^2)^2, z^-12 ] T29.26 : Triangle type {2,8,40} Group order 160 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^7 * y * z^-5 * x * y^-1 * z^-1 * x * y^-1 * z^-3 * x * z ] T29.27 : Triangle type {2,8,40} Group order 160 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, x * z^13 * y^-1 * z^-6 ] T29.28 : Triangle type {2,12,12} Group order 168 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z * y * z^-1 * x * y^-1 * z^-1 * x * z, y^-2 * z^2 * y^-5 * z * y^-1 * z ] T29.29 : Triangle type {2,18,18} Group order 144 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^2 * z^-2 * y^10 * z^-2 * y^2 ] T29.30 : Triangle type {2,32,32} Group order 128 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-8 * y^11 * z^-1 * y^9 * z^-1 * y ] T29.31 : Triangle type {2,32,32} Group order 128 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^-5 * z^3 * y^-6 * z * y^-1 ] T29.32 : Triangle type {2,32,32} Group order 128 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^-1 * z^5 * y^-9 * z ] T29.33 : Triangle type {2,59,118} Group order 118 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^45 * y^-12 * z ] T29.34 : Triangle type {2,60,60} Group order 120 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^46 * y^-13 ] T29.35 : Triangle type {2,116,116} Group order 116 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^44 * y^-12 * z ] T29.36 : Triangle type {3,4,4} Group order 336 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * y^-1 * z^-1 * y * x * z * y * z^-1 ] T29.37 : Triangle type {3,4,8} Group order 192 Action chiral Defining relators: [ x^3, x * y * z, y^4, (x^-1 * z * y)^2, z^-3 * x^-1 * y^-1 * z * y^-1 ] T29.38 : Triangle type {3,4,8} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, (x^-1 * z * y)^2, z^-1 * y * z^-1 * x^-1 * z^2 * y ] T29.39 : Triangle type {3,4,8} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-2 * y * x^-1 * z * y^2, z^-1 * y * z^-1 * x^-1 * z^2 * y ] T29.40 : Triangle type {3,4,8} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, (x^-1 * z * y)^2, (z^-1 * y)^3 ] T29.41 : Triangle type {3,4,8} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^2, z^-1 * x^-1 * z * y^-1 * x * z^2 * y ] T29.42 : Triangle type {3,4,8} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^8, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y ] T29.43 : Triangle type {3,4,8} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^8, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T29.44 : Triangle type {3,4,8} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^2, x^-1 * z^2 * y^-1 * x * z^3 ] T29.45 : Triangle type {3,4,8} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * x * y^-1 * x * y^-1 * z^-1 ] T29.46 : Triangle type {3,4,8} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-2 * y * x^-1 * z * y^2, z^-3 * x^-1 * y^-1 * z * y ] T29.47 : Triangle type {3,6,6} Group order 168 Action chiral Defining relators: [ x^3, x * y * z, z^-1 * x * y^-1 * x * z * y^-1, y^-2 * z * y^-1 * x * y^-1 * z^2 ] T29.48 : Triangle type {3,6,6} Group order 168 Action chiral Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * x * y^-1 * z^-1 ] T29.49 : Triangle type {3,6,6} Group order 168 Action chiral Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y * z^-1 * y * z^-1 * y * z^-1 * x * y^3 * z^-2 * y ] T29.50 : Triangle type {3,10,10} Group order 120 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, (y * z^-1 * y^2)^2 ] T29.51 : Triangle type {3,10,10} Group order 120 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, (y * z^-1)^2, (x^-1 * z * y)^2, z^-2 * x^-1 * y^-1 * x * z * y * z^-1 ] T29.52 : Triangle type {3,10,10} Group order 120 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^3 * x^-1 * y^-1 * z, z * y * z^-1 * x^-1 * z^2 ] T29.53 : Triangle type {3,15,15} Group order 105 Action chiral Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z * y^-2 * x * z * y^-1 ] T29.54 : Triangle type {3,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, (y * z^-1)^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T29.55 : Triangle type {3,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T29.56 : Triangle type {3,87,87} Group order 87 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-20 * z * y^-8 ] T29.57 : Triangle type {4,4,9} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, (x * z^-1 * y)^2, z^4 * y^-1 * x^-1 * z^4 ] T29.58 : Triangle type {4,4,9} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, y^-1 * z^-1 * y * x^-1 * z * y^-1 * z, z^-2 * x * z^3 * y * z^-3 ] T29.59 : Triangle type {4,4,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, z * y^-1 * z^-2 * x^-1 * z^4 ] T29.60 : Triangle type {4,4,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^7 * y * z^-3 * x^-1 * y^-1 * x * z^4 ] T29.61 : Triangle type {4,4,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T29.62 : Triangle type {4,4,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, z * y * z^-2 * x^-1 * z^4 ] T29.63 : Triangle type {4,4,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^-6 * x^-1 * y^-1 * z^-5 * x * z * y^-1 * z^-2 ] T29.64 : Triangle type {4,4,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z * y * x^2 * z * y^-1, z^3 * y^-1 * z^-1 * x * z^3 ] T29.65 : Triangle type {4,4,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-2)^2, z^-3 * x * y^-1 * x * y^-1 * z^-3 ] T29.66 : Triangle type {4,4,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, z^3 * y * x^-1 * z^4 ] T29.67 : Triangle type {4,4,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y^-1 * z^-1 * x^-2 * z^2 * x^-1, z^3 * y * x^-1 * z^4 ] T29.68 : Triangle type {4,4,30} Group order 120 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^4, y * x^-1 * y^-1 * x * z^-2, y^-1 * z^-1 * y * x * z * x^-1, z^-3 * x^-1 * z * y^-1 * z^-1 ] T29.69 : Triangle type {4,4,30} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^30 ] T29.70 : Triangle type {4,4,58} Group order 116 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^18 * y * x^-1 * z^10 ] T29.71 : Triangle type {4,5,5} Group order 160 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, z^2 * y^-1 * x^-1 * z^2, x^-1 * z * y * x * z * y ] T29.72 : Triangle type {4,5,5} Group order 160 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, z^2 * y^-1 * x^-1 * z^2, x^-1 * z * y * x * y^-1 * z^-1 ] T29.73 : Triangle type {4,8,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z * y^-1 * z^-1 * x^-1 * z^3 ] T29.74 : Triangle type {4,8,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^8 ] T29.75 : Triangle type {4,8,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-2 * x^-1 * z^3, y^8 ] T29.76 : Triangle type {4,8,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^2 * y * x^-1 * z^3 ] T29.77 : Triangle type {4,8,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * z^4 * y^-1 * z^-1 * x^-1 * y^-1 * z^-4 ] T29.78 : Triangle type {4,8,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^2 * y * z^-3 * x^-1 * y^-1 * x^-1 * z^5 ] T29.79 : Triangle type {4,12,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, y^-2 * z * y^-1 * z * y^-5 * z^2 ] T29.80 : Triangle type {4,12,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^3 * z^-2, x^-1 * z * y * x * z * y ] T29.81 : Triangle type {4,12,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * y^-2 * z, z^-1 * y^2 * x^-1 * y^3 ] T29.82 : Triangle type {4,12,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, (y * z^-1 * y)^2, x^-1 * z * y * x * z * y, (y * z^-2)^2 ] T29.83 : Triangle type {4,12,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * z * y^-1, y^-1 * z^2 * y^-3 * z * y^-1 * z * y^-2 * z ] T29.84 : Triangle type {4,12,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, (z^-1 * y)^3, y^3 * x^-1 * y * z^-2 ] T29.85 : Triangle type {4,12,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-3 * z * y^-4 * z^3 * y^-1 ] T29.86 : Triangle type {4,12,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y^-5 * z * y^-1 * z * y^-4 ] T29.87 : Triangle type {4,12,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, (y * z^-1 * y)^2 ] T29.88 : Triangle type {4,21,28} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-4 * x * y^-1 * z * y^-1 ] T29.89 : Triangle type {4,40,40} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-3 * z * y^-7 * z * y^-1 * z * y^-4 * z * y^-1 ] T29.90 : Triangle type {4,40,40} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y^2 * z^-1 * y^3 * z^-2 * y^6 * z^-1 * y * z^-1 * y * z^-1 * y ] T29.91 : Triangle type {5,6,6} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, x^-5, y^2 * x^-1 * z^2, x^-1 * y^-1 * x^2 * z * x^-1 ] T29.92 : Triangle type {5,6,6} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, (y * z^-1)^2, x^-5, x^-1 * y^-1 * x^2 * z * x^-1, y^6 ] T29.93 : Triangle type {6,6,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, (x * y^-1)^2, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y ] T29.94 : Triangle type {6,6,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, (x * z * y)^2 ] T29.95 : Triangle type {6,8,8} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, y * z^-1 * x^-1 * y * z^-1, x^6, y^2 * x^2 * z^-1 * y ] T29.96 : Triangle type {6,8,8} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^6, z * y * x^2 * y^-2, z^-2 * x^2 * z * y, z^-1 * x^-1 * y^-1 * x * z^-2 ] T29.97 : Triangle type {6,8,8} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, y * z^-1 * x^-1 * y^-1 * z, x^6, z * y^-1 * x^2 * z^2 ] T29.98 : Triangle type {6,8,8} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, x^6, (y * z^-1 * y)^2 ] T29.99 : Triangle type {6,8,8} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^6, z * y^-1 * x^2 * z^2, y^2 * x^2 * z^-1 * y, y * z^-1 * x^2 * y^-1 * z ] T29.100 : Triangle type {6,8,8} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, y^3 * x^-1 * z^3 ] T29.101 : Triangle type {6,8,8} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z * y * x^-1 * y^-2, z^-2 * x^-1 * z * y, x^6 ] T29.102 : Triangle type {6,8,8} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, z * y * x^-1 * y^-2, x^6 ] T29.103 : Triangle type {6,8,8} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^6, x^-1 * z * y * x * y^-1 * z^-1 ] T29.104 : Triangle type {6,8,8} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^8 ] T29.105 : Triangle type {6,12,12} Group order 84 Action chiral Defining relators: [ x * y * z, y * z^-1 * x^-1 * y^-1 * z^-1, x^6, y^2 * x^2 * z^2 ] T29.106 : Triangle type {6,12,12} Group order 84 Action chiral Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, z^-2 * y^2 * z^-1 * y ] T29.107 : Triangle type {6,36,36} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z * y^-1 * z^5 * y^-2 * z^2 ] T29.108 : Triangle type {8,8,20} Group order 80 Action reflexible [n] Defining relators: [ x * y * z, (x * y^-1)^2, z^2 * x^-1 * y^-1 * z, (x * z^-1 * x)^2 ] T29.109 : Triangle type {8,8,20} Group order 80 Action reflexible [n] Defining relators: [ x * y * z, (x * y^-1)^2, y^-1 * z^-1 * x^-1 * z^2 ] T29.110 : Triangle type {8,8,20} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^4 * y^-1 * z^-1 * x^-1 * z^4 ] T29.111 : Triangle type {8,8,20} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, y * z^-1 * x^-1 * z^3 * y * x^-1 * z^4 ] T29.112 : Triangle type {9,18,18} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, y^-2 * x^2 * y^-1 * z, y^2 * x^2 * z^2 ] T29.113 : Triangle type {9,18,18} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, (y * z^-1)^2, x^-9 ] T29.114 : Triangle type {10,14,35} Group order 70 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * z^3, x^-10 ] T29.115 : Triangle type {16,32,32} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-16 ] T29.116 : Triangle type {16,32,32} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^-7 * z * y ] T29.117 : Triangle type {16,32,32} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-1 * z^2 * x^-5 * z^2 ] T29.118 : Triangle type {16,32,32} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, y * x^-7 * z ] T29.119 : Triangle type {16,32,32} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, z * x^-1 * z^3 * x^-3 * z^4 ] T29.120 : Triangle type {16,32,32} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * y^-2, z^-1 * x * z^-1 * x * z^-2 ] T29.121 : Triangle type {30,60,60} Group order 60 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^2 * x^-3 * y^4 ] T29.122 : Triangle type {30,60,60} Group order 60 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-30, y * z^-1 ] T29.123 : Triangle type {59,59,59} Group order 59 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^-25 * x * y^-4, x * z^-1 ] T29.124 : Triangle type {59,59,59} Group order 59 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-11 * x * y^-8 ] T29.125 : Triangle type {59,59,59} Group order 59 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^3 * y^-9 * x * y^-1 * x * y^-1 ] T29.126 : Triangle type {59,59,59} Group order 59 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-1 * y * x^-1 * y^2 * x^-4 * y^4 ] T29.127 : Triangle type {59,59,59} Group order 59 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-1 * y^2 * x^-6 * y^2 ] T29.128 : Triangle type {59,59,59} Group order 59 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y * x^-4 * y^4 ] T29.129 : Triangle type {59,59,59} Group order 59 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, x^5 * y^-3 ] T29.130 : Triangle type {59,59,59} Group order 59 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^3 * y^-6 * z^2 ] T29.131 : Triangle type {59,59,59} Group order 59 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-3 * y^2 * x^-8 ] T29.132 : Triangle type {59,59,59} Group order 59 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^7 * z^-2 ] Genus 30 T30.1 : Triangle type {2,4,33} Group order 264 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-19 * x * z^7 * y^-1 * x * y^-1 * z^-5 ] T30.2 : Triangle type {2,4,62} Group order 248 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-62 ] T30.3 : Triangle type {2,4,120} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-53 * x * y^-1 * z^-6 ] T30.4 : Triangle type {2,6,32} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-8 * x * z^9 * y * x * y^-1 * z^-1 * x * y^-1 * z^-11 ] T30.5 : Triangle type {2,8,22} Group order 176 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-3 * x * z^3 * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-11 ] T30.6 : Triangle type {2,12,14} Group order 168 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^-2 * x * z^5 * y^-1 * z^-6 ] T30.7 : Triangle type {2,14,70} Group order 140 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^4 * y * x * y^-1 * z^-4, (y^-2 * z^4 * y^-1)^2 ] T30.8 : Triangle type {2,22,66} Group order 132 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y^-9 * z^2 * y^-7 * z^2 * y^-2 ] T30.9 : Triangle type {2,26,65} Group order 130 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^5 * y * z^-4 * x, y * z^-4 * y^6 * z^-1 * y ] T30.10 : Triangle type {2,33,33} Group order 132 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-29 * z * y^-1 ] T30.11 : Triangle type {2,61,122} Group order 122 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^47 * y^-12 * z ] T30.12 : Triangle type {2,62,62} Group order 124 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^48 * y^-13 ] T30.13 : Triangle type {2,120,120} Group order 120 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^46 * y^-12 * z ] T30.14 : Triangle type {3,3,61} Group order 183 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z * y * z^-3 * x * z^4 ] T30.15 : Triangle type {3,31,93} Group order 93 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-22 * z * y^-6 * z^2 ] T30.16 : Triangle type {3,32,32} Group order 96 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^21 * y^-8 * z * y^-1 ] T30.17 : Triangle type {3,90,90} Group order 90 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-21 * z * y^-8 ] T30.18 : Triangle type {4,4,31} Group order 124 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^31 ] T30.19 : Triangle type {4,4,60} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^19 * y * x^-1 * z^10 ] T30.20 : Triangle type {4,6,10} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^5 * y^-1 * x^-1 * z^4 ] T30.21 : Triangle type {4,6,10} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^2 * y^-1 * x * z^2 ] T30.22 : Triangle type {4,12,16} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^3 * x^-1 * y^-1 * z * y, z^2 * y * z^-1 * x^-1 * z^4 ] T30.23 : Triangle type {4,21,84} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^-3 * z * y^-2 * z * y^-1 * z * y^-1 * z * y^-5 * z^3 * y^-1 * z ] T30.24 : Triangle type {4,22,22} Group order 88 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-10 * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-4 ] T30.25 : Triangle type {4,28,42} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-4 * x * z^2 * y^-1 ] T30.26 : Triangle type {4,80,80} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^2 * z^-1 * y^3 * z^-2 * y^6 * z^-1 * y * z^-1 * y * z^-2 ] T30.27 : Triangle type {5,16,80} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^2 * z^-9 * y * z^-1 * y^3 ] T30.28 : Triangle type {5,75,75} Group order 75 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z * y^-1 * z * y^-1 * z^9 * y^-1 ] T30.29 : Triangle type {5,75,75} Group order 75 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, z^2 * y^-1 * z * y^-1 * z^10 ] T30.30 : Triangle type {6,6,16} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-9 * x^-1 * y * x^-1 * y * x^-1 * y * z^-4 ] T30.31 : Triangle type {6,13,78} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^-2 * z * y^-1 * z^5 * y^-4 ] T30.32 : Triangle type {6,14,14} Group order 84 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^6, y^2 * z^-1 * y * z^-1 * x^-1 * z^-1 * y * z^-1 * y^5 * z^-1 ] T30.33 : Triangle type {6,72,72} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z * y^-1 * z^5 * x * y^-4 ] T30.34 : Triangle type {7,11,77} Group order 77 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, y^-2 * z^5 * y^-2 * z^2 ] T30.35 : Triangle type {7,12,12} Group order 84 Action reflexible [n] Defining relators: [ x * y * z, y * x^2 * z, z * x^-2 * y * x^-1, z^-1 * y * z^-1 * y^4 * z^-1 * y * z^-3 ] T30.36 : Triangle type {7,12,12} Group order 84 Action reflexible [n] Defining relators: [ x * y * z, x * y^-1 * x * z^-1, x^-3 * y^-1 * z^-1, y^3 * z^-1 * y^5 * z^-2 * y ] T30.37 : Triangle type {7,12,12} Group order 84 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^-7, y^-5 * z * y^-1 * z^2 * y^-1 * z * y^-1 ] T30.38 : Triangle type {7,70,70} Group order 70 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z^5 * y^-3 * z ] T30.39 : Triangle type {7,70,70} Group order 70 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z^5 * y^-1 * z^3 ] T30.40 : Triangle type {7,70,70} Group order 70 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z^5 * y^-4 ] T30.41 : Triangle type {8,8,11} Group order 88 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^4 * y^-1 * x * y^-1 * x^-1 * y * x^-1 * z^4 ] T30.42 : Triangle type {8,10,20} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, y * x^-2 * z * x^-1, (y^-1 * z * y^-1 * z * y^-1)^2 ] T30.43 : Triangle type {8,18,72} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z^4 * y^-4 ] T30.44 : Triangle type {11,66,66} Group order 66 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-11 ] T30.45 : Triangle type {11,66,66} Group order 66 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^-3 * x^2 * y^-3 ] T30.46 : Triangle type {11,66,66} Group order 66 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-11 ] T30.47 : Triangle type {11,66,66} Group order 66 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-1 * y^3 * x^-3 * y^3 ] T30.48 : Triangle type {11,66,66} Group order 66 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-11 ] T30.49 : Triangle type {12,18,18} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^2 * z^-2, x^-5 * z * y ] T30.50 : Triangle type {12,18,18} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, z * y^-1 * x * z, y * x^-2 * y^2 ] T30.51 : Triangle type {13,65,65} Group order 65 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, x^-1 * z^2 * x^-4 * z^3 ] T30.52 : Triangle type {13,65,65} Group order 65 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-4 * z, x^-2 * z * x^-1 * z^3 * x^-6 * z ] T30.53 : Triangle type {13,65,65} Group order 65 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, x^-1 * z^3 * x^-5 * z^2 ] T30.54 : Triangle type {13,65,65} Group order 65 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^-3 * y * x^-8 * z * x^-1 ] T30.55 : Triangle type {13,65,65} Group order 65 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x * y^-4 * x^5 * y^-1 * x ] T30.56 : Triangle type {13,65,65} Group order 65 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, z * x^-4 * z^4 ] T30.57 : Triangle type {14,14,35} Group order 70 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z^2 * y^-1 * x * z^2 ] T30.58 : Triangle type {14,14,35} Group order 70 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^4 * y^-2, z^-1 * y^3 * z^-1 * y, z * y^-1 * z^-1 * x * z^2 ] T30.59 : Triangle type {14,14,35} Group order 70 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-2 * x * z^2, z^-3 * y * x * z^-3 ] T30.60 : Triangle type {16,64,64} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, x^-2 * z * x^-1 * z^3 * x^-3 * z^4 ] T30.61 : Triangle type {16,64,64} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y^2 * z^-2 * y^2 * x^-4 * y^2 ] T30.62 : Triangle type {16,64,64} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-16 ] T30.63 : Triangle type {16,64,64} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^-3 * y^2 * z^-3 ] T30.64 : Triangle type {21,63,63} Group order 63 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^-1 * y * x^-7 * y^2 ] T30.65 : Triangle type {21,63,63} Group order 63 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^9 * y^-1 * x^7 * z^-1 * x^4 ] T30.66 : Triangle type {21,63,63} Group order 63 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^9 * x^-1 * y^6 ] T30.67 : Triangle type {21,63,63} Group order 63 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * x^5 * y^-2, y^-1 * z^4 * y^-2 * z^2 ] T30.68 : Triangle type {21,63,63} Group order 63 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-3 * x^5 * z^-3 * x * z^-3 ] T30.69 : Triangle type {22,22,33} Group order 66 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y * x^-1 * y * x^-1 * y * z^-1 * y ] T30.70 : Triangle type {22,22,33} Group order 66 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * y * x^-1 * y * z^-1, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2 ] T30.71 : Triangle type {22,22,33} Group order 66 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * y^-1 * z^-1, y^-2 * x^2 * y^-2 ] T30.72 : Triangle type {22,22,33} Group order 66 Action reflexible [m] Defining relators: [ x * y * z, z * y^-1 * x * z, z^-1 * y * x^-1 * y^-2, x^5 * z^-1 * x * z^-1 ] T30.73 : Triangle type {22,22,33} Group order 66 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^4 * x^-1 * y^-1 * z^4 * x^-1 * z * x^-1 ] T30.74 : Triangle type {31,62,62} Group order 62 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-7 * x^3 * y^-7 ] T30.75 : Triangle type {31,62,62} Group order 62 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-12 * x^3 * y^-6 * x ] T30.76 : Triangle type {31,62,62} Group order 62 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, x^-5 * y^4 ] T30.77 : Triangle type {31,62,62} Group order 62 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-3 * x^3 * y^-7 ] T30.78 : Triangle type {31,62,62} Group order 62 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z^3 * x^-6 * z ] T30.79 : Triangle type {31,62,62} Group order 62 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-8 * y^2 ] T30.80 : Triangle type {31,62,62} Group order 62 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^2 * z^-2 * x^7 * z^-3 * x * z^-1 * x ] T30.81 : Triangle type {31,62,62} Group order 62 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4 * y^-2, z^6 * x^-1 * z^4 ] T30.82 : Triangle type {31,62,62} Group order 62 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^5 * x^-2 * y^4 * z^-1 * y^2 ] T30.83 : Triangle type {31,62,62} Group order 62 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^2 * y^-4 * z^4 ] T30.84 : Triangle type {31,62,62} Group order 62 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-2 * z^2 * x^-7 ] T30.85 : Triangle type {31,62,62} Group order 62 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-7 * y^2 ] T30.86 : Triangle type {31,62,62} Group order 62 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^6 * z^-2 ] T30.87 : Triangle type {31,62,62} Group order 62 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, x^-1 * y * z^-2 * y^5 * z^-1 * y ] T30.88 : Triangle type {31,62,62} Group order 62 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-31, y * z^-1 ] T30.89 : Triangle type {61,61,61} Group order 61 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^-26 * x * y^-4, x * z^-1 ] T30.90 : Triangle type {61,61,61} Group order 61 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-11 * x * y^-5 * x * y^-3 ] T30.91 : Triangle type {61,61,61} Group order 61 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^3 * y^-4 * x^3 * y^-3 * x * y^-3 ] T30.92 : Triangle type {61,61,61} Group order 61 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^2 * x^-1 * y^3 * x^-3 * y^4 ] T30.93 : Triangle type {61,61,61} Group order 61 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-1 * y^3 * x^-4 * y^3 ] T30.94 : Triangle type {61,61,61} Group order 61 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^3 * x^-2 * y^4 ] T30.95 : Triangle type {61,61,61} Group order 61 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, y^-2 * x^3 * y^-3 ] T30.96 : Triangle type {61,61,61} Group order 61 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, x^-8 * z^3 ] T30.97 : Triangle type {61,61,61} Group order 61 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, y * x^-4 * y^4 ] T30.98 : Triangle type {61,61,61} Group order 61 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, x^-1 * y^3 * x^-3 * y^4 ] T30.99 : Triangle type {61,61,61} Group order 61 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^5 * z^-2 * y^6 ] Genus 31 T31.1 : Triangle type {2,3,21} Group order 504 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^-1 * x * z * y * z^-1 * x * z * y * z^-2 * x * z^2 * y^-1 * z^-2 ] T31.2 : Triangle type {2,3,30} Group order 450 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-1 * x * z^4 * y * z^-3 * x * y * z^-1 * x * z^5 * y^-1 * z^-3 ] T31.3 : Triangle type {2,4,6} Group order 720 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^6, z * y * z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1 * x ] T31.4 : Triangle type {2,4,14} Group order 336 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z * y * z^-1 * y * z^-1 * x * z^4 ] T31.5 : Triangle type {2,4,14} Group order 336 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (z^-1 * y)^3, x * z * y * x * z^2 * y^2 * z^-2 * x * y^-1 * z^-1, x * z^3 * y * z^-1 * x * z^2 * y^-1 * z^-2 ] T31.6 : Triangle type {2,4,16} Group order 320 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, y * x * z * y * x * y^-1 * z^-2 * x * z^2 ] T31.7 : Triangle type {2,4,16} Group order 320 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^7 * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x * z^2 ] T31.8 : Triangle type {2,4,24} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z * y * z^-2 * x * y^-1 * z^-3 * x, (y^-1 * z)^6 ] T31.9 : Triangle type {2,4,24} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z * y * z^-2 * x * y^-1 * z^-3 * x, y^-1 * z * y * z^-2 * y * x * y^-1 * z^3 * y^-1 * z ] T31.10 : Triangle type {2,4,28} Group order 280 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^6 * y * z^-1 * x * y^-1 * z^-5 * x ] T31.11 : Triangle type {2,4,64} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-64 ] T31.12 : Triangle type {2,4,64} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-17 * x * z^6 * y * z^-8 ] T31.13 : Triangle type {2,4,124} Group order 248 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-55 * x * y^-1 * z^-6 ] T31.14 : Triangle type {2,5,20} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^-5, z * y * z^-1 * x * y^-1 * z^-2 * x, (z * y^-1 * z)^3 ] T31.15 : Triangle type {2,6,6} Group order 360 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^6, z^6, x * y^-1 * z * y^-2 * z^-2 * y * z^-1 ] T31.16 : Triangle type {2,6,33} Group order 198 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^19 * y * x * y^-1 * z^-8 * x * z^4 ] T31.17 : Triangle type {2,6,93} Group order 186 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^15 * y * z^-1 * x * z^4 * y * z^-1 * x * y * z^-6 * x * z ] T31.18 : Triangle type {2,15,30} Group order 150 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-5 * z^-1 * y^4, y^-1 * z^3 * y^-3 * z * y^-7 ] T31.19 : Triangle type {2,16,16} Group order 160 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, y^-1 * z^5 * y^-7 * z * y^-2 ] T31.20 : Triangle type {2,16,16} Group order 160 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z^-1 * y * z^-1 * y^2 * z^-2 * y ] T31.21 : Triangle type {2,18,36} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z^2 * y^-1 * z^-3, z * y^-4 * z^2 * y^-1 * z ] T31.22 : Triangle type {2,24,24} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y * z^-3 * y^4 * z^-3 * y ] T31.23 : Triangle type {2,24,24} Group order 144 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y * x * z * y^3 * z^-2 * x * z ] T31.24 : Triangle type {2,24,24} Group order 144 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T31.25 : Triangle type {2,24,24} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-3 * z^-1 * y^2, y^-1 * z^7 * y^-1 * z^5 * y^-7 * z * y^-1 * z ] T31.26 : Triangle type {2,28,28} Group order 140 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^-2 * z^-1 * y * z^-1, y^-4 * z * y^-6 * z * y^-1 * z ] T31.27 : Triangle type {2,63,126} Group order 126 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^49 * y^-12 * z ] T31.28 : Triangle type {2,64,64} Group order 128 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-8 * y^11 * z^-1 * y^10 * z^-1 ] T31.29 : Triangle type {2,64,64} Group order 128 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^50 * y^-13 ] T31.30 : Triangle type {2,124,124} Group order 124 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^48 * y^-12 * z ] T31.31 : Triangle type {3,3,15} Group order 225 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-3 * x^-1 * z^4 * y^-1 * z^-2 ] T31.32 : Triangle type {3,4,4} Group order 360 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^4, z^4, (x * y^-1 * z^-1 * y)^2, (x * z * y^-1 * z^-1)^2 ] T31.33 : Triangle type {3,6,7} Group order 168 Action chiral Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^6, (z^-1 * y)^3, y^-1 * z^-1 * y * x^-1 * z * y * x^-1 ] T31.34 : Triangle type {3,6,7} Group order 168 Action chiral Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * z * y, z^3 * y^-1 * x^-1 * z^3 ] T31.35 : Triangle type {3,6,7} Group order 168 Action chiral Defining relators: [ x^3, x * y * z, y * x^-1 * y^-1 * x * z^2, z^3 * y^-1 * x^-1 * z^3 ] T31.36 : Triangle type {3,6,7} Group order 168 Action chiral Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^6, z * y^2 * x * y^-1 * z ] T31.37 : Triangle type {3,6,10} Group order 150 Action reflexible [m] Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^6, z * y^2 * x^-1 * z^3 ] T31.38 : Triangle type {3,6,12} Group order 144 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^-3 * x^-1 * z^2 * y^-1 ] T31.39 : Triangle type {3,6,12} Group order 144 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y^6, z^-1 * y^2 * x^-1 * y^3 ] T31.40 : Triangle type {3,6,42} Group order 126 Action chiral Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^6, z^-2 * y * x^-1 * y * z^-2 ] T31.41 : Triangle type {3,15,35} Group order 105 Action chiral Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, z^2 * y^-1 * x * z * y^-1 ] T31.42 : Triangle type {3,32,96} Group order 96 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-23 * z * y^-6 * z^2 ] T31.43 : Triangle type {3,33,33} Group order 99 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-24 * z * y^-6 * z^2 ] T31.44 : Triangle type {3,93,93} Group order 93 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-22 * z * y^-7 * z ] T31.45 : Triangle type {4,4,7} Group order 168 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z^2, z^2 * y * x * z^-1 * x^-1 ] T31.46 : Triangle type {4,4,8} Group order 160 Action chiral Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, z * y * x^-1 * z * y * x^-1 * z * y^-1 * z * y^-1 ] T31.47 : Triangle type {4,4,8} Group order 160 Action chiral Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, z * y * x^-1 * z * y * x * z * y^-1 * z * y^-1 ] T31.48 : Triangle type {4,4,8} Group order 160 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z^8 ] T31.49 : Triangle type {4,4,8} Group order 160 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, y * x^-1 * y * x^-1 * y * x * z ] T31.50 : Triangle type {4,4,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y, z^2 * y * x^-1 * z^3 ] T31.51 : Triangle type {4,4,12} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^-3 * x^-1 * z^2 * y^-1 ] T31.52 : Triangle type {4,4,12} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^3 * x^-1 * z^2 * y^-1 ] T31.53 : Triangle type {4,4,14} Group order 140 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, x^-1 * y * x^-2 * y^-1 * z^-1 * y, y^-1 * z^-1 * x^-1 * y * x^-1 * z^4 ] T31.54 : Triangle type {4,4,32} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^10 * y^-1 * z^-1 * x * z^4 ] T31.55 : Triangle type {4,4,32} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^-6 * x^-1 * y^-1 * z^-5 * x * z * y * z^-2 ] T31.56 : Triangle type {4,4,32} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-21 * x * y * z^-10 ] T31.57 : Triangle type {4,4,32} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^10 * y^-1 * z^-1 * x^-1 * z^4 ] T31.58 : Triangle type {4,4,62} Group order 124 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^21 * y * x^-1 * z^9 ] T31.59 : Triangle type {4,6,6} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y^6, z^6, y * x^-1 * y * x^-1 * y^-1 * x * z ] T31.60 : Triangle type {4,6,6} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y^6, (x * z^-2)^2, z^6 ] T31.61 : Triangle type {4,6,6} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^6, x^-1 * z^2 * y * z^-1 * x * z^2 * y * z^-1 ] T31.62 : Triangle type {4,6,12} Group order 120 Action chiral Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, x^-1 * y * z^-1 * x^-1 * z * x^-1 * z ] T31.63 : Triangle type {4,9,12} Group order 108 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * y * x * y^-1 * z^-1 ] T31.64 : Triangle type {4,9,12} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * y * z^-2, y^-9 ] T31.65 : Triangle type {4,10,20} Group order 100 Action chiral Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^2 * y^-1 * x * z * y^-1 ] T31.66 : Triangle type {4,10,20} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^3 * x * z^-1 * y ] T31.67 : Triangle type {4,12,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-2 * x^-1 * z * y^-1, (y^-3 * z * y^-2)^2 ] T31.68 : Triangle type {4,12,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, y^-3 * z^2 * y^-1 * z * y^-2 * z * y^-2 ] T31.69 : Triangle type {4,12,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^2 * x^-1 * y * z^-2 ] T31.70 : Triangle type {4,12,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T31.71 : Triangle type {4,12,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * y^2 * z^-2 ] T31.72 : Triangle type {4,12,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^2 * z^-2 ] T31.73 : Triangle type {4,22,44} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^2 * z^-1 * y^2 * z^-1 * y * z^-3 * y^5 * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T31.74 : Triangle type {4,42,84} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, z^2 * y^-1 * z * y^-2 * z * y^-1 * z * y^-1 * z * y^-5 * z^3 * y^-1 * z ] T31.75 : Triangle type {5,5,10} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, x^-5, z * y * x^-1 * y^-1 * x, (z^-1 * x)^3 ] T31.76 : Triangle type {6,8,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, x^6, y^8 ] T31.77 : Triangle type {6,8,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-2 * x^2 * z^-2 ] T31.78 : Triangle type {6,10,15} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^-3 * x^-1 * z^2 ] T31.79 : Triangle type {6,12,28} Group order 84 Action chiral Defining relators: [ x * y * z, z^-1 * y * x^-1 * z * y, y^-1 * z * x^-1 * z^2 ] T31.80 : Triangle type {6,26,39} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^-2 * z * y^-1 * z^5 * y^-1 * z^3 ] T31.81 : Triangle type {8,10,40} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z^5 * y^-1 * z^3 ] T31.82 : Triangle type {8,10,40} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, (y^-1 * z^4)^2 ] T31.83 : Triangle type {8,16,16} Group order 80 Action chiral Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * y * x^-1 * y^-1 * z, y^-2 * x^2 * y^-2 ] T31.84 : Triangle type {8,16,16} Group order 80 Action chiral Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x * y^-2 * x * y^-1 * z^-1 ] T31.85 : Triangle type {8,16,16} Group order 80 Action chiral Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-1 * z^-1, x^8 ] T31.86 : Triangle type {8,36,72} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, z^5 * x^-1 * z^4 ] T31.87 : Triangle type {8,36,72} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z^4 * y^-2 * z^2 ] T31.88 : Triangle type {9,24,72} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-9, z^-3 * y^2 * z^-3 ] T31.89 : Triangle type {9,24,72} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-9 ] T31.90 : Triangle type {10,35,70} Group order 70 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * y^-1 * z^3, x^-10 ] T31.91 : Triangle type {10,35,70} Group order 70 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^4, z^-4 * x * z^-3 ] T31.92 : Triangle type {10,35,70} Group order 70 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * y^-3 * z^3, x^-10 ] T31.93 : Triangle type {12,18,36} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^-2 * y * x^-8 * z * x^-1 ] T31.94 : Triangle type {12,18,36} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-2 * z^3, y * x^-5 * y^3 * z^-1 * y ] T31.95 : Triangle type {12,24,24} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^2 * y^-3 * x^3 * y^-3 * x^4 ] T31.96 : Triangle type {12,24,24} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^2 * z^-1, x^2 * z^-1 * x^7 * z^-1 * x^2 ] T31.97 : Triangle type {12,24,24} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, (z^-1 * y)^3 ] T31.98 : Triangle type {12,24,24} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y^2 * x^-3 * y^4, z^2 * x^-3 * z^4 ] T31.99 : Triangle type {12,24,24} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^-4 * y * x^-1 * y ] T31.100 : Triangle type {12,24,24} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y * z^-1 * y ] T31.101 : Triangle type {15,15,15} Group order 75 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^4 * x^-5 * z, y^-1 * z^5 * y^-4 ] T31.102 : Triangle type {18,18,18} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y * x * y^-1, y^-1 * x^3 * y^-2 ] T31.103 : Triangle type {22,33,66} Group order 66 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, x^-1 * y * x^-1 * y^4 * x^-2 * y^4 ] T31.104 : Triangle type {22,33,66} Group order 66 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^3, x^-7 * z^3 ] T31.105 : Triangle type {22,33,66} Group order 66 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-2 * x * y^-4 * x^2 * y^-4 * x * y^-1 * x * y^-1 * x ] T31.106 : Triangle type {22,33,66} Group order 66 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x * z^-3 * x^8 ] T31.107 : Triangle type {22,33,66} Group order 66 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^7 * z^-2 ] T31.108 : Triangle type {22,33,66} Group order 66 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-7 * x * z^-4 * x * z^-1 ] T31.109 : Triangle type {22,33,66} Group order 66 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * x^-6, y^5 * z^-4 ] T31.110 : Triangle type {22,33,66} Group order 66 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^17 * y^-1 * x * y^-1 * x * y^-1 * x ] T31.111 : Triangle type {22,33,66} Group order 66 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^-1 * y * z^-3 * x^2 * z^-4 ] T31.112 : Triangle type {32,64,64} Group order 64 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-32, y * z^-1 ] T31.113 : Triangle type {32,64,64} Group order 64 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-14 * y^2 * x^-1 ] T31.114 : Triangle type {32,64,64} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-7 * z^2 ] T31.115 : Triangle type {32,64,64} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^3 * z^-2 * y^6 * z^-1 * y^2 ] T31.116 : Triangle type {32,64,64} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, x^-1 * z^2 * x^-5 * z^2 ] T31.117 : Triangle type {32,64,64} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, z^6 * x^-1 * z^4 ] T31.118 : Triangle type {32,64,64} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, y * x^-1 * y, z^17 * x^-2 * z^3 ] T31.119 : Triangle type {32,64,64} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-2 * z^5 * x^2 * y^-3 ] T31.120 : Triangle type {32,64,64} Group order 64 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^-1 * y * x^-8 * y ] T31.121 : Triangle type {63,63,63} Group order 63 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^26 * x^-1 * y^5, x * z^-1 ] T31.122 : Triangle type {63,63,63} Group order 63 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, x^-2 * z * x^-1 * z^3 * x^-4 * z^3 ] T31.123 : Triangle type {63,63,63} Group order 63 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * x^3 * y^-2, z^6 * x^-1 * z^4 ] Genus 32 T32.1 : Triangle type {2,4,66} Group order 264 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-66 ] T32.2 : Triangle type {2,4,128} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-57 * x * y^-1 * z^-6 ] T32.3 : Triangle type {2,5,10} Group order 310 Action chiral Defining relators: [ x^2, x * y * z, y^-5, z * y * z^-2 * y^2 * z^-2 * x * y^-1, x * y^-1 * z^2 * y^2 * z^-1 * x * y^-1 * z^-1 ] T32.4 : Triangle type {2,5,10} Group order 310 Action chiral Defining relators: [ x^2, x * y * z, y^-5, z^2 * y * x * y^-1 * z^-2 * x ] T32.5 : Triangle type {2,6,6} Group order 372 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, z * y * x * z * y * x * z * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x ] T32.6 : Triangle type {2,6,34} Group order 204 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-19 * x * z^5 * y^-1 * z^-9 ] T32.7 : Triangle type {2,6,96} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^18 * y * x * z^7 * y^-1 * z^-3 * x * z^2 ] T32.8 : Triangle type {2,8,44} Group order 176 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-3 * x * z^3 * y * x * y^-1 * z^-14 ] T32.9 : Triangle type {2,10,18} Group order 180 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^-2 * x * z^9 * y^-1 * z^-6 ] T32.10 : Triangle type {2,10,80} Group order 160 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^7 * y * z^-2 * x * z^6 ] T32.11 : Triangle type {2,16,20} Group order 160 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, x * z^3 * y * x * z * y^3 * x * y^-1 * z^-3 ] T32.12 : Triangle type {2,18,72} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^-5 * z^4 * y^-4 * z^4 * y^-1 ] T32.13 : Triangle type {2,34,68} Group order 136 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-10 * y^21 * z^-2 ] T32.14 : Triangle type {2,65,130} Group order 130 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^51 * y^-12 * z ] T32.15 : Triangle type {2,66,66} Group order 132 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^52 * y^-13 ] T32.16 : Triangle type {2,128,128} Group order 128 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^50 * y^-12 * z ] T32.17 : Triangle type {3,6,6} Group order 186 Action chiral Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, x * z * y * z^-1 * x^-1 * y^-1 * x * z * y * z^-1 * y ] T32.18 : Triangle type {3,6,6} Group order 186 Action chiral Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y * z^-1 * y^2 * z^-2 * y * x * y^2 * z^-1 * y * z^-1 ] T32.19 : Triangle type {3,10,20} Group order 120 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^10 ] T32.20 : Triangle type {3,34,34} Group order 102 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^21 * y^-3 * z * y^-7 * z ] T32.21 : Triangle type {3,96,96} Group order 96 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-23 * z * y^-8 ] T32.22 : Triangle type {4,4,33} Group order 132 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-21 * x * y * z^-11 ] T32.23 : Triangle type {4,4,64} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-21 * x * y^-1 * z^-10 ] T32.24 : Triangle type {4,8,14} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, y * x^-1 * z^2 * y * x * z^4 * y * z^-1 * x^-1 * z^4 ] T32.25 : Triangle type {4,12,48} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^3 * y * x^-1 * z^4 ] T32.26 : Triangle type {4,44,44} Group order 88 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, z * y^-9 * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-2 * z * y^-1 ] T32.27 : Triangle type {5,5,5} Group order 155 Action chiral Defining relators: [ x * y * z, x^-5, x * y^-2 * x * z * y, y^-5 ] T32.28 : Triangle type {5,5,5} Group order 155 Action chiral Defining relators: [ x * y * z, x^-5, y^-1 * z^-1 * x^-1 * z * x^-1 ] T32.29 : Triangle type {5,17,85} Group order 85 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, z^5 * y^-1 * z^9 * y^-1 * z ] T32.30 : Triangle type {5,18,18} Group order 90 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^-5, y^-6 * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-4 ] T32.31 : Triangle type {5,80,80} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^2 * z^-9 * y * z^-1 * y * z^-2 ] T32.32 : Triangle type {5,80,80} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-5, z^-1 * y * z^-9 * y * z^-1 * y * z^-2 ] T32.33 : Triangle type {6,6,17} Group order 102 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-6 * x^-1 * z^5 * y^-1 * z^-5 ] T32.34 : Triangle type {6,6,48} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^-1 * x * z^3 * y * x * z^3 * y^-1 * z^-7 ] T32.35 : Triangle type {6,14,42} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^5 * x^-1 * z^-5 * y * z^-1 * y * z^-1 ] T32.36 : Triangle type {6,39,78} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^-2 * z * y^-1 * z^5 * y^-2 * z^2 ] T32.37 : Triangle type {8,8,22} Group order 88 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^4 * y^-1 * x * y^-1 * x * z^5 ] T32.38 : Triangle type {8,20,20} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^8, y^3 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T32.39 : Triangle type {9,10,10} Group order 90 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^9, (y * z^-1 * y * z^-1 * y)^2 ] T32.40 : Triangle type {9,72,72} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-9, z^-4 * y * z^-3 ] T32.41 : Triangle type {9,72,72} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-9 ] T32.42 : Triangle type {10,10,40} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-2 * x^2 * y^-2, z * y * z^-2 * x^-1 * z^4 ] T32.43 : Triangle type {10,10,40} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-2)^2, z^2 * y * z^-1 * x^-1 * z^4 ] T32.44 : Triangle type {10,16,16} Group order 80 Action reflexible [n] Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, z * x^-2 * y * x^-1, z^-1 * y^2 * z^-2 * y^3 ] T32.45 : Triangle type {10,16,16} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, z^-1 * y * z^-1 * y * z^-1 * x^-1 * y * z^-1 * y ] T32.46 : Triangle type {12,36,36} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * y * z^-2, x^-5 * z * y ] T32.47 : Triangle type {14,35,70} Group order 70 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, x^-1 * z^3 * x^-4 * z^2 ] T32.48 : Triangle type {14,35,70} Group order 70 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^-14 ] T32.49 : Triangle type {14,35,70} Group order 70 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-5 * z * x^-7 * y * x^-1 ] T32.50 : Triangle type {14,35,70} Group order 70 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * x^-3 * z, y^-2 * z^3 * y^-1 * x * y^-4 ] T32.51 : Triangle type {14,35,70} Group order 70 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x * y^-5 * x^7 ] T32.52 : Triangle type {17,68,68} Group order 68 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-4 * y * z^-3, x^-5 * y^4 ] T32.53 : Triangle type {17,68,68} Group order 68 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, x * z^-1 * x * z^-11 ] T32.54 : Triangle type {17,68,68} Group order 68 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-1 * y^4 * x^-6 ] T32.55 : Triangle type {17,68,68} Group order 68 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, x^-1 * y * x^-1 * y^4 * x^-3 * y^3 ] T32.56 : Triangle type {17,68,68} Group order 68 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^4 * x^-1 * y^4 ] T32.57 : Triangle type {17,68,68} Group order 68 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^2 * z^-1 * x * z^-1 * x^10 * z^-1 * x * z^-1 ] T32.58 : Triangle type {17,68,68} Group order 68 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, x^-1 * y^4 * x^-2 * y^4 ] T32.59 : Triangle type {17,68,68} Group order 68 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-8 * y * x^-7 * z * x^-1 ] T32.60 : Triangle type {18,18,36} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^-2 * z * x^-5 * z * x^-1 ] T32.61 : Triangle type {18,18,36} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-2 * x^-1 * z * y^-1, y * x * z^-3 * y * z^-1 * y * z^-3 ] T32.62 : Triangle type {33,66,66} Group order 66 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-8 * x * y^-8 ] T32.63 : Triangle type {33,66,66} Group order 66 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^7 * z^-1 ] T32.64 : Triangle type {33,66,66} Group order 66 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y * x^-1 * y * x^-1 * y^4 * x^-2 * y^4 ] T32.65 : Triangle type {33,66,66} Group order 66 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^-4 * y^2 * z^-4 ] T32.66 : Triangle type {33,66,66} Group order 66 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-33, y * z^-1 ] T32.67 : Triangle type {34,34,34} Group order 68 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^-4 * x * z^-6 * x^2 * y * z^-5 ] T32.68 : Triangle type {34,34,34} Group order 68 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, x^2 * z^-10 ] T32.69 : Triangle type {34,34,34} Group order 68 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^3, x^-6 * z^4 ] T32.70 : Triangle type {65,65,65} Group order 65 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^27 * x^-1 * y^5, x * z^-1 ] T32.71 : Triangle type {65,65,65} Group order 65 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, x^-1 * z^2 * x^-4 * z^3 ] T32.72 : Triangle type {65,65,65} Group order 65 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * y^-3 * z^3, x^-1 * z^3 * x^-7 ] T32.73 : Triangle type {65,65,65} Group order 65 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^15 * x^-1 * y^6 ] T32.74 : Triangle type {65,65,65} Group order 65 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^7 * z^-1, y^-1 * z^4 * y^-1 * z^3 ] T32.75 : Triangle type {65,65,65} Group order 65 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^3 * y^-1, y^4 * z^-4 * y * z^-5 * y * z^-1 * y * z^-1 ] Genus 33 T33.1 : Triangle type {2,3,8} Group order 1536 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^8, x * z^3 * y * x * z * y * x * z * y * x * z^2 * y^2 * z^-2 * x * y^-1 * z^-2 ] T33.2 : Triangle type {2,3,12} Group order 768 Action chiral Defining relators: [ x^2, y^3, x * y * z, z^12, y * z^-1 * x * z^3 * y * x * z * y^-2 * z^-2 * x * z^2 ] T33.3 : Triangle type {2,3,12} Group order 768 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z * y * z^-3 * x * y^-1 * z^-4 * x, x * z * y * x * z * y * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T33.4 : Triangle type {2,3,12} Group order 768 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^12, z^-2 * x * z^3 * y * z^-2 * x * z^2 * y^-1 * z^-1 ] T33.5 : Triangle type {2,3,12} Group order 768 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^12, x * z^2 * y * z^-1 * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 ] T33.6 : Triangle type {2,4,6} Group order 768 Action chiral Defining relators: [ x^2, x * y * z, y^4, z^6, z * y * z^-2 * y * x * y^-1 * z^2 * y^-1 * z^-1 * x ] T33.7 : Triangle type {2,4,6} Group order 768 Action chiral Defining relators: [ x^2, x * y * z, y^4, z^6, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z^2 * y * z^-1 * y * z^-1 * y * x * y^-1 * z * y^-1 * z^2 * y^-1 * z^-1 * x ] T33.8 : Triangle type {2,4,6} Group order 768 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^6, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 * x * z * y^-1 * z^-2 ] T33.9 : Triangle type {2,4,6} Group order 768 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^6, (y * z^-2)^4, z^-2 * y * x * z * y^-2 * z^-1 * x * y^-1 * z * y^-1 * z^-1 * y ] T33.10 : Triangle type {2,4,6} Group order 768 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^6, (y * z^-1)^4, x * z * y * z^-1 * x * z * y * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-2 ] T33.11 : Triangle type {2,4,6} Group order 768 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^6, x * z * y^-1 * z * y * z^-1 * y * z^-1 * x * y^-1 * z * y^-1 * z^-1 * y ] T33.12 : Triangle type {2,4,8} Group order 512 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, y * z^-1 * y * z^-1 * y * z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T33.13 : Triangle type {2,4,8} Group order 512 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * z^-2 * x * y^-1 * z^-3 * x, y * x * z * y^-1 * z * y^-2 * z^-1 * x * y^-1 * z * y^-1 * z^-2 ] T33.14 : Triangle type {2,4,8} Group order 512 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * z^-2 * x * y^-1 * z^-3 * x, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T33.15 : Triangle type {2,4,8} Group order 512 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^8, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T33.16 : Triangle type {2,4,8} Group order 512 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * z^-1 * x * z * y^2 * z^-1 * x * z^2 * y^-1, z^2 * y * z^-1 * y * x * y^-1 * z^-2 * x * y^-1 * z ] T33.17 : Triangle type {2,4,8} Group order 512 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^8, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T33.18 : Triangle type {2,4,8} Group order 512 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^8, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1 ] T33.19 : Triangle type {2,4,8} Group order 512 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, x * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^-2 ] T33.20 : Triangle type {2,4,12} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z * y^-1 * z * y^-1 * z * y^-1 * z^-4 * x ] T33.21 : Triangle type {2,4,12} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z * y^-1 * z * y^-1 * z * y^-1 * z^-4 * x, z^2 * y^-1 * z * y * z^-1 * y^2 * z^-1 * x * y^-1 * z^2 ] T33.22 : Triangle type {2,4,12} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (y^-1 * z^2)^4 ] T33.23 : Triangle type {2,4,12} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^2 * y^-1 * z * y * z^-1 * y^2 * z^-1 * x * y^-1 * z^2, z^-4 * x * z^5 * y^-1 * z^-2 ] T33.24 : Triangle type {2,4,12} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^-2 * y * z^-1 * x * y^-1 * z^-2 * y * z^-2, x * z * y * z^-1 * x * z^6 * y^-1 * z^-2 ] T33.25 : Triangle type {2,4,12} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^-4 * x * z^5 * y^-1 * z^-2 ] T33.26 : Triangle type {2,4,12} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y^-2 * z^-3 * y, z^5 * y * x * z^4 * y^-1 * z^-1 * x ] T33.27 : Triangle type {2,4,12} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, y^-1 * z * y * x * z * y * x * y^-1 * z * y^-1 * z^-1 * x * z, z^-12 ] T33.28 : Triangle type {2,4,20} Group order 320 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-3 * x * z^10 * y^-1 * x * y^-1 * z^-5 ] T33.29 : Triangle type {2,4,36} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-20 * x * z^8 * y * x * z * y^-1 * z^-5 ] T33.30 : Triangle type {2,4,36} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^2 * y^-2 * z^-3 * y, z^-3 * x * z * y * x * z^6 * y^-1 * z^-1 * x * y^-1 * z^-4 ] T33.31 : Triangle type {2,4,36} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-22 * x * z^7 * y^-1 * z^-6 ] T33.32 : Triangle type {2,4,68} Group order 272 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-60 * x * y * z^-7 ] T33.33 : Triangle type {2,4,132} Group order 264 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-59 * x * y^-1 * z^-6 ] T33.34 : Triangle type {2,5,10} Group order 320 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^-5, z * y^2 * z^-1 * y^2 * z^-2 * x * z, z * y * z^-2 * y^2 * z^-1 * y * x * z ] T33.35 : Triangle type {2,6,6} Group order 384 Action chiral Defining relators: [ x^2, x * y * z, y^6, z^6, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, z * y^-2 * z * y^3 * z^-1 * x * y^-1 * z^-1 * x ] T33.36 : Triangle type {2,6,6} Group order 384 Action chiral Defining relators: [ x^2, x * y * z, y^6, z^6, z^-1 * y * x * y^-2 * z * y^-1 * z^-2 ] T33.37 : Triangle type {2,6,6} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z^6, x * z^2 * y^-2 * z^2 * y^-1 * z^-1, (y * z^-1 * y)^4 ] T33.38 : Triangle type {2,6,6} Group order 384 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, z^6, (y * z^-1 * y)^4 ] T33.39 : Triangle type {2,6,6} Group order 384 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^6, z^6, z^-1 * x * y^-1 * z * y^2 * x * z * y^-1 * z^-1, z^-1 * x * z^2 * y^2 * x * y^-2 * z^-1 ] T33.40 : Triangle type {2,6,6} Group order 384 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T33.41 : Triangle type {2,6,6} Group order 384 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^6, (z^-1 * y)^3, z^6, (z^-1 * y^2 * z^-1)^3 ] T33.42 : Triangle type {2,6,7} Group order 336 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2 * y)^2, z^-3 * x * y * z^-3 ] T33.43 : Triangle type {2,6,7} Group order 336 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^-3 * x * y * z^-3, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T33.44 : Triangle type {2,8,8} Group order 256 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, z^8 ] T33.45 : Triangle type {2,8,8} Group order 256 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^8, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, z^8 ] T33.46 : Triangle type {2,8,8} Group order 256 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, z^8 ] T33.47 : Triangle type {2,8,8} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^8, (y * z^-3)^2, z^8, y^-1 * z * y^-3 * z^-1 * y * x * z ] T33.48 : Triangle type {2,8,8} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, z^8 ] T33.49 : Triangle type {2,8,8} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^8, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, z^-2 * x * y^-2 * z^-3 * y ] T33.50 : Triangle type {2,8,8} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^8, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y ] T33.51 : Triangle type {2,8,8} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, z^8, z^-2 * x * y^-2 * z^-3 * y ] T33.52 : Triangle type {2,8,8} Group order 256 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^8, y * x * y^-1 * z * y^2 * z^-1 * x * z^2 ] T33.53 : Triangle type {2,8,8} Group order 256 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z * y * x * z * y * x * y^-1 * z^2 * y^-2 * z^-1 * x ] T33.54 : Triangle type {2,8,8} Group order 256 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T33.55 : Triangle type {2,8,8} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, (y * z^-2 * y)^2, (y * z^-3)^2 ] T33.56 : Triangle type {2,8,8} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^8, (y * z^-3)^2, z^8, x * z * y^-3 * z^-1 * y^2 * z^-1 ] T33.57 : Triangle type {2,8,8} Group order 256 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^8, (y * z^-1)^4, z^8, x * z * y^-3 * z^-1 * y^2 * z^-1, y^2 * x * y^-2 * z * y^-1 * z^-2 ] T33.58 : Triangle type {2,8,8} Group order 256 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, (y * z^-2 * y)^2, (y * z^-1)^4 ] T33.59 : Triangle type {2,8,24} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z^2 * y^-1 * z^-3, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4 ] T33.60 : Triangle type {2,8,24} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, z^2 * y^-3 * z^-2 * x * z ] T33.61 : Triangle type {2,8,24} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, z^-1 * x * y^-2 * z^-2 * y, x * z^6 * y * x * z^2 * y^-1 * z^-2 ] T33.62 : Triangle type {2,8,24} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, x * z^4 * y * z^-1 * x * y^-1 * z^-5 ] T33.63 : Triangle type {2,8,24} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-5 * x * z^4 * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-7 ] T33.64 : Triangle type {2,8,24} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z * y * z^-2 * x * z^3 * y * z^-2 * x * z^2 * y * z^-2 * x * y * z^-6 * x * z^2 ] T33.65 : Triangle type {2,8,24} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-1 * x * z * y * z^-2 * x * y^-1 * x * z * y^-1 * z^-4 ] T33.66 : Triangle type {2,8,24} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-1 * x * z * y * z^-2 * x * y^-1 * z^-6 ] T33.67 : Triangle type {2,8,24} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, (y * z^-1 * y^2)^2, z^2 * y * z^-2 * x * z * y^-1 * z^-5 * x ] T33.68 : Triangle type {2,8,24} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^6 * y * z^-5 * x ] T33.69 : Triangle type {2,8,88} Group order 176 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, x * z^6 * y^-1 * z^-15 ] T33.70 : Triangle type {2,8,88} Group order 176 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-1 * x * z^5 * y * z^-15 ] T33.71 : Triangle type {2,12,12} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-4 * z^-1 * y * z^-1 * y, z * y^-4 * z * y^-1 * z^-1 * x ] T33.72 : Triangle type {2,12,12} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, z * y^-4 * z * y^-1 * z^-1 * x ] T33.73 : Triangle type {2,12,12} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, (z^-1 * y)^3, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1 ] T33.74 : Triangle type {2,12,12} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-1 * y * z^-1 * y, y^12 ] T33.75 : Triangle type {2,12,12} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z^2 * y^-1 * z^-3, y^12 ] T33.76 : Triangle type {2,12,12} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-2 * y * z^-1, x * y^-1 * z * y^-2 * z^-4, y^12 ] T33.77 : Triangle type {2,12,12} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-1 * y * z^-1, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, y^-12 ] T33.78 : Triangle type {2,12,12} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, x * z^2 * y^-2 * z^-3 * y ] T33.79 : Triangle type {2,12,12} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y * z^-1 * y * z^-1 * y^5 * z^-1 * y * z^-1 ] T33.80 : Triangle type {2,12,28} Group order 168 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^-1 * x * z * y * x * z^5 * y * x * y^-1 * z^-4 ] T33.81 : Triangle type {2,14,77} Group order 154 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y * z^-3 * x * y^-1 * z^-5 ] T33.82 : Triangle type {2,20,20} Group order 160 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^2 * z^-1 * y^6 * z^-1 * y^7 * z^-2 * y ] T33.83 : Triangle type {2,36,36} Group order 144 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, z^-1 * y * z^-2 * y^10 * z^-4 ] T33.84 : Triangle type {2,36,36} Group order 144 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-32 * z * y^-1 ] T33.85 : Triangle type {2,36,36} Group order 144 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-12 * y^24 ] T33.86 : Triangle type {2,46,69} Group order 138 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, z * y^-9 * z^2 * y^-7 * z^4 ] T33.87 : Triangle type {2,67,134} Group order 134 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^53 * y^-12 * z ] T33.88 : Triangle type {2,68,68} Group order 136 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^54 * y^-13 ] T33.89 : Triangle type {2,132,132} Group order 132 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^52 * y^-12 * z ] T33.90 : Triangle type {3,3,4} Group order 768 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^4, x * z * x^-1 * z * x^-1 * y^-1 * z^-1 * x * z * y * x^-1 * y^-1 * z^-1, (x * z * y)^4 ] T33.91 : Triangle type {3,3,6} Group order 384 Action chiral Defining relators: [ x^3, x * y * z, y^3, z^6, y * z^-1 * x^-1 * y * x^-1 * z * y * x * z ] T33.92 : Triangle type {3,3,6} Group order 384 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, y^-1 * x * y^-1 * x * z * y * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1 * x^-1 * z * y * x ] T33.93 : Triangle type {3,3,6} Group order 384 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (x * z * y^-1 * z^-1)^2 ] T33.94 : Triangle type {3,3,6} Group order 384 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^6, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x ] T33.95 : Triangle type {3,3,67} Group order 201 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^3 * y * z^-1 * x^-2 * z^4 ] T33.96 : Triangle type {3,4,4} Group order 384 Action chiral Defining relators: [ x^3, x * y * z, y^4, z^4, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y^-1 ] T33.97 : Triangle type {3,4,4} Group order 384 Action chiral Defining relators: [ x^3, x * y * z, y^4, z^4, y^-2 * z^-1 * x^-1 * z * y^-1 * z, (x * z * y^-1 * z^-1 * y)^2 ] T33.98 : Triangle type {3,4,4} Group order 384 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^4, z^4, (z^-1 * y)^3, (z^-1 * x^-1 * y^-1)^3 ] T33.99 : Triangle type {3,4,4} Group order 384 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y * x * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z, z^-1 * y * x^-1 * y^-2 * x * y^-1 * z * y^2 ] T33.100 : Triangle type {3,4,4} Group order 384 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^4, z^4, z^-1 * y * x^-1 * y * x^-1 * y^2 * x * y^-1, y * z^-1 * x^-1 * y * x^-1 * y * z^-1 * x^-1 * z ] T33.101 : Triangle type {3,4,4} Group order 384 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^4, z^4, (x^-1 * z * y)^2, (x * z * y^-1 * z^-1 * y)^2 ] T33.102 : Triangle type {3,4,12} Group order 192 Action chiral Defining relators: [ x^3, x * y * z, y^4, z * y^-1 * z^-1 * x^-1 * z * y^-1 * z ] T33.103 : Triangle type {3,4,12} Group order 192 Action chiral Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, y * z^-1 * x * y^-1 * x * z^3 ] T33.104 : Triangle type {3,4,12} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-3 * x^-1 * z^2 * y^-1, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y ] T33.105 : Triangle type {3,4,12} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * x^-1 * y^-1 * x * z * y ] T33.106 : Triangle type {3,4,12} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y * x * z ] T33.107 : Triangle type {3,4,12} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y^-1 * x * z^2, z^-2 * x^-1 * y^-1 * x * y^-1 * z^-1 * y ] T33.108 : Triangle type {3,4,12} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y^-1 * x * z^2, (x * z * y)^2 ] T33.109 : Triangle type {3,4,12} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-3 * x^-1 * z^2 * y, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y ] T33.110 : Triangle type {3,4,12} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, (x * z * y)^2, (z^-1 * y)^3 ] T33.111 : Triangle type {3,6,6} Group order 192 Action chiral Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-1 * z^-1, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T33.112 : Triangle type {3,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * y^2 * x^-1 * y^3, y * z^-2 * x^-1 * y * z^-2, y * z^-1 * x^-1 * y^-1 * x * z * y * z^-1 ] T33.113 : Triangle type {3,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^6, (y * z^-1)^4 ] T33.114 : Triangle type {3,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, (y * z^-1)^2, y^6, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T33.115 : Triangle type {3,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^6, z^6, z * y^-1 * z^-1 * x^-1 * y^-2 * z, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1 ] T33.116 : Triangle type {3,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^6, (x * z * y)^2, z^6, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T33.117 : Triangle type {3,7,7} Group order 168 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^-7, (y * z^-1)^4 ] T33.118 : Triangle type {3,7,7} Group order 168 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * y^-1 * z, x^-1 * z * y^-1 * x * z^2, y^-7 ] T33.119 : Triangle type {3,10,30} Group order 120 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^10 ] T33.120 : Triangle type {3,34,102} Group order 102 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-23 * z * y^-1 * z * y^-7 * z ] T33.121 : Triangle type {3,99,99} Group order 99 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-24 * z * y^-7 * z ] T33.122 : Triangle type {4,4,4} Group order 256 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, z^-2 * x^-1 * z * y^-1, x^-1 * y^-1 * z^-1 * y * x * y^-1 * x^2 * y^-1 * z * x^-1 * y^-1 * z ] T33.123 : Triangle type {4,4,4} Group order 256 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, x^-1 * y * x^-1 * y * x^2 * y^-1 * z * y^-1 * z^-1 ] T33.124 : Triangle type {4,4,4} Group order 256 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, (x * y^-1)^4 ] T33.125 : Triangle type {4,4,4} Group order 256 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, z^-2 * x^-1 * z * y^-1, x^-1 * y^-1 * z^-1 * y * x * y^-1 * x^2 * y^-1 * z * x^-1 * y^-1 * z^-1 ] T33.126 : Triangle type {4,4,4} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, x^-1 * y * x^-1 * y * x^-1 * y^2 * z^-1 * y ] T33.127 : Triangle type {4,4,4} Group order 256 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, (x * y^-1)^4 ] T33.128 : Triangle type {4,4,4} Group order 256 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, (x^-1 * z * y)^2, (x * z * y)^2, (x * y^-1)^4 ] T33.129 : Triangle type {4,4,4} Group order 256 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T33.130 : Triangle type {4,4,4} Group order 256 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, y^-1 * z^-1 * y * x * z * x^-1 ] T33.131 : Triangle type {4,4,6} Group order 192 Action chiral Defining relators: [ x * y * z, x^4, y^4, (y^-1 * x)^3, z^6, z^-1 * y * x^-2 * y^-1 * z^-2 ] T33.132 : Triangle type {4,4,6} Group order 192 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^4, y * x^-1 * y^-1 * x * z^-2, (y^-1 * x)^3, z^6 ] T33.133 : Triangle type {4,4,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^6, y * x * z^-1 * x^-1 * z * y^-1 * z^-1, y^-1 * z^-2 * x^-1 * y^-1 * z * x^-1, y * x^-1 * y * x^2 * z^2 * x^-1 ] T33.134 : Triangle type {4,4,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (y^-1 * x)^3, (x * z^-1 * y)^2, z^6, z^-3 * x^-1 * z^2 * y^-1 ] T33.135 : Triangle type {4,4,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (y^-1 * x)^3, z^6, y * x * z^-1 * x^-1 * z * y^-1 * z^-1, y^-1 * z^-2 * x^-1 * y^-1 * z * x^-1 ] T33.136 : Triangle type {4,4,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^6, z^-3 * x^-1 * z^2 * y^-1, y * x^-1 * y * x^2 * z^2 * x^-1 ] T33.137 : Triangle type {4,4,6} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^6, (y * z^-1)^4, z * y * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T33.138 : Triangle type {4,4,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, z^6, y^-1 * z * y * x^-1 * y^-1 * z^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1 ] T33.139 : Triangle type {4,4,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^6, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z * x^-1 * y * x^-1 * y^2 * x ] T33.140 : Triangle type {4,4,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, z^6 ] T33.141 : Triangle type {4,4,6} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (y * z^-2)^2, z^6, y * x^-1 * y * x^2 * z^2 * x^-1 ] T33.142 : Triangle type {4,4,6} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^6, x^-1 * z^2 * y * x * z * y^-1 * z^-1 ] T33.143 : Triangle type {4,4,6} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^6, x^-1 * z^2 * y * x * z^2 * y ] T33.144 : Triangle type {4,4,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1 ] T33.145 : Triangle type {4,4,10} Group order 160 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^-3 * x^-1 * z * y^-1 * z^-1 ] T33.146 : Triangle type {4,4,10} Group order 160 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z^10 ] T33.147 : Triangle type {4,4,18} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^2, z^18 ] T33.148 : Triangle type {4,4,18} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, (x * z^-1 * y)^2, z^3 * y^-1 * z^-1 * x * z^4 ] T33.149 : Triangle type {4,4,18} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-2 * z^2 * x^-1, z^3 * y * z^-1 * x * y * z^-1 * x^-1 * z^2 ] T33.150 : Triangle type {4,4,18} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-13 * x * y * z^-4 ] T33.151 : Triangle type {4,4,34} Group order 136 Action reflexible [n] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^4 * x^-1 * z^2 * y^-1 * z ] T33.152 : Triangle type {4,4,34} Group order 136 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-22 * x * y * z^-11 ] T33.153 : Triangle type {4,4,66} Group order 132 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-21 * x * y^-1 * z^-11 ] T33.154 : Triangle type {4,6,20} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^5 * y^-1 * x * z^4 ] T33.155 : Triangle type {4,8,8} Group order 128 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, z^-1 * y^2 * x * z^-1 * x, x^-1 * z * y * x^-1 * y^-1 * z^-1 ] T33.156 : Triangle type {4,8,8} Group order 128 Action chiral Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, y * x * y^-1 * x * z^-2 ] T33.157 : Triangle type {4,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^8 ] T33.158 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, x^-1 * z * y * x * y^-1 * z^-1 ] T33.159 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y^-1 * x * y^-1 * x * z^2 ] T33.160 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, y^8 ] T33.161 : Triangle type {4,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, z^-2 * y * x^-1 * z * y^2 ] T33.162 : Triangle type {4,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, z^-1 * y^2 * x * z^-1 * x, (x^-1 * z * y)^2 ] T33.163 : Triangle type {4,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, z^-1 * y^2 * x * z^-1 * x, x^-1 * z * y * x * y^-1 * z^-1 ] T33.164 : Triangle type {4,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, y^8 ] T33.165 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, (x^-1 * z * y)^2, (x * z * y)^2 ] T33.166 : Triangle type {4,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^8 ] T33.167 : Triangle type {4,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * z * y * z^-1, z^-2 * y * x^-1 * z * y^-2 ] T33.168 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, (x^-1 * z * y)^2 ] T33.169 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, (x * z^-1 * y)^2 ] T33.170 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, y^8 ] T33.171 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, z^8 ] T33.172 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, z * y^2 * x^-1 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1 ] T33.173 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, z^8 ] T33.174 : Triangle type {4,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, y^8 ] T33.175 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z * y^2 * x^-1 * z * x^-1, (x * z^-1 * y)^2, (y * z^-1 * y)^2 ] T33.176 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, z^-1 * y^2 * x^-1 * z * y * z^-1, y * z^-1 * y * x^-1 * z^2 * y ] T33.177 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z * y^2 * x * z^-1 * x, x * z^-1 * y * x^-1 * y^-1 * z^-1, (y * z^-1 * y)^2 ] T33.178 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, z * y^2 * x * z^-1 * x, y^8 ] T33.179 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, (y * z^-1 * y)^2, y^3 * x^-1 * z^3 ] T33.180 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, z * y * x^-1 * y^-2, (x * z * y^-1)^2, x^-1 * y * x^-2 * z^3 ] T33.181 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y^8, z^8 ] T33.182 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, z^8 ] T33.183 : Triangle type {4,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, z^-2 * y * x^-1 * y^-1 * z^-1 * y ] T33.184 : Triangle type {4,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, (y * z^-1)^4 ] T33.185 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-1)^4 ] T33.186 : Triangle type {4,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, z^-1 * x * y^-1 * x * z * y, z * y^2 * x * z * x^-1, y^8 ] T33.187 : Triangle type {4,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y^8 ] T33.188 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, z * y^2 * x * z * x^-1, y^8 ] T33.189 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * z^2 * y^-1, z^-2 * y * x^-1 * z * y^2 ] T33.190 : Triangle type {4,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, y^3 * x^-1 * z^3, y^8 ] T33.191 : Triangle type {4,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y^-1 * z * y^2 * x^-1 * y^-1 * z * y^-1 * z ] T33.192 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, y * z^-1 * y * x^-1 * z * y^-1 * z, z^8 ] T33.193 : Triangle type {4,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * z^2 * y^-1, y^8 ] T33.194 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, x^-1 * z * y * x * z * y, y^8, (y * z^-1)^4 ] T33.195 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, x^-1 * z * y * x * y^-1 * z^-1, y^8, (y * z^-1 * y^2)^2 ] T33.196 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, x^-1 * z * y * x * z * y, y^8, (y * z^-1 * y^2)^2 ] T33.197 : Triangle type {4,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * z^2 * y^-1, y^8 ] T33.198 : Triangle type {4,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^8, z^8 ] T33.199 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, y^8 ] T33.200 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, z * x^-1 * y^-1 * x * y^-1 * z, y^8 ] T33.201 : Triangle type {4,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * y^-1 * z^-2, z^-2 * y * x^-1 * z * y^-2 ] T33.202 : Triangle type {4,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, z * x^-1 * y^-1 * x * y^-1 * z, z * y^-2 * x * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1 ] T33.203 : Triangle type {4,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, (x^-1 * z * y)^2, (x * z * y)^2 ] T33.204 : Triangle type {4,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, x^-1 * z * y * x * y^-1 * z^-1 ] T33.205 : Triangle type {4,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, z * x^-1 * y^-1 * x * y^-1 * z, z * y^-2 * x * z * x^-1, (x^-1 * z * y)^2 ] T33.206 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, z^-1 * x * y^-1 * x * z * y, z^-1 * y^2 * x * z^-1 * x ] T33.207 : Triangle type {4,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, z^-1 * y^2 * x * z^-1 * x ] T33.208 : Triangle type {4,16,48} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^5 * z^-1 * y * z^-1 ] T33.209 : Triangle type {4,16,48} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-2 * x^-1 * z^3, y^5 * z^-1 * y * z^-1 ] T33.210 : Triangle type {4,23,92} Group order 92 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^7 * z^-1 * y * z^-1 * y^10 * z^-1 * y ] T33.211 : Triangle type {4,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, y^-2 * z * y^-1 * z * y^-4 * z * y^-2 ] T33.212 : Triangle type {4,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * z * y^-1, y^-1 * z^2 * y^-3 * z * y^-1 * z * x * y^-3 ] T33.213 : Triangle type {4,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^3 * z^-2, x^-1 * z * y * x * y^-1 * z^-1 ] T33.214 : Triangle type {4,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * y * z^-2 ] T33.215 : Triangle type {4,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, (y^-3 * z * y^-2)^2 ] T33.216 : Triangle type {4,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y^-5 * z * y^-3 * z * y^-2 ] T33.217 : Triangle type {4,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y^-9 * z^4 * y^-5 * z * y^-1 * z * y^-1 * z^2 ] T33.218 : Triangle type {4,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-9 * z * y^-5 * z * y^-1 * z * y^-5 * z ] T33.219 : Triangle type {4,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-3 * z * y^-5 * z^3 ] T33.220 : Triangle type {4,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-3 * z * y^-3 * x * y^-2 * z * y^-1 * z ] T33.221 : Triangle type {4,88,88} Group order 88 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y^5 * z^-1 * y * z^-3 * y^5 * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T33.222 : Triangle type {4,88,88} Group order 88 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y^2 * z^-1 * y^2 * z^-1 * y * z^-3 * y^5 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T33.223 : Triangle type {5,5,5} Group order 160 Action reflexible [m,n] Defining relators: [ x * y * z, x^-5, (x * y^-2)^2, y^-5, z * y * x^-2 * y * z^-1 * x ] T33.224 : Triangle type {5,6,10} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, (x * y^-1)^2, (y * z^-1)^2, x^-5 ] T33.225 : Triangle type {5,6,10} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, x^-5, y * x * y^-1 * x * y^-1 * z^-1 ] T33.226 : Triangle type {5,6,10} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x^-5, x * z^-1 * x^2 * y^-2, (y^-1 * x)^3 ] T33.227 : Triangle type {6,8,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-1 * z * x^-1 * y^-1 * z, x^6, (x * z * y^-1)^2 ] T33.228 : Triangle type {6,8,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y^-1 * z * x^-1 * y^-1 * z, x^6, z^-1 * x^-1 * y^-1 * x * z * y ] T33.229 : Triangle type {6,8,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, x^6, x^-1 * z * y * x * y^-1 * z^-1 ] T33.230 : Triangle type {6,8,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^8 ] T33.231 : Triangle type {6,12,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y^-2 * x^2 * y^-1 * z ] T33.232 : Triangle type {6,12,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, z^-1 * y^3 * z^-2 ] T33.233 : Triangle type {6,12,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, (y * z^-1)^2, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * y^-1 * z, (x * z * y)^2 ] T33.234 : Triangle type {6,12,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, x^6, y^3 * x^-1 * y^-1 * z * y ] T33.235 : Triangle type {6,12,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-1 * z^-1, y^-1 * z^-1 * x^-1 * z * y^-1, x^6 ] T33.236 : Triangle type {6,12,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^6, x^-1 * z * y * x * y^-1 * z^-1 ] T33.237 : Triangle type {6,28,28} Group order 84 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^6, z^-1 * y * z^-1 * y * z^-1 * x^-1 * z^-1 * y * z^-1 * y^4 * z^-1 * y ] T33.238 : Triangle type {7,12,84} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z * y^-1 * z^5 * y^-3 * z ] T33.239 : Triangle type {7,77,77} Group order 77 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, y^-2 * z^5 * y^-1 * z^3 ] T33.240 : Triangle type {7,77,77} Group order 77 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, y^-2 * z^5 * y^-3 * z ] T33.241 : Triangle type {7,77,77} Group order 77 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-7, y^-2 * z^9 ] T33.242 : Triangle type {8,8,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z * y^-1 * x * z, z^-1 * y^2 * x * z^-1 * x, x^8 ] T33.243 : Triangle type {8,8,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * x^-2 * z^2, (y^-1 * x)^3, y^3 * x * z^2 ] T33.244 : Triangle type {8,8,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * z^-1 * x * z, (y^-1 * x)^3, (x * z^-1 * y)^2 ] T33.245 : Triangle type {8,8,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^3 * z * y, x^-1 * y^-1 * x^2 * z^-2, y^-1 * z^-1 * x^2 * z * y^-1, (x * z^-1 * y)^2 ] T33.246 : Triangle type {8,8,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, y^2 * x^-1 * y^-1 * z, z * y * z^-1 * x^-1 * z^3 ] T33.247 : Triangle type {8,8,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, y^2 * x^-1 * y^-1 * z, z * y * z^-1 * x^-1 * z^3 ] T33.248 : Triangle type {8,8,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, (x * y^-1 * x)^2, z * y * x^-1 * y^-1 * x * z^3 ] T33.249 : Triangle type {8,8,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^-6 * x * y^-1 * x * y * x^-1 * y * z^-3 ] T33.250 : Triangle type {8,8,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, z * y^-1 * z^-1 * x^-1 * z^3, x^8 ] T33.251 : Triangle type {8,8,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, x^-1 * z^2 * y^-1 * z^-1 * x^-1 * z * y^-1 * z^-3 * x^-1 * y^-1 * z^-2 ] T33.252 : Triangle type {8,8,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, y^-1 * z^-1 * x * y^-1 * x * z^3 ] T33.253 : Triangle type {8,8,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, z * y^-1 * x * y^-1 * x * z^3 ] T33.254 : Triangle type {8,8,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, (x * z^-1 * y)^2, y * z^-1 * x^-1 * y^-1 * x * z^3 ] T33.255 : Triangle type {8,8,44} Group order 88 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^2 * y^-1 * z^-3 * x^-1 * y^-1 * x * z^4 ] T33.256 : Triangle type {8,8,44} Group order 88 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, y^-1 * z^-1 * x * z^4 * y * x * z^4 ] T33.257 : Triangle type {8,20,40} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^-1 * z^4 * y^-5 ] T33.258 : Triangle type {8,20,40} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z^5 * x * y^-4 ] T33.259 : Triangle type {10,20,20} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * y^-2, z^-1 * x^4 * z^-3 ] T33.260 : Triangle type {10,20,20} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^10 ] T33.261 : Triangle type {12,12,14} Group order 84 Action reflexible [n] Defining relators: [ x * y * z, y^-1 * z * x^-1 * z^2, y^-1 * x^3 * y^-2, z^-1 * y * x^2 * z * y ] T33.262 : Triangle type {12,12,14} Group order 84 Action reflexible [n] Defining relators: [ x * y * z, z^-2 * x^-1 * y^-1 * z^-1, y^2 * x^2 * z^-2, (y^-1 * x)^3 ] T33.263 : Triangle type {12,12,14} Group order 84 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, y^-1 * x * y^-1 * x * y^-1 * x * z^4 ] T33.264 : Triangle type {12,72,72} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-5 * x^5 * y^-1 ] T33.265 : Triangle type {12,72,72} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x * y^-5 * x^5 * y^-1 * x ] T33.266 : Triangle type {18,24,72} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x * y^-1 * x^4 * y^-1 * x^8 * y^-1 * x * y^-1 * x ] T33.267 : Triangle type {18,24,72} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, (x^-2 * z^4)^2 ] T33.268 : Triangle type {18,36,36} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^18 ] T33.269 : Triangle type {18,36,36} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * x^4 * y^-3, z^4 * x^-2 * z^4 ] T33.270 : Triangle type {23,69,69} Group order 69 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^2 * z^-1 * y^9 ] T33.271 : Triangle type {23,69,69} Group order 69 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, x^-1 * y^3 * x^-6 ] T33.272 : Triangle type {23,69,69} Group order 69 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-1 * x^3 * y^-2 * x^5 * y^-4 * x * y^-1 * x * y^-1 * x ] T33.273 : Triangle type {23,69,69} Group order 69 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, (z^-3 * x * z^-1)^3 ] T33.274 : Triangle type {23,69,69} Group order 69 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^5 * x^-1 * y^4 ] T33.275 : Triangle type {23,69,69} Group order 69 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x * z^-3 * x^8 ] T33.276 : Triangle type {23,69,69} Group order 69 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-13 * z * x^-7 * z^2 * x^-1 ] T33.277 : Triangle type {23,69,69} Group order 69 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-6 * z^3, y^5 * z^-4 ] T33.278 : Triangle type {23,69,69} Group order 69 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^5 * y^-3, z^-4 * y * z^-4 ] T33.279 : Triangle type {23,69,69} Group order 69 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^-5 * y * x^3 * z^-3 ] T33.280 : Triangle type {23,69,69} Group order 69 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-4 * y^3 * x^-6 ] T33.281 : Triangle type {34,68,68} Group order 68 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-34, y * z^-1 ] T33.282 : Triangle type {34,68,68} Group order 68 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, z^-5 * x^2 * z^-3 ] T33.283 : Triangle type {34,68,68} Group order 68 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^-2 * y^4 * x^-6 ] T33.284 : Triangle type {34,68,68} Group order 68 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^-10 * z * y^-3 ] T33.285 : Triangle type {34,68,68} Group order 68 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^6 * z^-2 ] T33.286 : Triangle type {34,68,68} Group order 68 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, y^2 * z^-1 * y^6 * z^-3 ] T33.287 : Triangle type {34,68,68} Group order 68 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-12 * x^4 * y^-8 ] T33.288 : Triangle type {34,68,68} Group order 68 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, x^-1 * y^4 * x^-4 * y^2 ] T33.289 : Triangle type {67,67,67} Group order 67 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^28 * x^-1 * y^5, x * z^-1 ] T33.290 : Triangle type {67,67,67} Group order 67 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-13 * x^2 * y^-8 ] T33.291 : Triangle type {67,67,67} Group order 67 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^4 * y^-4 * x^2 * y^-4 * x * y^-1 * x * y^-1 * x ] T33.292 : Triangle type {67,67,67} Group order 67 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^3 * x^-1 * y^4 * x^-2 * y^4 ] T33.293 : Triangle type {67,67,67} Group order 67 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-2 * y^4 * x^-3 * y^3 ] T33.294 : Triangle type {67,67,67} Group order 67 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-1 * y^3 * x^-2 * y^4 ] T33.295 : Triangle type {67,67,67} Group order 67 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, x^-5 * y^4 ] T33.296 : Triangle type {67,67,67} Group order 67 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^5 * y^-3, z^-4 * y * x^2 * z^-3 ] T33.297 : Triangle type {67,67,67} Group order 67 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^4 * y^-2 * x^-3 * z^3 ] T33.298 : Triangle type {67,67,67} Group order 67 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * y^-1 * x * y^-3, x^-2 * y^2 * x^-7 ] T33.299 : Triangle type {67,67,67} Group order 67 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-7 * y^4 * z^-4 ] T33.300 : Triangle type {67,67,67} Group order 67 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^3 * x^-2 * y^4 ] Genus 34 T34.1 : Triangle type {2,4,5} Group order 1320 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^-2 * x * y * z^-2, x * z * y^-1 * z^2 * y^-1 * z * y^-1 * z^2 * y^-1 * z * y^-1 * z^-2 ] T34.2 : Triangle type {2,4,5} Group order 1320 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^-2 * x * y * z^-2, x * z * y * z^-1 * y * z^-1 * y * z^-1 * y^2 * z^-1 * x * y^-1 * z^-1 * y * z^-1 * y * z^-1 ] T34.3 : Triangle type {2,4,15} Group order 360 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y * z^-2 * y * z^-1 * x * z * y^-1 * z^-2 ] T34.4 : Triangle type {2,4,70} Group order 280 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-62 * x * y * z^-7 ] T34.5 : Triangle type {2,4,136} Group order 272 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-60 * x * y^-1 * z^-7 ] T34.6 : Triangle type {2,5,5} Group order 660 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^-5, z^-2 * x * y * z^-2, x * y^-1 * z * y * z^-1 * y^2 * z^-1 * x * y^-2 * z^-1 ] T34.7 : Triangle type {2,5,5} Group order 660 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^-5, z^-2 * x * y * z^-2, z^-1 * y * z^-1 * x * z * y^2 * z^-1 * y * x * y^-1 * z^-1 ] T34.8 : Triangle type {2,6,36} Group order 216 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, z^5 * y * z^-1 * x * y^-1 * z^-4 * x ] T34.9 : Triangle type {2,6,36} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^21 * y * x * z * y^-1 * z^-5 * x * z^7 ] T34.10 : Triangle type {2,6,36} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^14 * y * z^-2 * x * z^8 * y * x * y^-1 * z^-8 * x * z ] T34.11 : Triangle type {2,6,102} Group order 204 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-15 * x * z^8 * y * x * y * z^-6 * x * z^2 * y^-1 ] T34.12 : Triangle type {2,8,10} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^2 * y^3 * x * z^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T34.13 : Triangle type {2,9,12} Group order 216 Action chiral Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, y^-9, z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1, x * z^3 * y^2 * z^-4 ] T34.14 : Triangle type {2,9,12} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, y^-9, z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-1 * z^-4 ] T34.15 : Triangle type {2,10,10} Group order 220 Action chiral Defining relators: [ x^2, x * y * z, y * x * z * y^2 * x * y^-1 * z, x * z * y^-3 * z^-1 * y^2 * z^-1, y^10 ] T34.16 : Triangle type {2,10,10} Group order 220 Action chiral Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-1 * y * z^-1, z^-2 * y * x * y^-1 * z^2 * y^-1 * z^-1, y^10 ] T34.17 : Triangle type {2,10,85} Group order 170 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, x * z^6 * y * z^-3 * x * y * z^-6 ] T34.18 : Triangle type {2,12,42} Group order 168 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^4 * y * z^-3 * x * y * z^-5 ] T34.19 : Triangle type {2,15,15} Group order 180 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, z * y * z^-1 * y^2 * z^-1 * x * y^-1 ] T34.20 : Triangle type {2,36,72} Group order 144 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, z^2 * y^-3 * z^4 * y^-4 * z^3 * y^-1 * z ] T34.21 : Triangle type {2,69,138} Group order 138 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^55 * y^-12 * z ] T34.22 : Triangle type {2,70,70} Group order 140 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^56 * y^-13 ] T34.23 : Triangle type {2,136,136} Group order 136 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^54 * y^-12 * z ] T34.24 : Triangle type {3,6,24} Group order 144 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, x^-1 * z^2 * y^-1 * x * z^3 ] T34.25 : Triangle type {3,6,24} Group order 144 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^-1 * x^-1 * z * y^-1 * x * z^2 * y^-1 ] T34.26 : Triangle type {3,8,12} Group order 144 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, z^-1 * x^-1 * y * x^-1 * y * x * y^-1 ] T34.27 : Triangle type {3,15,20} Group order 120 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y * x^-1 * y * x^-1 * y^2 * z^-1 ] T34.28 : Triangle type {3,35,105} Group order 105 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-24 * z * y^-1 * z * y^-7 * z ] T34.29 : Triangle type {3,36,36} Group order 108 Action chiral Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, y^6 * z^-1 * y * z^-2 * y^2 ] T34.30 : Triangle type {3,36,36} Group order 108 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-25 * z * y^-1 * z * y^-7 * z ] T34.31 : Triangle type {3,36,36} Group order 108 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z * y^-2 * z * y^-6 * z^2 ] T34.32 : Triangle type {3,36,36} Group order 108 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^23 * y^-3 * z * y^-7 * z ] T34.33 : Triangle type {3,102,102} Group order 102 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-23 * z * y^-1 * z * y^-8 ] T34.34 : Triangle type {4,4,35} Group order 140 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1, z * y * z^-2 * x * z^3 ] T34.35 : Triangle type {4,4,35} Group order 140 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^22 * y * x^-1 * y * x^-1 * z^11 ] T34.36 : Triangle type {4,4,68} Group order 136 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-22 * x * y^-1 * z^-11 ] T34.37 : Triangle type {4,6,8} Group order 144 Action chiral Defining relators: [ x * y * z, x^4, (x * z^-1)^2, y^6, y^-2 * z^-1 * x^-1 * z^2 * y^-1 ] T34.38 : Triangle type {4,6,8} Group order 144 Action chiral Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, y * x * y^-1 * x * z^-2 ] T34.39 : Triangle type {4,6,8} Group order 144 Action chiral Defining relators: [ x * y * z, x^4, z^-1 * x * y^-1 * x * z * y, x * z * y^-1 * x * y^-1 * z^-1 ] T34.40 : Triangle type {4,6,8} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^6, x^-1 * z * y * x * z * y ] T34.41 : Triangle type {4,6,30} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^3 * y^-1 * z^-2 * x^-1 * z^4 ] T34.42 : Triangle type {4,8,28} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, y * x^-1 * z^2 * y * x * z^4 * y * z^-1 * x * z^4 ] T34.43 : Triangle type {4,9,36} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z * y^-4 * z^3 ] T34.44 : Triangle type {4,10,10} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^2 * y^-1 * x * z^2, y^3 * x * z^-1 * y, (z^-1 * y)^3 ] T34.45 : Triangle type {4,12,18} Group order 108 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z * y^3 * z^-1 * x ] T34.46 : Triangle type {4,12,18} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^4 * y^-1 * x * z^4 ] T34.47 : Triangle type {4,46,92} Group order 92 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^4 * z^-3 * y * z^-1 * y * z^-1 * y^10 * z^-1 * y ] T34.48 : Triangle type {5,10,10} Group order 110 Action chiral Defining relators: [ x * y * z, x^-5, z * y * x^-1 * y^-1 * z, z^-2 * x^2 * z * y ] T34.49 : Triangle type {5,10,10} Group order 110 Action chiral Defining relators: [ x * y * z, x^-5, z^-2 * x^-1 * y^2, y^2 * x^2 * y^-1 * z^-1 ] T34.50 : Triangle type {5,10,10} Group order 110 Action chiral Defining relators: [ x * y * z, (x * y^-1)^2, x^-5, y^2 * x^2 * z^2 ] T34.51 : Triangle type {5,10,10} Group order 110 Action chiral Defining relators: [ x * y * z, (x * y^-1)^2, x^-5, z^-1 * x * z^-1 * x * z * y ] T34.52 : Triangle type {5,10,10} Group order 110 Action chiral Defining relators: [ x * y * z, x^-5, y * z^-1 * x^-1 * y^-1 * z^-1, x^-1 * y^-1 * x^2 * z * x^-1 ] T34.53 : Triangle type {5,10,10} Group order 110 Action chiral Defining relators: [ x * y * z, x^-5, y^-1 * z^-1 * x^-1 * z * y^-1, x^-1 * y^-1 * x^2 * z * x^-1 ] T34.54 : Triangle type {5,10,10} Group order 110 Action chiral Defining relators: [ x * y * z, x^-5, y^-1 * z^-1 * x^-1 * z * y^-1, z * x^-1 * y^-1 * x * y^-1 * z ] T34.55 : Triangle type {5,10,10} Group order 110 Action chiral Defining relators: [ x * y * z, x^-5, z * y * x^2 * z^2, y * x^-1 * y^-1 * x * z^-1 * y ] T34.56 : Triangle type {5,18,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z * y^-1 * z * y^-1 * z * y^-4 * z^5 * y^-1 * z^2 ] T34.57 : Triangle type {5,85,85} Group order 85 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, z^3 * y^-1 * z * y^-1 * z^9 * y^-1 * z ] T34.58 : Triangle type {5,85,85} Group order 85 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-5, y^-4 * z * y^-1 * z^9 * y^-1 * z ] T34.59 : Triangle type {6,6,18} Group order 108 Action reflexible [n] Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, z^-1 * y * x^2 * z^-1 * y, z * y^-1 * z^-1 * x^-1 * z^3 ] T34.60 : Triangle type {6,6,18} Group order 108 Action chiral Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, x^-1 * y * x^-2 * y^-2 * z, z * y * x * y^-1 * x * z^3 ] T34.61 : Triangle type {6,6,18} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^7 * y * z^-5 * x * z^5 ] T34.62 : Triangle type {6,6,18} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^6 * y^-1 * z^-1 * x^-1 * y * x * z^3 * y * x * z^2 * y * z^-1 * x^-1 * z ] T34.63 : Triangle type {6,6,51} Group order 102 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^4 * y^-1 * z^-1 * x^-1 * y * z^-4 * x^-1 * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z ] T34.64 : Triangle type {6,9,9} Group order 108 Action chiral Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, x^-1 * y^-1 * x^2 * y^-1 * z ] T34.65 : Triangle type {6,9,9} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^2 * x^-1 * z^2, x^6, y^-1 * z * y^-1 * z^4 * y^-1 * z ] T34.66 : Triangle type {6,12,16} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T34.67 : Triangle type {6,15,30} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y^2 * x * z^-2 ] T34.68 : Triangle type {6,15,30} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, y^-3 * x * z * y^-1 ] T34.69 : Triangle type {6,15,30} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z * y^-1 * z * y^-4 * z^4 * y^-3 ] T34.70 : Triangle type {6,28,84} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, z^9 * x * y^-4 * z ] T34.71 : Triangle type {6,42,42} Group order 84 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^6, y^5 * x^-1 * z^-5 * y^4 ] T34.72 : Triangle type {9,27,27} Group order 81 Action chiral Defining relators: [ x * y * z, x * y^-1 * x * z^-1, x^4 * z * y, y^-2 * z^2 * y^-1 * z * y^-3 ] T34.73 : Triangle type {9,27,27} Group order 81 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-9, y^-1 * z^4 * x * y^-4 ] T34.74 : Triangle type {10,16,80} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^-10 ] T34.75 : Triangle type {10,20,40} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, y^-2 * x^2 * y^-2 ] T34.76 : Triangle type {10,20,40} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * z * y^-1, z^-2 * y^2 * z^-2 ] T34.77 : Triangle type {10,20,40} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-3 * z^3 ] T34.78 : Triangle type {12,12,21} Group order 84 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, x * z^-2 * x^-2 * z * y^-1, z^3 * x^-1 * z^2 * y^-1, z^2 * y * z^-1 * x * z^3 ] T34.79 : Triangle type {15,25,75} Group order 75 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-2 * y * x^-5 * y^4 * x^-2 ] T34.80 : Triangle type {15,25,75} Group order 75 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, y^-1 * z^9 ] T34.81 : Triangle type {15,25,75} Group order 75 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * x^-4 * z, y^-2 * z^4 * x * y^-4 ] T34.82 : Triangle type {15,25,75} Group order 75 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^4 * z^-2 * x^7 * y^-1 * x * y^-1 * x ] T34.83 : Triangle type {16,16,20} Group order 80 Action chiral Defining relators: [ x * y * z, y * x^-2 * y * z^-1, y^-1 * z * x^-1 * z^2 ] T34.84 : Triangle type {16,16,20} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, z^-1 * x^-1 * y * x^-1 * y * z^-2 ] T34.85 : Triangle type {18,72,72} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-1 * y * x^-1 * y^10 * x^-1 * y ] T34.86 : Triangle type {18,72,72} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-1 * z^4 * x^-6 ] T34.87 : Triangle type {24,36,72} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-4 * x^4 * z^-8 ] T34.88 : Triangle type {24,36,72} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^-2 * y * x^-7 * y^2 * x^-1 ] T34.89 : Triangle type {24,36,72} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^12 * y^-1 * x^8 * y^-1 * x * y^-1 * x ] T34.90 : Triangle type {24,36,72} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^5 * y^-3 * z, x^-1 * z^3 * x^-6 ] T34.91 : Triangle type {35,70,70} Group order 70 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-4 * z * y^-7 * x * y^-3 * z * y^-2 ] T34.92 : Triangle type {35,70,70} Group order 70 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-3 * z^4 * x^-6 ] T34.93 : Triangle type {35,70,70} Group order 70 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, (x^-6 * y * x^-2)^2 ] T34.94 : Triangle type {35,70,70} Group order 70 Action reflexible [m] Defining relators: [ x * y * z, y * x^-1 * y, z^19 * x^-2 * z^3 ] T34.95 : Triangle type {35,70,70} Group order 70 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6 * y^-2, y^-1 * z^5 * y^-4 ] T34.96 : Triangle type {35,70,70} Group order 70 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, z^4 * x^-1 * z^4 ] T34.97 : Triangle type {35,70,70} Group order 70 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4 * y^-2, z^2 * y^-1 * z^9 ] T34.98 : Triangle type {35,70,70} Group order 70 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-35, y * z^-1 ] T34.99 : Triangle type {36,36,36} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^-1 * y * x^-1 * y * x^-6 ] T34.100 : Triangle type {69,69,69} Group order 69 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^29 * x^-1 * y^5, x * z^-1 ] T34.101 : Triangle type {69,69,69} Group order 69 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^-4 * x * y^-3 ] T34.102 : Triangle type {69,69,69} Group order 69 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^-3 * y^4 * z^-4 ] T34.103 : Triangle type {69,69,69} Group order 69 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-1 * y * x^-1 * y * x^-1 * y^4 * x^-3 * y^3 ] Genus 35 T35.1 : Triangle type {2,4,8} Group order 544 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, x * z * y^-1 * z * y * x * z * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T35.2 : Triangle type {2,4,8} Group order 544 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, y^-1 * z * y^-1 * z * y * x * z * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y * z^-1 * x * z ] T35.3 : Triangle type {2,4,12} Group order 408 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, y^-1 * z * y * x * z * y * x * y^-1 * z^-1 * x * z * y^-1 * z ] T35.4 : Triangle type {2,4,72} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-64 * x * y * z^-7 ] T35.5 : Triangle type {2,4,72} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-22 * x * z^4 * y * z^-2 * x * z * y^-1 * z^-5 ] T35.6 : Triangle type {2,4,140} Group order 280 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-62 * x * y^-1 * z^-7 ] T35.7 : Triangle type {2,6,20} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-1)^4, x * z^2 * y * x * z * y^-1 * z^-5 ] T35.8 : Triangle type {2,6,20} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, y * z^-3 * x * y^-1 * z^-4 ] T35.9 : Triangle type {2,6,105} Group order 210 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^11 * y * z^-2 * x * z^3 * y * z^-7 * x * y^-1 * z^-8 * x * z ] T35.10 : Triangle type {2,8,8} Group order 272 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, y^-1 * z * y * x * z * y * x * y^-1 * z^-1 * y * z^-1 * x * z ] T35.11 : Triangle type {2,8,8} Group order 272 Action chiral Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, z^2 * y * x * y^-1 * z^-2 * x ] T35.12 : Triangle type {2,8,8} Group order 272 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z * y * x * z * y * x * y^-1 * z * y^-1 * z * y^-1 * z^-1 * x ] T35.13 : Triangle type {2,8,48} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-5 * x * z^4 * y * x * y^-1 * z^-1 * x * y^-1 * z^-11 ] T35.14 : Triangle type {2,8,48} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^7 * y * z^-2 * x * z^2 * y * z^-2 * x * y^-1 * z^-8 * x ] T35.15 : Triangle type {2,12,12} Group order 204 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z * y^-1 * z * y^-2 * z^-1 * x * z * y^-1 ] T35.16 : Triangle type {2,12,16} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^7 * y * x * z * y * x * y * x * y^-1 * z^-3 * x * z ] T35.17 : Triangle type {2,12,16} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, z^-2 * x * z * y^-1 * z^-4, y^12 ] T35.18 : Triangle type {2,12,84} Group order 168 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^5 * y * z^-3 * x * z * y^-1 * z^-3 * x, y^12 ] T35.19 : Triangle type {2,16,80} Group order 160 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^4 * y * x * z^5 ] T35.20 : Triangle type {2,16,80} Group order 160 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y * z^-1 * x * z * y^-1 * z^-3, (y^-5 * z^3)^2 ] T35.21 : Triangle type {2,20,40} Group order 160 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^-9 * z^3 * y^-5 * z^3 ] T35.22 : Triangle type {2,20,40} Group order 160 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-4 * z^-1 * y^3, y^-1 * z^8 * y^-11 ] T35.23 : Triangle type {2,21,21} Group order 168 Action reflexible [n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y * z^-1, y^2 * z^-1 * y^6 * z^-2 * y^8 * z^-2 ] T35.24 : Triangle type {2,22,77} Group order 154 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^2 * y^-4 * z^5 ] T35.25 : Triangle type {2,71,142} Group order 142 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^57 * y^-12 * z ] T35.26 : Triangle type {2,72,72} Group order 144 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-11 * y^23 * z^-1 ] T35.27 : Triangle type {2,72,72} Group order 144 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^58 * y^-13 ] T35.28 : Triangle type {2,140,140} Group order 140 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^56 * y^-12 * z ] T35.29 : Triangle type {3,15,30} Group order 120 Action reflexible [m] Defining relators: [ x^3, x * y * z, z * y^-2 * x * y^-1 * z ] T35.30 : Triangle type {3,20,20} Group order 120 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (x^-1 * z * y)^2, y^6 * z^-1 * y^2 * z^-1 ] T35.31 : Triangle type {3,105,105} Group order 105 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-24 * z * y^-1 * z * y^-6 * z^2 ] T35.32 : Triangle type {4,4,4} Group order 272 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y * z^-1 * x^-1 * y^-1 * z^-1 * x^3 * z * x^-1 * z * x^-1 * y^-1 ] T35.33 : Triangle type {4,4,4} Group order 272 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * x * y^-1 * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z ] T35.34 : Triangle type {4,4,6} Group order 204 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^-1 * z ] T35.35 : Triangle type {4,4,36} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-8 * x * z^3 * y * z^-1 * x^-1 * y * z^-4 ] T35.36 : Triangle type {4,4,36} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-8 * x * z^3 * y * z^-1 * x^-1 * z * y^-1 * z^-3 ] T35.37 : Triangle type {4,4,36} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^23 * y * x^-1 * y * x^-1 * z^11 ] T35.38 : Triangle type {4,4,70} Group order 140 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^22 * y * x^-1 * z^12 ] T35.39 : Triangle type {4,6,60} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^3 * y^-1 * z^-2 * x * z^4 ] T35.40 : Triangle type {4,8,8} Group order 136 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z * y^-1 * z * y * x^-1 * z * y^-1 * z * y^-1 ] T35.41 : Triangle type {4,8,8} Group order 136 Action chiral Defining relators: [ x * y * z, x^4, (y * z^-1)^2, x * y^-2 * x * z * y ] T35.42 : Triangle type {4,8,8} Group order 136 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z * y^-2 * z^-1 * x^-1 * z * y^-1 * z * y^-1 ] T35.43 : Triangle type {4,8,8} Group order 136 Action chiral Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * x^-1 * y^-1 * z, (x * y^-2)^2 ] T35.44 : Triangle type {4,8,8} Group order 136 Action chiral Defining relators: [ x * y * z, x^4, (x * y^-2)^2, y * z^-1 * y^2 * z^-2 ] T35.45 : Triangle type {4,8,56} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^5 * y^-1 * z^-3 * x^-1 * y^-1 * x^-1 * z^4 ] T35.46 : Triangle type {4,8,56} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^5 * y^-1 * z^-3 * x^-1 * y^-1 * x * z^4 ] T35.47 : Triangle type {4,10,12} Group order 120 Action chiral Defining relators: [ x * y * z, x^4, (x * z^-1)^2, (y * z^-2)^2, y^3 * x^-1 * y^-2 * z^-1, z^-1 * x * z * y^-1 * x * y^-1 * z^-2 ] T35.48 : Triangle type {4,10,12} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z * y * z^-1 * x^-1 * z^3, y^10 ] T35.49 : Triangle type {4,48,48} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-9 * z * y^-5 * z * y^-1 * z * y^-4 * z * y^-1 ] T35.50 : Triangle type {4,48,48} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y^-9 * z^4 * y^-5 * z * y^-1 * z * y^-3 ] T35.51 : Triangle type {6,6,10} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, (x * y^-1 * x)^2, (x * y^-2)^2, x * z * y * x^-1 * y^-1 * z^-2 ] T35.52 : Triangle type {6,6,10} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, x^-1 * z * y^-1 * x * z^2, z^2 * y * x^-1 * z * y^-1 ] T35.53 : Triangle type {6,12,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-4 * x^-1 * z^2 * y * z^-1 ] T35.54 : Triangle type {6,12,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-2, x^6 ] T35.55 : Triangle type {6,16,16} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^6, y^6 * z^-1 * y * z^-1 * y * x * z^-1 * y * z^-1 * y * z^-1 * y ] T35.56 : Triangle type {6,16,16} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^6 * z^-2 ] T35.57 : Triangle type {6,18,45} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * y^3 * z^-1 * y, z * y^-1 * z^-1 * x * z^2 ] T35.58 : Triangle type {6,18,45} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^2 * y * x^-1 * z^2 ] T35.59 : Triangle type {6,84,84} Group order 84 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^6, y^5 * x^-1 * z^-5 * y * z^-3 ] T35.60 : Triangle type {8,8,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^2 * y * x * z^3 * y * z^-1 * x * z^4 ] T35.61 : Triangle type {8,8,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^-6 * x^-1 * y * x^-1 * y * z^-4 ] T35.62 : Triangle type {8,8,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z * y^-1 * x^2 * z * y^-1, y * z^-2 * x^-1 * z^3 ] T35.63 : Triangle type {8,8,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z * y^-1 * x^2 * z * y^-1, z^2 * y * x^-1 * z^3 ] T35.64 : Triangle type {8,11,88} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, y^-2 * z^5 * y^-1 * z^3 ] T35.65 : Triangle type {8,12,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, (y * z^-1 * y)^2 ] T35.66 : Triangle type {8,12,12} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * x^-1 * y * z^-1 * y ] T35.67 : Triangle type {8,12,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, y * x^-2 * z * x^-1, y^-1 * z^5 * y^-2 * z * y^-1 * z^2 ] T35.68 : Triangle type {8,12,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^8, y^4 * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T35.69 : Triangle type {8,80,80} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z^9 ] T35.70 : Triangle type {8,80,80} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z^5 * y^-4 ] T35.71 : Triangle type {8,80,80} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z^5 * y^-2 * z^2 ] T35.72 : Triangle type {10,40,40} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x * y^-1 * x * y^-2, x * z^-1 * x^3 * z^-3 ] T35.73 : Triangle type {10,40,40} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * y^-2 * z^2, x^-10 ] T35.74 : Triangle type {10,40,40} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-10 ] T35.75 : Triangle type {10,40,40} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^-10 ] T35.76 : Triangle type {11,77,77} Group order 77 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^-11 ] T35.77 : Triangle type {11,77,77} Group order 77 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * z^3, x^-11 ] T35.78 : Triangle type {11,77,77} Group order 77 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * y^-1 * z^3, x^-1 * y * x^-5 * y^3 * z^-1 * y^2 ] T35.79 : Triangle type {11,77,77} Group order 77 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-4 * x * y^-3, x^-1 * z^3 * x^-2 * z^4 ] T35.80 : Triangle type {11,77,77} Group order 77 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^4, z^3 * x^-2 * z^4 ] T35.81 : Triangle type {12,12,42} Group order 84 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, x * z^-2 * x^-2 * z * y^-1, z^3 * x^-1 * z^2 * y^-1, z^3 * y^-1 * x * z^3 ] T35.82 : Triangle type {15,75,75} Group order 75 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^3 * y^-3 * x^6 * y^-1 * x * y^-1 * x ] T35.83 : Triangle type {15,75,75} Group order 75 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-2 * z^3, y^-3 * x^8 * y^-2 ] T35.84 : Triangle type {16,16,40} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * y^-1 * x * z^2 ] T35.85 : Triangle type {16,16,40} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-2 * x * z^2, y * z^-3 * y * x^2 * z^-3 ] T35.86 : Triangle type {16,16,40} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * z^-1 * x, z^-1 * y^3 * z^-1 * y, z * y^-1 * z^-1 * x * z^2 ] T35.87 : Triangle type {20,20,20} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^3 * z^-1 * y, x^6 * y^-2 ] T35.88 : Triangle type {20,20,20} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, z^-1 * y * x^-1 * y^-2, x * y^-1 * z^2 * y^-3 * x * y^-4 ] T35.89 : Triangle type {20,20,20} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-4 * x^4 * y^-4 ] T35.90 : Triangle type {36,72,72} Group order 72 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-36, y * z^-1 ] T35.91 : Triangle type {36,72,72} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^2 * y^-3 * x^6 * y^-1 * x^2 ] T35.92 : Triangle type {36,72,72} Group order 72 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-1 * z * y^-1 * z^5 * y^-4 ] T35.93 : Triangle type {36,72,72} Group order 72 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^13 * z^-2 * x^4 ] T35.94 : Triangle type {71,71,71} Group order 71 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^30 * x^-1 * y^5, x * z^-1 ] T35.95 : Triangle type {71,71,71} Group order 71 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-17 * x * y^-6 ] T35.96 : Triangle type {71,71,71} Group order 71 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-2 * x * y^-2 * x * y^-5 * x * y^-4 * x * y^-1 * x ] T35.97 : Triangle type {71,71,71} Group order 71 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-1 * y * x^-1 * y^10 * x^-2 ] T35.98 : Triangle type {71,71,71} Group order 71 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x * y^-5 * x^5 * y^-1 * x ] T35.99 : Triangle type {71,71,71} Group order 71 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x * y^-4 * x^5 * y^-1 ] T35.100 : Triangle type {71,71,71} Group order 71 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, z^-4 * x * z^-3 ] T35.101 : Triangle type {71,71,71} Group order 71 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^4, x^-5 * z^4 ] T35.102 : Triangle type {71,71,71} Group order 71 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^-2 * z^2 * x^-7 ] T35.103 : Triangle type {71,71,71} Group order 71 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, y^-2 * z^5 * y^-1 * z^3 ] T35.104 : Triangle type {71,71,71} Group order 71 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * y^-3 * z, x^-7 * y^3 ] T35.105 : Triangle type {71,71,71} Group order 71 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^2 * z^-1 * x^7 * z^-1 * x^4 ] Genus 36 T36.1 : Triangle type {2,3,16} Group order 672 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, x * z * y * z^-2 * x * z * y * x * y^-1 * z^3 * y^-1 * z^-2 ] T36.2 : Triangle type {2,3,16} Group order 672 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^2 * y * z^-1 * x * z * y * x * y^-1 * z^-2 * x * z^3 ] T36.3 : Triangle type {2,3,20} Group order 600 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-2 * x * z^11 * y * z^-1 * x * z^6 * y^-1 ] T36.4 : Triangle type {2,4,14} Group order 392 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z * y * x * y^-1 * z^-1 * x, z^-6 * y * x * y^-1 * z^-1 * y * z^-6 ] T36.5 : Triangle type {2,4,39} Group order 312 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-23 * x * z^9 * y^-1 * x * z * y^-1 * z^-4 ] T36.6 : Triangle type {2,4,74} Group order 296 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-66 * x * y * z^-7 ] T36.7 : Triangle type {2,4,144} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-64 * x * y^-1 * z^-7 ] T36.8 : Triangle type {2,5,15} Group order 300 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^-5, x * z^2 * y^-1 * z^-3, (z^-1 * y)^5 ] T36.9 : Triangle type {2,6,8} Group order 336 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, z^8, y * x * y^-1 * z * y^2 * x * z * y^-1 * z^-1 ] T36.10 : Triangle type {2,6,8} Group order 336 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (z^-1 * y)^3, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T36.11 : Triangle type {2,6,10} Group order 300 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^10 ] T36.12 : Triangle type {2,6,10} Group order 300 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, z * y * z^-1 * x * y^-1 * z^-2 * x, z^10 ] T36.13 : Triangle type {2,6,38} Group order 228 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^26 * y * x * y^-1 * z^-1 * x * y^-1 * z^-3 * x * z^5 ] T36.14 : Triangle type {2,8,26} Group order 208 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^10 * y * x * z * y * x * y * x * y^-1 * z^-3 * x * z^8 ] T36.15 : Triangle type {2,10,20} Group order 200 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, y * z^-2 * x * z^8 * y * x * z^3 * y^-1 * z^-1 * x * z^3 ] T36.16 : Triangle type {2,10,20} Group order 200 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^7 * y * x * z * y * x * z * y * x * y * x * y^-1 * z^-3 * x * y^-1 * z^-1 * x * z ] T36.17 : Triangle type {2,10,20} Group order 200 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^10 ] T36.18 : Triangle type {2,10,90} Group order 180 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^8 * y * z^-3 * x * z^6 ] T36.19 : Triangle type {2,14,14} Group order 196 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^2 * x * z * y * x * y^-6 * z^-1 * x * y^-1 * z^-1 * y, z^-3 * x * z^2 * y * x * z * y * x * y * x * y^-1 * z^-4 ] T36.20 : Triangle type {2,14,14} Group order 196 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^-2 * z * y^-2 * z * y^-3 * z * y^-3 * z, y^-14 ] T36.21 : Triangle type {2,14,84} Group order 168 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^4 * y * z^-2 * x * z * y^-1 * z^-3 * x, y^-3 * z^3 * y^-5 * z^3 ] T36.22 : Triangle type {2,20,80} Group order 160 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-4 * y^2 * z^-4 ] T36.23 : Triangle type {2,21,28} Group order 168 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z * y^-3 * z^3, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T36.24 : Triangle type {2,26,78} Group order 156 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-1 * y^9 * z^-3 * y^9 * z^-2 * y ] T36.25 : Triangle type {2,38,76} Group order 152 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-13 * y^11 * z^-1 * y^12 ] T36.26 : Triangle type {2,39,39} Group order 156 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-35 * z * y^-1 ] T36.27 : Triangle type {2,50,75} Group order 150 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y^-13 * z^2 * y^-8 * z * y^-1 ] T36.28 : Triangle type {2,73,146} Group order 146 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^59 * y^-12 * z ] T36.29 : Triangle type {2,74,74} Group order 148 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^60 * y^-13 ] T36.30 : Triangle type {2,144,144} Group order 144 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^58 * y^-12 * z ] T36.31 : Triangle type {3,3,8} Group order 336 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^8, z * y * x^-1 * y * x^-1 * y^-1 * z^-2 * x ] T36.32 : Triangle type {3,3,8} Group order 336 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^8, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z, z^3 * y * x^-1 * z^2 * y^-1 * x ] T36.33 : Triangle type {3,3,10} Group order 300 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^10 ] T36.34 : Triangle type {3,3,38} Group order 228 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z * y^-1 * z^-4 * x^-1 * z^4 ] T36.35 : Triangle type {3,3,73} Group order 219 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^4 * y * x * z^4 ] T36.36 : Triangle type {3,7,21} Group order 147 Action chiral Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y^3 * x^-1 * y^-1 * z^2, y^-7 ] T36.37 : Triangle type {3,10,10} Group order 150 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, (z^-1 * y)^3, y^10 ] T36.38 : Triangle type {3,10,10} Group order 150 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, (z^-1 * y)^3, z * y * z^-1 * x^-1 * y^-3 ] T36.39 : Triangle type {3,10,10} Group order 150 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (y * z^-1 * y)^2, y^3 * x^-1 * y^-1 * x * z * y^3 ] T36.40 : Triangle type {3,20,30} Group order 120 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2 ] T36.41 : Triangle type {3,37,111} Group order 111 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-26 * z * y^-1 * z * y^-7 * z ] T36.42 : Triangle type {3,38,38} Group order 114 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^25 * y^-3 * z * y^-7 * z ] T36.43 : Triangle type {3,108,108} Group order 108 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-25 * z * y^-1 * z * y^-6 * z^2 ] T36.44 : Triangle type {4,4,7} Group order 196 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^3 * y^-1 * x^-1 * z^3 ] T36.45 : Triangle type {4,4,37} Group order 148 Action reflexible [n] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-3 * y * x * z^-3 ] T36.46 : Triangle type {4,4,37} Group order 148 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^24 * y * x^-1 * y * x^-1 * z^11 ] T36.47 : Triangle type {4,4,72} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^23 * y * x^-1 * z^12 ] T36.48 : Triangle type {4,6,6} Group order 168 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-1 * y)^2, z^6, z^-1 * x^-1 * z * y * x * z^2 * y ] T36.49 : Triangle type {4,10,15} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, y * x * z^-1 * x^-1 * z * x^-1 * z ] T36.50 : Triangle type {4,25,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^-10 * z * y^-1 * z * y^-1 * z * y^-7 * z * y^-2 ] T36.51 : Triangle type {4,26,26} Group order 104 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^4 * z^-2 * y^4 * z^-1 * y^14 * z^-1 ] T36.52 : Triangle type {4,96,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^-9 * z^4 * y^-5 * z * y^-1 * z * y^-1 * z * y^-1 ] T36.53 : Triangle type {5,6,6} Group order 150 Action reflexible [m,n] Defining relators: [ x * y * z, x^-5, y^2 * x^-1 * z^2, y * x * y^-1 * x * y^-1 * z^-1, y^6 ] T36.54 : Triangle type {5,6,6} Group order 150 Action reflexible [m,n] Defining relators: [ x * y * z, x^-5, y * z^-1 * x^-1 * y^-1 * z, y * x^-1 * y^-1 * x * z * y, y^6 ] T36.55 : Triangle type {5,19,95} Group order 95 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z^2 * y^-1 * z^10 * y^-1 * z * y^-1 * z^2 ] T36.56 : Triangle type {5,20,20} Group order 100 Action chiral Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-1 * y * z^-1, y^2 * x^2 * z^2 ] T36.57 : Triangle type {5,20,20} Group order 100 Action reflexible [n] Defining relators: [ x * y * z, z^-1 * x^2 * y^-1, x^-1 * y^-1 * x * z^-1, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 * y^-6 * z * y^-2 ] T36.58 : Triangle type {5,20,20} Group order 100 Action reflexible [n] Defining relators: [ x * y * z, (y * z^-1)^2, x^-5, y^2 * x^2 * z^2, x^-1 * z * y * x * y^-1 * z^-1 ] T36.59 : Triangle type {5,20,20} Group order 100 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^-5, y^-2 * z * y^-7 * z * y^-1 * z * y^-3 * z * y^-1 * z * y^-1 ] T36.60 : Triangle type {5,20,20} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2 ] T36.61 : Triangle type {5,20,20} Group order 100 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^-5 ] T36.62 : Triangle type {5,20,20} Group order 100 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-5, y^-2 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z * y^-10 ] T36.63 : Triangle type {5,90,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, z^2 * y^-1 * z * y^-1 * z * y^-4 * z^5 * y^-1 * z^2 ] T36.64 : Triangle type {5,90,90} Group order 90 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z * y^-1 * z * y^-1 * z * y^-4 * z^5 * y^-1 * z * y^-1 ] T36.65 : Triangle type {6,6,19} Group order 114 Action reflexible [n] Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, x^6, (x * y^-1 * x)^2, x * z^-2 * y * z^-2 ] T36.66 : Triangle type {6,6,19} Group order 114 Action reflexible [n] Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z * x^-1 * y^-1 * x * z * x^-1, y^-1 * z^-2 * x^-1 * z^2 ] T36.67 : Triangle type {6,6,19} Group order 114 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^7 * y * x^-1 * y * x^-1 * z^3 * y * z^-1 * x^-1 * z^5 ] T36.68 : Triangle type {6,12,48} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T36.69 : Triangle type {7,13,91} Group order 91 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z * y^-1 * z * y^-4 * x^2 * y^-5 ] T36.70 : Triangle type {7,14,14} Group order 98 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-7, y^2 * z^-1 * y * z^-5 * y^4 * z^-1 ] T36.71 : Triangle type {7,14,14} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, (x * y^-1)^2, y^2 * x^-1 * z * y, x^-7 ] T36.72 : Triangle type {7,14,14} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, (x * z^-1 * x)^2, y^-1 * x * y^-1 * x * y^-2, x^-7 ] T36.73 : Triangle type {7,14,14} Group order 98 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^-7, y^-6 * z * y^-1 * z * y^-2 * z * y^-1 * z ] T36.74 : Triangle type {7,14,14} Group order 98 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^-7, x^-1 * y^-1 * x^3 * z * x^-2 ] T36.75 : Triangle type {7,84,84} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z * y^-1 * z^9 ] T36.76 : Triangle type {7,84,84} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, z^2 * y^-1 * z^9 ] T36.77 : Triangle type {7,84,84} Group order 84 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z * y^-1 * z^5 * y^-4 ] T36.78 : Triangle type {8,8,13} Group order 104 Action reflexible [n] Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, z * y * z^-1 * x * z^2, x^8 ] T36.79 : Triangle type {8,8,13} Group order 104 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^8 * y^-1 * x^-1 * z^4 ] T36.80 : Triangle type {9,10,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^9, y^-1 * z * y^-4 * x * y^-4 ] T36.81 : Triangle type {9,81,81} Group order 81 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-9, z^5 * x^-1 * z^4 ] T36.82 : Triangle type {9,81,81} Group order 81 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-9, y^-1 * z^4 * y^-4 ] T36.83 : Triangle type {9,81,81} Group order 81 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-9, y^-1 * z^4 * y^-1 * z^3 ] T36.84 : Triangle type {10,10,10} Group order 100 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, (x * y^-2)^2, y^2 * x * z * y^3 * x * y^-3 * z ] T36.85 : Triangle type {10,10,10} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, x^4 * z^-2, y^-10 ] T36.86 : Triangle type {10,10,10} Group order 100 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-1 * y, x^10, y^-10 ] T36.87 : Triangle type {10,10,10} Group order 100 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^10, y^-1 * z * y^-4 * x * y^-4 ] T36.88 : Triangle type {10,10,45} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-2 * x^2 * y^-2, z^4 * y * x^-1 * z^4 ] T36.89 : Triangle type {10,10,45} Group order 90 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-2)^2, z^-1 * x * z^3 * y^-1 * x * z * y * z^-2 ] T36.90 : Triangle type {10,80,80} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^-1 * z^4 * x^-2 * z^4 ] T36.91 : Triangle type {10,80,80} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, z^4 * x^-1 * z^4 ] T36.92 : Triangle type {12,14,84} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * y^-1 * z^3, x * y^-5 * x^5 * y^-2 ] T36.93 : Triangle type {12,21,28} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * y^-3 * z^3, x^2 * y^-3 * x^3 * z^-3 * x^4 ] T36.94 : Triangle type {13,78,78} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, x^-2 * z^4 * x^-4 * z^2 ] T36.95 : Triangle type {13,78,78} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-2 * z * x^-1 * z^4 * x^-5 * z ] T36.96 : Triangle type {13,78,78} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-1 * z * x^-1 * z * x^-1 * z^4 * x^-6 ] T36.97 : Triangle type {13,78,78} Group order 78 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^2 * z^-2 * x^5 * y^-2 * x^4 ] T36.98 : Triangle type {13,78,78} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-3 * y^4, x^-1 * z^3 * x^-3 * z^3 ] T36.99 : Triangle type {13,78,78} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * x^-2 * z^2, y^-5 * x^5 * y^-1 ] T36.100 : Triangle type {14,14,42} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * z^-1 * x^-1 * z^3, y^-3 * x^2 * y^-3 ] T36.101 : Triangle type {14,14,42} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^4 * y^-2, z^-1 * y^3 * z^-1 * y, z^2 * y * x^-1 * z^3 ] T36.102 : Triangle type {14,14,42} Group order 84 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, x * z^-2 * x^-2 * z * y^-1, z^-3 * x^-1 * z^2 * y^-1, z^-3 * x^2 * z^-3 ] T36.103 : Triangle type {14,21,21} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * y * x^-1 * y * z^-1, y * z^-1 * y * x^-1 * z * y, (z^-1 * x)^3 ] T36.104 : Triangle type {14,21,21} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, z * y^-1 * x * z, y * z^-1 * y * x * z * y, x * z^-1 * x^3 * z^-1 * x * z^-1 ] T36.105 : Triangle type {14,21,21} Group order 84 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * y^2, z * x^-2 * z^2, x^-1 * z * y * x * y^-1 * z^-1 ] T36.106 : Triangle type {16,20,80} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, y^3 * x^-1 * y * x^-10 * y * x^-1 ] T36.107 : Triangle type {16,20,80} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, y^-1 * z^5 * y^-1 * z^3 ] T36.108 : Triangle type {19,76,76} Group order 76 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-1 * z * y^-2 * x^4 * y^-4 ] T36.109 : Triangle type {19,76,76} Group order 76 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-1 * x * y^-8 * z * y^-1 * x * y^-1 ] T36.110 : Triangle type {19,76,76} Group order 76 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, x * z^-2 * x^5 * z^-4 * x * z^-1 * x * z^-1 * x ] T36.111 : Triangle type {19,76,76} Group order 76 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^6 * z^-2 * x^8 * z^-1 * x * z^-1 * x ] T36.112 : Triangle type {19,76,76} Group order 76 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-1 * z^4 * x^-6 ] T36.113 : Triangle type {19,76,76} Group order 76 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^-1 * z^3 * x^-5 * z ] T36.114 : Triangle type {19,76,76} Group order 76 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^4 * x^-1 * z^4 ] T36.115 : Triangle type {19,76,76} Group order 76 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, y^-1 * z * y^-1 * z^9 ] T36.116 : Triangle type {19,76,76} Group order 76 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-19 ] T36.117 : Triangle type {20,20,40} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, z^-1 * y^3 * z^-1 * y ] T36.118 : Triangle type {20,20,40} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-2 * x^2 * z^-2 ] T36.119 : Triangle type {25,75,75} Group order 75 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-6 * z, y^-1 * z^3 * y^-1 * x * y^-4 ] T36.120 : Triangle type {25,75,75} Group order 75 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-9 * y^3 * x^-2 ] T36.121 : Triangle type {25,75,75} Group order 75 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x * y^-1, z^-3 * x^2 * z^-2 * x^5 * z^-4 * x * z^-1 * x * z^-2 ] T36.122 : Triangle type {25,75,75} Group order 75 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^10 * z^-1 * x^2 * y^-1 * x^12 ] T36.123 : Triangle type {25,75,75} Group order 75 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, y^-1 * z * y^-1 * z^5 * y^-1 * z^3 ] T36.124 : Triangle type {25,75,75} Group order 75 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^2 * x^-9 * y ] T36.125 : Triangle type {25,75,75} Group order 75 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-3 * y^4, y^-1 * z^8 ] T36.126 : Triangle type {25,75,75} Group order 75 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-7 * x * y^-5 ] T36.127 : Triangle type {26,26,39} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^4 * y^-2, y^-3 * x^-1 * z^2 ] T36.128 : Triangle type {26,26,39} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z * y * z^-1, x^5 * y^-1 * z^-2 ] T36.129 : Triangle type {26,26,39} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * y * x^-1 * y * z^-1, z^-1 * y * x^-1 * y^-2, z * x^-1 * z * x^-1 * z^3 ] T36.130 : Triangle type {26,26,39} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * y^-1 * z^-1, (y * z^-2)^2 ] T36.131 : Triangle type {26,26,39} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, z * y * x^-1 * z, z^-1 * x^-2 * y^-1 * x, y^2 * z^-1 * y^2 * x^-1 * y^3 * z^-1 ] T36.132 : Triangle type {26,26,39} Group order 78 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^6 * y^-2 * z^4 * x^-1 * z * x^-1 ] T36.133 : Triangle type {37,74,74} Group order 74 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, y^-3 * x^4 * y^-1 * x^8 * y^-1 * x * y^-1 * x ] T36.134 : Triangle type {37,74,74} Group order 74 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^2 * y^-3 * x^5 * z^-1 * x^3 ] T36.135 : Triangle type {37,74,74} Group order 74 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * y^-3 * z, x^-8 * y^2 ] T36.136 : Triangle type {37,74,74} Group order 74 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, y^-1 * z^5 * y^-3 * z ] T36.137 : Triangle type {37,74,74} Group order 74 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^6 * x^-2 * z^4 ] T36.138 : Triangle type {37,74,74} Group order 74 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^6 * x^-1 * z^4 ] T36.139 : Triangle type {37,74,74} Group order 74 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-2 * z^3, y^-2 * z^2 * y^-2 * x * y^-4 ] T36.140 : Triangle type {37,74,74} Group order 74 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-5 * x^2 * z^-9 ] T36.141 : Triangle type {37,74,74} Group order 74 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-2 * z * y^-3 * x^4 * y^-2 ] T36.142 : Triangle type {37,74,74} Group order 74 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^-1 * z^3 * x^-3 * z^3 ] T36.143 : Triangle type {37,74,74} Group order 74 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^-9 * x * z^-9 ] T36.144 : Triangle type {37,74,74} Group order 74 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-4 * x^4 * y^-5 * x * y^-1 * x ] T36.145 : Triangle type {37,74,74} Group order 74 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-7 * z, y^4 * x^-1 * y^4 ] T36.146 : Triangle type {37,74,74} Group order 74 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4 * z^-2, y^5 * x^-2 * y^4 * z^-1 * y^2 ] T36.147 : Triangle type {37,74,74} Group order 74 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6 * z^-2, y^-2 * z^4 * x * y^-4 ] T36.148 : Triangle type {37,74,74} Group order 74 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-3 * z^4 * x^-6 ] T36.149 : Triangle type {37,74,74} Group order 74 Action reflexible [m] Defining relators: [ x * y * z, y * x^-1 * y, z^20 * x^-1 * z^4 ] T36.150 : Triangle type {37,74,74} Group order 74 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-37, y * z^-1 ] T36.151 : Triangle type {38,38,38} Group order 76 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^12 * x^-2 * y^6 ] T36.152 : Triangle type {38,38,38} Group order 76 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, (y^3 * z^-1 * y^3)^2 ] T36.153 : Triangle type {38,38,38} Group order 76 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-2 * z^3, (x * y^-4)^2 ] T36.154 : Triangle type {38,38,38} Group order 76 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-1 * z^3 * x^-5 * z, y^-1 * z^5 * y^-3 * z ] T36.155 : Triangle type {73,73,73} Group order 73 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^31 * x^-1 * y^5, x * z^-1 ] T36.156 : Triangle type {73,73,73} Group order 73 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-17 * x^2 * y^-6 ] T36.157 : Triangle type {73,73,73} Group order 73 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-1 * x^3 * y^-2 * x * y^-5 * x * y^-4 * x * y^-1 * x ] T36.158 : Triangle type {73,73,73} Group order 73 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-1 * y * x^-1 * y^12 ] T36.159 : Triangle type {73,73,73} Group order 73 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^-6 * x^5 * y^-2 ] T36.160 : Triangle type {73,73,73} Group order 73 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^2 * x^-4 * y^5 ] T36.161 : Triangle type {73,73,73} Group order 73 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^3, x^-7 * y^3 ] T36.162 : Triangle type {73,73,73} Group order 73 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-8 * y, z^4 * x^-1 * z^4 ] T36.163 : Triangle type {73,73,73} Group order 73 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^6 * x^-1 * z^4 ] T36.164 : Triangle type {73,73,73} Group order 73 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-1 * z^4 * x^-5 * z ] T36.165 : Triangle type {73,73,73} Group order 73 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-4 * x^2 * z^-5 * y * z^-4 ] T36.166 : Triangle type {73,73,73} Group order 73 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-3 * z^3 * y^-1 * x * y^-4 ] T36.167 : Triangle type {73,73,73} Group order 73 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, y^-1 * z^4 * y^-3 * z ] Genus 37 T37.1 : Triangle type {2,3,8} Group order 1728 Action chiral Defining relators: [ x^2, y^3, x * y * z, z^8, y * x * z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z, z^2 * y * z^-1 * x * z^2 * y * z^-3 * x * z * y * x^2 * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * x * z * y^-1 * z^-2 * x, z * y * x * z * y * z^-1 * x * z * y * x * z^2 * y * x * z * y * x * z^2 * y^-1 * z^-3 * x ] T37.2 : Triangle type {2,3,12} Group order 864 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^12, z * y * x * z^3 * y * x * z * y^-1 * x * y^-1 * z^-1 * x * z^2, x * z * y * x * z * y * x * z * y * x * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 ] T37.3 : Triangle type {2,3,15} Group order 720 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^-1 * x * z * y * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-1, z^-5 * x * z * y * x^2 * z * y^-1 * z^-9 ] T37.4 : Triangle type {2,3,18} Group order 648 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z * y * z^-1 * x * z * y * x * y^-1 * z^2 * y^-1 * z^-1 * x * z, y * x * z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z ] T37.5 : Triangle type {2,3,18} Group order 648 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^6 * y * x * y^-2 * z^-4 * x, z^2 * y * x * z^3 * y * x * y^-1 * x * z * y^-1 * z^-1 * x * z, y * x * z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z ] T37.6 : Triangle type {2,3,24} Group order 576 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, y * z^-1 * x * z^3 * y * x * z * y^-1 * z^-3 * x * z, z * y * x * z * y * z^-1 * x * z * y * x * z^7 ] T37.7 : Triangle type {2,3,24} Group order 576 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T37.8 : Triangle type {2,3,24} Group order 576 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^-2 * x * z * y * x * z^2 * y^-1 * z^-1 * x * y^-1 * z^-1, z * y * z^-4 * x * y * z^-2 * x * z^7 ] T37.9 : Triangle type {2,4,6} Group order 864 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^6, (y * z^-2)^4, x * z * y * z^-1 * y * x * z * y^-1 * z^-1 * x * y^-1 * z^-1 * y * z^-2 ] T37.10 : Triangle type {2,4,8} Group order 576 Action chiral Defining relators: [ x^2, x * y * z, y^4, z^8, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, y^-1 * z * y^-1 * z * y * z^-1 * x * y^-1 * z^3 * y^-1 * z ] T37.11 : Triangle type {2,4,8} Group order 576 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (z^-1 * y)^3, z^8, z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T37.12 : Triangle type {2,4,8} Group order 576 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y * z^-2 * x * z * y^2 * z^-1 * x * z^3 ] T37.13 : Triangle type {2,4,8} Group order 576 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y * x * z * y * x * z * y * x * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 * y * z^-1 * x ] T37.14 : Triangle type {2,4,8} Group order 576 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z * y^-1 * z^-1 * y * z^-1 * x ] T37.15 : Triangle type {2,4,10} Group order 480 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-2 * y * z^-1)^2, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T37.16 : Triangle type {2,4,12} Group order 432 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, (y^-1 * z)^6, z^-12 ] T37.17 : Triangle type {2,4,12} Group order 432 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z^3 * y^-1 * z^-4, z^-1 * y * z^-2 * x * y^-1 * z^-3 * y * z^-1, (y^-1 * z)^6 ] T37.18 : Triangle type {2,4,12} Group order 432 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, (y^-1 * z)^6, z^-4 * x * z^5 * y^-1 * z^-2 ] T37.19 : Triangle type {2,4,12} Group order 432 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1, y^-1 * z^2 * y^-1 * z * y^-1 * z^-3 * x * z, (y^-1 * z)^6 ] T37.20 : Triangle type {2,4,20} Group order 360 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, (y^-1 * z)^6, x * z * y * x * z * y * x * y^-1 * z^-5 ] T37.21 : Triangle type {2,4,40} Group order 320 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-26 * x * z^5 * y * z^-2 * x * y^-1 * z^-5 ] T37.22 : Triangle type {2,4,40} Group order 320 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-3 * x * z^10 * y * x * z * y^-1 * z^-4 ] T37.23 : Triangle type {2,4,76} Group order 304 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-68 * x * y * z^-7 ] T37.24 : Triangle type {2,4,148} Group order 296 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-66 * x * y^-1 * z^-7 ] T37.25 : Triangle type {2,6,6} Group order 432 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * y^-1 * z * y^-3 * z^-1 * y * z^-1 * y^2, x * z^2 * y^-1 * z * y^-1 * z^2 * y^-1 * z^-2 ] T37.26 : Triangle type {2,6,6} Group order 432 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^6, y^-1 * z * y^-1 * z^-2 * y^2 * z^-1 * y^2 * z^-1 * y^2 * z^-1 * y^2 * z^-1 * y * x ] T37.27 : Triangle type {2,6,12} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T37.28 : Triangle type {2,6,12} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, x * y^-1 * z * y^-2 * z^-4, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T37.29 : Triangle type {2,6,12} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-1 * z^-4 ] T37.30 : Triangle type {2,6,12} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, x * z^2 * y^-1 * z^-3, x * y^-1 * z * y^-3 * z^-1 * y * z^-1 * y^2 ] T37.31 : Triangle type {2,6,12} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, z^12 ] T37.32 : Triangle type {2,6,12} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-1)^4, z^-2 * x * z^3 * y^-1 * z^-6 ] T37.33 : Triangle type {2,6,15} Group order 270 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, y * x * z^2 * y * z^-1 * x * z * y * x * y^-1 * z^-5 * x * z^2 ] T37.34 : Triangle type {2,6,30} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, z^-2 * x * z * y * x * y^-1 * z^-5 ] T37.35 : Triangle type {2,6,39} Group order 234 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^13 * y * x * z^15 * y * z^-1 * x * z^8 ] T37.36 : Triangle type {2,6,111} Group order 222 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^17 * y * z^-2 * x * z^7 * y^-1 * z^-8 * x * z ] T37.37 : Triangle type {2,8,8} Group order 288 Action chiral Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, (y * z^-1)^4, y^-2 * z * y^3 * x * y^-1 * z^-1 * x ] T37.38 : Triangle type {2,8,8} Group order 288 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, x * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^-2 ] T37.39 : Triangle type {2,8,8} Group order 288 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, (y^-1 * z)^6 ] T37.40 : Triangle type {2,9,18} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y^-9, z^2 * y^-3 * z^4, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T37.41 : Triangle type {2,10,10} Group order 240 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (y * z^-2 * y)^2, y * x * z * y^2 * x * y^-1 * z^-1, z * y * z^-1 * x * y^-1 * z^-2 * x ] T37.42 : Triangle type {2,12,12} Group order 216 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^12 ] T37.43 : Triangle type {2,12,12} Group order 216 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z^-1 * y^4 * z^-3, y^-1 * z * y^-3 * z^-2 * x * y^-1, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T37.44 : Triangle type {2,12,12} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z^2 * y^-1 * z^-3, x * y^-4 * z^-2 * y * z^-1, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y^12 ] T37.45 : Triangle type {2,12,12} Group order 216 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^12 ] T37.46 : Triangle type {2,12,12} Group order 216 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, x * z * y^-3 * z * y^-1 * z^-1 * y, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T37.47 : Triangle type {2,12,24} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-4 * z^-2 * y * z^-1, z * y^-4 * z * y^-1 * z^-1 * x ] T37.48 : Triangle type {2,12,24} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, (y * z^-2)^2 ] T37.49 : Triangle type {2,12,24} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, x * z^3 * y^-1 * z^-4, y^12 ] T37.50 : Triangle type {2,12,24} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y^12 ] T37.51 : Triangle type {2,20,20} Group order 180 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-1 * y^5 * z^-1 * y * z^-1 * y ] T37.52 : Triangle type {2,21,42} Group order 168 Action reflexible [m] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^2 * z^-7 * y^11 * z^-1 ] T37.53 : Triangle type {2,27,54} Group order 162 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-3 * z^-1 * y^2, y * z^-1 * y^10 * z^-15 ] T37.54 : Triangle type {2,40,40} Group order 160 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-14 * y^11 * z^-1 * y^12 * z^-1 ] T37.55 : Triangle type {2,40,40} Group order 160 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^2 * z^-1 * y^6 * z^-1 * y^8 * z^-2 ] T37.56 : Triangle type {2,75,150} Group order 150 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^61 * y^-12 * z ] T37.57 : Triangle type {2,76,76} Group order 152 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^62 * y^-13 ] T37.58 : Triangle type {2,148,148} Group order 148 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^60 * y^-12 * z ] T37.59 : Triangle type {3,3,4} Group order 864 Action chiral Defining relators: [ x^3, x * y * z, y^3, z^4, y * x^-1 * y * x^-1 * y * x^-1 * y^-1 * z * y * x * z^-1 * x^-1, x * z * y * x * z * y * z^-1 * y * x * z^-1 * x * z * y, z * y * z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z * y^-1 * x ] T37.60 : Triangle type {3,3,4} Group order 864 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^3, z^4, y * x^-1 * y * x^-1 * y * x^-1 * y^-1 * z * y * x * z^-1 * x^-1, x * z * y * x * z * y * z^-1 * y * x * z^-1 * x * z * y, z * y^-1 * z^-1 * x^-1 * z * y * x^-1 * z * y * x * z * y^-1 * z^-1 * x ] T37.61 : Triangle type {3,3,6} Group order 432 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^6, (y * x^-1 * z)^3, z^2 * y^-1 * z^-1 * x^-1 * z^2 * y * x, (x^-1 * y^-1 * z^-1 * x * z * y)^2 ] T37.62 : Triangle type {3,3,9} Group order 324 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x, (x^-1 * z^3 * y)^2 ] T37.63 : Triangle type {3,3,9} Group order 324 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^3, z^-3 * x^-1 * z^2 * y^-1, (y * x^-1 * z)^3, z^-1 * x^-1 * y * x * z * y * x^-1 * y * x * z^-1 * x^-1 * y^-1 ] T37.64 : Triangle type {3,3,9} Group order 324 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^-3 * x^-1 * z^2 * y^-1, (y * x^-1 * z)^3, y * x^-1 * y * x * z * y * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 ] T37.65 : Triangle type {3,3,12} Group order 288 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, (x * z * y)^2 ] T37.66 : Triangle type {3,3,12} Group order 288 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * y^-1, x^-1 * z * y^-1 * z^-1 * x^-1 * y * z^-1 * x^-1 * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 * z^-3 ] T37.67 : Triangle type {3,3,12} Group order 288 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-1 * x * y^-1 * x * z * y^-1 * x, z^-4 * x^-1 * z^3 * y^-1 ] T37.68 : Triangle type {3,3,21} Group order 252 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, x^-1 * z * y^-1 * z^-1 * x * z * y * z^-1, (y * x^-1 * z)^3 ] T37.69 : Triangle type {3,4,4} Group order 432 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (z^-1 * x^-1 * y^-1)^3, z^-2 * y * z^-1 * x^-1 * z * y^-1 * z * y^-1 ] T37.70 : Triangle type {3,4,4} Group order 432 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (z^-1 * x^-1 * y^-1)^3, z^-1 * y * x^-1 * y^-2 * x * z * y^-1 * z * y^-1 ] T37.71 : Triangle type {3,4,6} Group order 288 Action chiral Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^6, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, x * z^-3 * x^-1 * y^-1 * x * z^2 * y * z^-1 ] T37.72 : Triangle type {3,4,6} Group order 288 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y * x * y^-1 * z^-1, z^6, z^-1 * x^-1 * y * z^-1 * x^-1 * y * z^-1 * x * z^-1 ] T37.73 : Triangle type {3,4,6} Group order 288 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^6, z^-2 * y * x^-1 * z * y^2, z * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x * z * y * x * z ] T37.74 : Triangle type {3,4,6} Group order 288 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^6, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, z^-1 * x^-1 * z^2 * x^-1 * y^-1 * x * z^2 * y * z^-1 ] T37.75 : Triangle type {3,4,6} Group order 288 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^6, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, x * z^-3 * x^-1 * y^-1 * x * z^2 * y^-1 * z^-1 ] T37.76 : Triangle type {3,4,12} Group order 216 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^2, z^-2 * x * y^-1 * x * y^-1 * z^-2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y ] T37.77 : Triangle type {3,5,15} Group order 180 Action reflexible [m] Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^-5, z * y * z^-1 * x^-1 * z^2 ] T37.78 : Triangle type {3,5,15} Group order 180 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^-5, y^-1 * z^-1 * y * x * z^2 ] T37.79 : Triangle type {3,6,6} Group order 216 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y * z^-2 * x^-1 * y^-2 * z, y * z^-1 * y^2 * x^-1 * y^-1 * z^3 ] T37.80 : Triangle type {3,6,6} Group order 216 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y^6, (z^-1 * y)^3, y^-2 * z^-1 * y^2 * x * y^-1 * z * y * x^-1 ] T37.81 : Triangle type {3,6,6} Group order 216 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, z^-1 * y * z^-1 * y * z^-1 * y * x^-1 * y^-1 * z^-2 * y * z^-1 * y ] T37.82 : Triangle type {3,6,6} Group order 216 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, y * x^-1 * y^-1 * z * y * x^-1 * y * x * z * y^-1 * z^-1 * x^-1 ] T37.83 : Triangle type {3,6,6} Group order 216 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y^6, (z^-1 * y)^3 ] T37.84 : Triangle type {3,6,8} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^6, z * y^2 * x^-1 * z^2, y^-1 * z^-1 * x * y^-1 * x * z * y^-1 * x ] T37.85 : Triangle type {3,6,14} Group order 168 Action chiral Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^6, y^-1 * z^-2 * x^-1 * z^3 ] T37.86 : Triangle type {3,6,18} Group order 162 Action reflexible [m] Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^6, z^-3 * x^-1 * z^2 * y^-1 ] T37.87 : Triangle type {3,6,18} Group order 162 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, y^6, z^-1 * y^2 * x^-1 * y^3 ] T37.88 : Triangle type {3,6,18} Group order 162 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^6, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^3 ] T37.89 : Triangle type {3,6,18} Group order 162 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^-2 * x * y^-1 * x * y^-1 * z^-2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T37.90 : Triangle type {3,6,18} Group order 162 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^2 * y * x^-1 * z^3, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T37.91 : Triangle type {3,8,24} Group order 144 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y ] T37.92 : Triangle type {3,8,24} Group order 144 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * z * y^-1 * z^-1 ] T37.93 : Triangle type {3,12,12} Group order 144 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^7 * z^-1 * y * z^-1 * y * z^-1 ] T37.94 : Triangle type {3,12,12} Group order 144 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, z^-1 * y^3 * z^-2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T37.95 : Triangle type {3,12,12} Group order 144 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, y^2 * z^-2 * y^6 * z^-1 * y ] T37.96 : Triangle type {3,12,12} Group order 144 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (x^-1 * z * y)^2, y^-2 * z^2 * y^-2 * z * x^-1 * z^3 * y^-1 * z ] T37.97 : Triangle type {3,12,12} Group order 144 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y * z^-1 * y * x^-1 * y^-1 * z^-2, z^-1 * y^4 * z^-3 ] T37.98 : Triangle type {3,12,12} Group order 144 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y * x^-1 * y^-1 * x * z * y, y^-1 * z * y^-5 * z * y^-1 * z^3 ] T37.99 : Triangle type {3,12,12} Group order 144 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, z * y * x^-1 * y^-1 * x * y^-1 * z * y^-1, y * x * y^-2 * x * y^-2 * z ] T37.100 : Triangle type {3,12,12} Group order 144 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^-1 * z * y * x^-1 * y^-3, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T37.101 : Triangle type {3,12,12} Group order 144 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T37.102 : Triangle type {3,14,42} Group order 126 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-2 * y * z^-1 * y^5 * z^-2 * y * z^-1 ] T37.103 : Triangle type {3,15,15} Group order 135 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, z^-3 * y^2 * z^-1 * y^6 * z^-2 * y ] T37.104 : Triangle type {3,30,30} Group order 120 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, y^7 * z^-1 * y * z^-1 ] T37.105 : Triangle type {3,38,114} Group order 114 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-27 * z * y^-1 * z * y^-7 * z ] T37.106 : Triangle type {3,39,39} Group order 117 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-28 * z * y^-1 * z * y^-7 * z ] T37.107 : Triangle type {3,111,111} Group order 111 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-26 * z * y^-1 * z * y^-8 ] T37.108 : Triangle type {4,4,4} Group order 288 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, (x * y^-1)^4, x * z^-1 * y * x^-2 * z * y^2 * z^-1, y * z^-1 * y * x^-2 * y^-1 * z^2 * x^-1 ] T37.109 : Triangle type {4,4,4} Group order 288 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, (x * y^-1)^4, y^-1 * z^-1 * y * x^-2 * z * y^-1 * z^-1 * x, x * z * x^-1 * y * x^-1 * y * z^-1 * y * z^-1 ] T37.110 : Triangle type {4,4,4} Group order 288 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, z * y^-1 * z^-2 * y * z^-1 * y * z^-1 * x^-1 * z * y^-1 * z * y^-1 ] T37.111 : Triangle type {4,4,4} Group order 288 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, z^2 * y * z^-1 * y * z^-1 * y * z^-1 * x^-1 * z * y^-1 * z * y^-1 ] T37.112 : Triangle type {4,4,5} Group order 240 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, (x * z * y)^2, z^2 * y * x^-1 * z * y^-1 * x ] T37.113 : Triangle type {4,4,5} Group order 240 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^2 * y^-1 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T37.114 : Triangle type {4,4,6} Group order 216 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * x * z^-1 * x^-1 * z * y * x, z^-3 * x^-1 * z^2 * y^-1 ] T37.115 : Triangle type {4,4,6} Group order 216 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z^6, z^-3 * x^-1 * z^2 * y^-1 ] T37.116 : Triangle type {4,4,6} Group order 216 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * z * y^-1, z^6, z^-1 * y * x * z^-1 * x^-1 * y^-1 * z * x^-1 * y^-1 ] T37.117 : Triangle type {4,4,6} Group order 216 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, z^-1 * y * x * z^-1 * x^-1 * y^-1 * z * y * x ] T37.118 : Triangle type {4,4,10} Group order 180 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x ] T37.119 : Triangle type {4,4,20} Group order 160 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^-2 * y * x^2 * z * y * z^-1 ] T37.120 : Triangle type {4,4,20} Group order 160 Action reflexible [n] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-4 * x^-1 * z * y^-1 * z^-2 ] T37.121 : Triangle type {4,4,20} Group order 160 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-11 * x * y^-1 * x * y^-1 * z^-7 ] T37.122 : Triangle type {4,4,20} Group order 160 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z^3 * y^-1 * z^-1 * x * z * y * z^-2 * x^-1 * z ] T37.123 : Triangle type {4,4,20} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^7 * y * z^-4 * x^-1 * y^-1 * z^-7 * x ] T37.124 : Triangle type {4,4,38} Group order 152 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^25 * y * x^-1 * y * x^-1 * z^11 ] T37.125 : Triangle type {4,4,74} Group order 148 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^24 * y * x^-1 * z^12 ] T37.126 : Triangle type {4,5,10} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, z^2 * y^-1 * x * z^2, x^-1 * z * y * x * y^-1 * z^-1 ] T37.127 : Triangle type {4,5,10} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, z^2 * y^-1 * x * z^2, x^-1 * z * y * x * z * y ] T37.128 : Triangle type {4,6,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, y * x^-1 * z * y * z^-1 * y * z^-1 * x^-1 * z, z^-4 * x^-1 * z^3 * y^-1 ] T37.129 : Triangle type {4,6,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, y^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^3 ] T37.130 : Triangle type {4,6,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^6, z^-2 * y * x^-1 * y^-1 * z^-1, x * z * y^2 * z^-2 ] T37.131 : Triangle type {4,6,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y^6, (z^-1 * x)^3 ] T37.132 : Triangle type {4,6,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^-3 * x^-1 * y * z^-2, x^-1 * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T37.133 : Triangle type {4,6,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y^6, (x * z^-2)^2, x^-1 * y^2 * x^-1 * y * x * z^-1, z^-2 * x^-1 * y^-1 * x * z * y * z^-1 ] T37.134 : Triangle type {4,6,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^6 ] T37.135 : Triangle type {4,6,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^4 * y^-1 * z^-3 * x * z^4 ] T37.136 : Triangle type {4,6,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, x^-1 * z^5 * y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * z^-2 ] T37.137 : Triangle type {4,6,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, z * y^2 * x^-1 * z * x^-1 ] T37.138 : Triangle type {4,6,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, (x * z^-1)^2, y * x * y^-1 * x * z^2, y^6 ] T37.139 : Triangle type {4,8,8} Group order 144 Action reflexible [n] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, x * y^-2 * x * z^-2 ] T37.140 : Triangle type {4,8,8} Group order 144 Action chiral Defining relators: [ x * y * z, x^4, (x * y^-2)^2, y^-1 * z * y^-1 * x * z * x^-1 ] T37.141 : Triangle type {4,8,8} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T37.142 : Triangle type {4,8,8} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T37.143 : Triangle type {4,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, z * y^-1 * z^-2 * x^-1 * z^4 ] T37.144 : Triangle type {4,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z * y * x^-1 * z * y * x^-1 * z^4 ] T37.145 : Triangle type {4,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, z * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T37.146 : Triangle type {4,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, z * y^-1 * z^-2 * x^-1 * z^4 ] T37.147 : Triangle type {4,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, y * x^-1 * z^2 * y * x^-1 * z^7 * y^-1 * x^-1 * z^4 ] T37.148 : Triangle type {4,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z * y * x^-1 * z * y * x * z^4 ] T37.149 : Triangle type {4,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y^8, z * y^-1 * z^-2 * x^-1 * z^4 ] T37.150 : Triangle type {4,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, z * y^-1 * z^-2 * x^-1 * z^4 ] T37.151 : Triangle type {4,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^2 * y * z^-1 * x^-1 * z^4 ] T37.152 : Triangle type {4,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^8, z * y^-1 * z^-2 * x^-1 * z^4 ] T37.153 : Triangle type {4,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^5 * y * x^-1 * z^2 * y^-1 * z^-1 * x^-1 * z^6 ] T37.154 : Triangle type {4,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, z^2 * y * z^-1 * x^-1 * z^4 ] T37.155 : Triangle type {4,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^8, z * y * x^-1 * z * y * x * z^4 ] T37.156 : Triangle type {4,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, z^2 * y * z^-1 * x^-1 * z^4 ] T37.157 : Triangle type {4,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, y * z^-1 * y * x^-1 * z * y^-1 * z, y * z^-3 * x^-1 * z^4 ] T37.158 : Triangle type {4,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z^-2 * y * x^-1 * y^-1 * z^-1 * y, y * z^-3 * x^-1 * z^4 ] T37.159 : Triangle type {4,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y^8, z * y * x^-1 * z * y * x^-1 * z^4 ] T37.160 : Triangle type {4,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y^8, z^2 * y * z^-1 * x^-1 * z^4 ] T37.161 : Triangle type {4,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, z * x^-1 * y^-1 * x * y^-1 * z, z^2 * y * z^-1 * x^-1 * z^4 ] T37.162 : Triangle type {4,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, z^-1 * y^2 * x * z^-1 * x, z^-3 * x^-1 * y^-1 * x * y^-1 * z^-3 ] T37.163 : Triangle type {4,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, y * z^-3 * x^-1 * z^4 ] T37.164 : Triangle type {4,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y^8, y * z^-3 * x^-1 * z^4 ] T37.165 : Triangle type {4,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * x^-1 * z^2, y^8, (y * z^-1 * y^2)^2 ] T37.166 : Triangle type {4,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^8, (y * z^-1 * y^2)^2 ] T37.167 : Triangle type {4,14,28} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * z * y^-5 * z * y^-1 * z * y^-1 * z * y^-1 ] T37.168 : Triangle type {4,18,36} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z * y^-5 * z * y^-1 ] T37.169 : Triangle type {4,26,52} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^8 * z^-2 * y^7 * z^-1 * y * z^-1 * y * z^-1 * y * z^-3 ] T37.170 : Triangle type {4,50,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^-10 * z * y^-1 * z * y^-1 * z * y^-6 * z^2 * y^-1 * z ] T37.171 : Triangle type {5,10,10} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, x^-5, y * z^-1 * x^-1 * y^-1 * z, x^-1 * y^-1 * x^2 * z * x^-1 ] T37.172 : Triangle type {5,10,22} Group order 110 Action chiral Defining relators: [ x * y * z, x^-5, z^-2 * x^-1 * y^-1 * z^-1, y^-2 * x^2 * z * y^-1 ] T37.173 : Triangle type {5,10,22} Group order 110 Action chiral Defining relators: [ x * y * z, x^-5, y^-1 * z^-1 * x^2 * y^-2, y * x^-1 * y^-1 * x * z^2 ] T37.174 : Triangle type {6,6,6} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y * z^-1, x^6, y^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T37.175 : Triangle type {6,6,6} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, y^6, (x * z * y)^2 ] T37.176 : Triangle type {6,6,6} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y^6, y^-1 * z^-1 * y * x * z * x^-1, z^6, y * x^-3 * z * x^-2 ] T37.177 : Triangle type {6,6,6} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, (x * y^-1)^2, (y * z^-1)^2, x^6, y^6, z^-1 * x * z^-1 * x^2 * z^-1 * x * z^-1 ] T37.178 : Triangle type {6,6,6} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, x^6, (x * z^-1 * x)^2, z^-1 * x^-1 * y^-1 * x * z * y, y^6 ] T37.179 : Triangle type {6,6,6} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, y^6, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T37.180 : Triangle type {6,6,15} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, y * x^-1 * y * x^-1 * z^3 ] T37.181 : Triangle type {6,12,12} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, y^-2 * x^2 * y^-2, z^-2 * x^2 * z^-2, (z^-1 * y)^3 ] T37.182 : Triangle type {6,12,12} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, x^6, y^-2 * x^2 * y^-2, (z^-1 * y)^3 ] T37.183 : Triangle type {6,12,12} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^6, (z^-1 * y)^3 ] T37.184 : Triangle type {6,12,12} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * y^3 * z^-2 ] T37.185 : Triangle type {6,12,12} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, (z^-1 * y)^3 ] T37.186 : Triangle type {6,12,12} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, (z^-1 * y)^3, y^-1 * z * y * x^-1 * y^-3 ] T37.187 : Triangle type {6,12,12} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * y^-1 * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, (z^-1 * y)^3 ] T37.188 : Triangle type {6,16,48} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^-2 * z^5 * x^-1 * z^5 * y^-1 * z * y^-2 ] T37.189 : Triangle type {6,16,48} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, z^-3 * y^2 * z^-3 ] T37.190 : Triangle type {6,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, (y * z^-1)^2, y^2 * x^-1 * z^2 ] T37.191 : Triangle type {6,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^6, y^-2 * x^2 * y^-1 * z, y^2 * x^2 * z^2 ] T37.192 : Triangle type {6,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y^4 * z^-3 ] T37.193 : Triangle type {6,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, x^6, x^-1 * z * y * x * y^-1 * z^-1 ] T37.194 : Triangle type {6,45,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z * y^-1 * z * y^-4 * z^5 * y^-1 * z ] T37.195 : Triangle type {6,45,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, z^2 * y^-1 * z * y^-4 * z^7 ] T37.196 : Triangle type {8,12,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, y^2 * x * z^-1, x^-1 * z * y * x * y^-1 * z^-1, x^8 ] T37.197 : Triangle type {8,12,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, y * x^-2 * y^2, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * x)^3 ] T37.198 : Triangle type {8,12,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, y^2 * x * z^-1, (x^-1 * z * y)^2 ] T37.199 : Triangle type {8,12,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, y * x^-2 * y^2, (x^-1 * z * y)^2 ] T37.200 : Triangle type {8,12,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * y * z^-2, x^8 ] T37.201 : Triangle type {8,12,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^3 * x^-1 * y * z^-1 * y, x^8 ] T37.202 : Triangle type {8,12,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^-1 * z^6 * y^-3 * z^2 ] T37.203 : Triangle type {8,12,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, y * z^-1 * y * z^-5 * y^2 * z^-2 ] T37.204 : Triangle type {8,12,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^2 * z^-2, x^8 ] T37.205 : Triangle type {8,12,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-2 * y^2 * z^-2 ] T37.206 : Triangle type {8,22,88} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, y^-2 * z^5 * x * y^-4 ] T37.207 : Triangle type {9,9,9} Group order 108 Action reflexible [n] Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, z^-1 * x^-1 * y * x^-1 * z * x^-1 * y^-1 ] T37.208 : Triangle type {9,9,9} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, (x * z * y)^2 ] T37.209 : Triangle type {10,15,30} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^-1 * z * x^-1 * y^-1 * z, y^-3 * x^2 * y^-3 ] T37.210 : Triangle type {10,15,30} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, (y * z^-1 * y)^2, (z^-1 * x)^3 ] T37.211 : Triangle type {10,15,30} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, y^2 * x * z^-1, z^-2 * x^-1 * z * y^-1, x^10 ] T37.212 : Triangle type {12,12,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y * x^2 * y^-1 * z^-1, y^-1 * z^-1 * x^2 * z * y^-1, z^-1 * x * y^-1 * x * z^-1 * y, (x * z * y)^2 ] T37.213 : Triangle type {12,12,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, (y * z^-1)^2 ] T37.214 : Triangle type {12,12,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x^4 * y^-3, z^-1 * x^4 * z^-3 ] T37.215 : Triangle type {12,12,12} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * x^4 * y^-3 ] T37.216 : Triangle type {12,21,84} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^3, y^2 * x^-4 * y^5 ] T37.217 : Triangle type {12,28,42} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^5 * x^-2 * z^2, y^-2 * z^2 * y^-2 * x^5 * y^-1 ] T37.218 : Triangle type {16,40,80} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-7 * z^2 * x^-5 * y^2 * x^-2 ] T37.219 : Triangle type {16,40,80} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-1 * z^3 * x^-4 * z^2, y^-1 * z^5 * x * y^-4 ] T37.220 : Triangle type {16,40,80} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^3 * x^-5 * y^3 * z^-1 * y^3 ] T37.221 : Triangle type {16,40,80} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^6 * x^-2 * z^4 ] T37.222 : Triangle type {20,40,40} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, z^8 * x^-2 * z^4 ] T37.223 : Triangle type {20,40,40} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * y^-2, x * z^-1 * x^3 * z^-3 ] T37.224 : Triangle type {20,40,40} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-11 * z^2 * x^-5 * y^2 * x^-2 ] T37.225 : Triangle type {20,40,40} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x * z^-1 * x^7 * y^-1 * x ] T37.226 : Triangle type {21,21,21} Group order 84 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y * x * y^-1, (x * z^-1)^2, y^-7 * x^3 * y^-2 ] T37.227 : Triangle type {21,21,21} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, y^-2 * x^2 * y^-1 * z, y^2 * x^2 * z^2, y^-1 * z^-1 * x^2 * z^-1 * x ] T37.228 : Triangle type {26,39,78} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^4 * x^-2 * y * x^-1 * y^4 * x^-1 * y^5 * x^-1 * y * x^-1 ] T37.229 : Triangle type {26,39,78} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, y^-1 * z^8 ] T37.230 : Triangle type {26,39,78} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, y^-1 * z * y^-1 * z^9 ] T37.231 : Triangle type {26,39,78} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * x^-4 * z^2, y^-1 * z^3 * y^-1 * x * y^-4 ] T37.232 : Triangle type {26,39,78} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-5 * x^2 * z^-5 * y * z^-4 ] T37.233 : Triangle type {26,39,78} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^3 * z^-2 * y^4 * z^-2 * y^4 ] T37.234 : Triangle type {26,39,78} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, z^5 * x^-1 * z^4 ] T37.235 : Triangle type {26,39,78} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^-1 * z * y^-1 * z^5 * y^-4 ] T37.236 : Triangle type {26,39,78} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * y^-4, x^-1 * z^3 * x^-6 ] T37.237 : Triangle type {26,39,78} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-4 * z^4 * x^-5 * y * x^-1 ] T37.238 : Triangle type {26,39,78} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^-10 * y * x^-2 * y * x^-1 * y * x^-11 ] T37.239 : Triangle type {27,27,27} Group order 81 Action reflexible [n] Defining relators: [ x * y * z, z^-1 * x^3 * z^-2, x * y^-1 * x^2 * y^-2 ] T37.240 : Triangle type {27,27,27} Group order 81 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-4 * z * y^-5 * z^2 * y^-3 ] T37.241 : Triangle type {38,76,76} Group order 76 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-2 * z^2 * y^-2 * x * y^-4 ] T37.242 : Triangle type {38,76,76} Group order 76 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^17 * x^-2 * y^7 ] T37.243 : Triangle type {38,76,76} Group order 76 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-7 * z, y^-1 * z^5 * y^-2 * z^2 ] T37.244 : Triangle type {38,76,76} Group order 76 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, x^-1 * z^4 * x^-4 * z^2 ] T37.245 : Triangle type {38,76,76} Group order 76 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-1 * y * x^-6 * y^3 * x^-1 ] T37.246 : Triangle type {38,76,76} Group order 76 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, (y^4 * z^-1 * y^3)^2 ] T37.247 : Triangle type {38,76,76} Group order 76 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-3 * z^5 * x * y^-4 ] T37.248 : Triangle type {38,76,76} Group order 76 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, y * x^-1 * y * x^-5 * y^6 ] T37.249 : Triangle type {38,76,76} Group order 76 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-38, y * z^-1 ] T37.250 : Triangle type {75,75,75} Group order 75 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^32 * x^-1 * y^5, x * z^-1 ] T37.251 : Triangle type {75,75,75} Group order 75 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * x * y^-4, x^-1 * z^3 * x^-4 * z^2 ] T37.252 : Triangle type {75,75,75} Group order 75 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-4 * x * y^-3, x^-1 * z^3 * x^-4 * z^2 ] Genus 38 T38.1 : Triangle type {2,4,78} Group order 312 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-70 * x * y * z^-7 ] T38.2 : Triangle type {2,4,152} Group order 304 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-68 * x * y^-1 * z^-7 ] T38.3 : Triangle type {2,6,6} Group order 444 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^6, x * y^-2 * z * y^-2 * z * y^-2 * z^-1 * x * y^-1 * z^-1 * y^2 * z^-1 * y^2 * z^-1 * y ] T38.4 : Triangle type {2,6,40} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^40 ] T38.5 : Triangle type {2,6,114} Group order 228 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^13 * y * x * z^14 * y * z^-8 * x * z ] T38.6 : Triangle type {2,8,15} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, x * z^2 * y * x * z^3 * y * z^-1 * x * y^-1 * z^-6 ] T38.7 : Triangle type {2,8,52} Group order 208 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^10 * y * x * z * y * x * y * x * y^-1 * z^-4 * x * y^-1 * z^-1 * x * z^5 ] T38.8 : Triangle type {2,10,95} Group order 190 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^8 * y * x * y * z^-5 * x * z^4 ] T38.9 : Triangle type {2,12,32} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^-5 * x * z * y * x * z * y * x * y^-1 * z^-6 ] T38.10 : Triangle type {2,28,42} Group order 168 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^4 * y * z^-2 * x * z * y^-1 * z^-3 * x, (y^-3 * z^3 * y^-1)^2 ] T38.11 : Triangle type {2,77,154} Group order 154 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^63 * y^-12 * z ] T38.12 : Triangle type {2,78,78} Group order 156 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^64 * y^-13 ] T38.13 : Triangle type {2,152,152} Group order 152 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^62 * y^-12 * z ] T38.14 : Triangle type {3,6,6} Group order 222 Action chiral Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, x * z * y * x * z * y * x * z * y^-1 * z * y ] T38.15 : Triangle type {3,6,6} Group order 222 Action chiral Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y * z^-2 * y^2 * z^-2 * y * x^-1 * y^-1 * z^-1 * y * z^-1 * y * z^-1 ] T38.16 : Triangle type {3,40,40} Group order 120 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^27 * y^-3 * z * y^-7 * z ] T38.17 : Triangle type {3,114,114} Group order 114 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-27 * z * y^-1 * z * y^-6 * z^2 ] T38.18 : Triangle type {4,4,39} Group order 156 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * y * x^-2 * z * y * z^-1 ] T38.19 : Triangle type {4,4,39} Group order 156 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^26 * y * x^-1 * y * x^-1 * z^11 ] T38.20 : Triangle type {4,4,76} Group order 152 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^25 * y * x^-1 * z^12 ] T38.21 : Triangle type {4,8,9} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z * y^2 * x^-1 * z * y^-1 * z, z^4 * y^-1 * x^-1 * z^4 ] T38.22 : Triangle type {4,10,30} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-2 * x^-1 * z^3, y^10 ] T38.23 : Triangle type {4,12,20} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^3 * x^-1 * y^-1 * z * y, z^5 * y^-1 * x * z^4 ] T38.24 : Triangle type {4,14,56} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, y^-2 * z * y^-5 * z * y^-1 * z * y^-1 * z * y^-1 ] T38.25 : Triangle type {4,15,15} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, y^2 * z^-1 * y * z^-3 * y^2 * z^-2 * y^4 ] T38.26 : Triangle type {4,52,52} Group order 104 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^4 * z^-2 * y^4 * z^-1 * y^13 * z^-1 * y ] T38.27 : Triangle type {5,95,95} Group order 95 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z^2 * y^-1 * z^10 * y^-1 * z * y^-3 ] T38.28 : Triangle type {5,95,95} Group order 95 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-5, z^14 * y^-1 * z * y^-1 * z^2 ] T38.29 : Triangle type {6,6,20} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^8 * y * x^-1 * y * x^-1 * z^3 * y * z^-1 * x^-1 * z^5 ] T38.30 : Triangle type {6,6,57} Group order 114 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^9 * y * x * z^3 * y * x * z^2 * y * z^-1 * x^-1 * z ] T38.31 : Triangle type {6,32,32} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^6, y * z^-1 * y^4 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T38.32 : Triangle type {8,8,26} Group order 104 Action reflexible [n] Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, z^-1 * y * x^-2 * z^2 * y ] T38.33 : Triangle type {8,8,26} Group order 104 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^7 * y^-1 * x * y^-1 * x * z^4 ] T38.34 : Triangle type {8,44,88} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, y^-2 * z^5 * y^-3 * z ] T38.35 : Triangle type {8,44,88} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, z * y^-1 * z^9 ] T38.36 : Triangle type {10,18,45} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x * y^-1 * x^8 * z^-1, y^-5 * x^-1 * z^4 ] T38.37 : Triangle type {12,12,16} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x * y^-1 * x * y^-1 * x^4 * y^-1 * x * y^-1 * x, y^-1 * x * z * y^-1 * x * y^-1 * x * z^4 ] T38.38 : Triangle type {12,42,84} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-5 * z^2, x^-2 * z * x^-1 * z^4 * x^-4 * z^2 ] T38.39 : Triangle type {14,42,42} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, x^-2 * z^4 * x^-4 * z^2 ] T38.40 : Triangle type {14,42,42} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^7 * z^-4 * x * z^-1 * x * z^-1 * x ] T38.41 : Triangle type {14,42,42} Group order 84 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^4 * x^-4 * z^2, y * x^-5 * y^3 * z^-1 * y ] T38.42 : Triangle type {15,18,18} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^4 * z * y, y^4 * z^-2 ] T38.43 : Triangle type {20,80,80} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-6 * y * x^-1 * y * x^-8 * y * x^-1 * y * x^-1 ] T38.44 : Triangle type {20,80,80} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * y^-2 * z^2, x * y^-4 * x^6 ] T38.45 : Triangle type {20,80,80} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y * x^-1 * y * z^-2 * y^8 ] T38.46 : Triangle type {21,28,28} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * y * z^-1, x^5 * y^-1 * x * z^-1 ] T38.47 : Triangle type {21,28,28} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * z * y^-1, z^-1 * x * z^-1 * x * z^-2 ] T38.48 : Triangle type {21,28,28} Group order 84 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-3 * y^-1 * x^2, x^5 * y^-1 * x * z^-1 ] T38.49 : Triangle type {39,78,78} Group order 78 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^39, y * z^-1 ] T38.50 : Triangle type {39,78,78} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^13 * x^-1 * y * x^-1 ] T38.51 : Triangle type {39,78,78} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * x^-3 * z^2, y^-2 * z^3 * y^-1 * x * y^-4 ] T38.52 : Triangle type {39,78,78} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^-1 * z^2 * x^-7 ] T38.53 : Triangle type {39,78,78} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^-6 * x * z^-3 * x^2 * z^-9 ] T38.54 : Triangle type {39,78,78} Group order 78 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, y^-1 * z * y^-1 * z^5 * y^-1 * z^3 ] T38.55 : Triangle type {77,77,77} Group order 77 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^33 * x^-1 * y^5, x * z^-1 ] T38.56 : Triangle type {77,77,77} Group order 77 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * y^-3 * z, x^-9 * y ] T38.57 : Triangle type {77,77,77} Group order 77 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-2 * z * x^-1 * z^4 * x^-4 * z^2 ] T38.58 : Triangle type {77,77,77} Group order 77 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x * y^-1, z^-7 * x^5 * z^-4 * x * z^-1 * x * z^-2 ] T38.59 : Triangle type {77,77,77} Group order 77 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^17 * x^-4 * y^6 ] T38.60 : Triangle type {77,77,77} Group order 77 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-6 * y * x^-9 ] T38.61 : Triangle type {77,77,77} Group order 77 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-4 * y, z^-5 * y * z^-5 * y * z^-1 * y * z^-2 ] T38.62 : Triangle type {77,77,77} Group order 77 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, y^-1 * z^8 ] Genus 39 T39.1 : Triangle type {2,3,12} Group order 912 Action chiral Defining relators: [ x^2, y^3, x * y * z, z * y * z^-3 * x * y^-1 * z^-4 * x, x * z^2 * y * x * z * y * z^-2 * y * z^-1 * x * z * y^-1 * z^-2 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z * y^-1 * z^-2 ] T39.2 : Triangle type {2,4,42} Group order 336 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-26 * x * z^9 * y^-1 * x * z * y^-1 * z^-4 ] T39.3 : Triangle type {2,4,80} Group order 320 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-72 * x * y * z^-7 ] T39.4 : Triangle type {2,4,80} Group order 320 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-26 * x * z^5 * y * z^-2 * x * z^2 * y^-1 * z^-3 ] T39.5 : Triangle type {2,4,156} Group order 312 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-70 * x * y^-1 * z^-7 ] T39.6 : Triangle type {2,8,9} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, z^-4 * x * y * z^-4 ] T39.7 : Triangle type {2,8,28} Group order 224 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^16 * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * x * z^5 ] T39.8 : Triangle type {2,8,28} Group order 224 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-4 * x * z^4 * y * z^-2 * x * z^7 * y * x * y^-1 * z^-8 ] T39.9 : Triangle type {2,8,104} Group order 208 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-7 * x * z^8 * y * x * y^-1 * z^-9 ] T39.10 : Triangle type {2,8,104} Group order 208 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-5 * x * z^3 * y * z^-2 * x * z^2 * y * z^-2 * x * z^2 * y^-1 * z^-2 * x * z^2 * y^-1 * z^-2 ] T39.11 : Triangle type {2,10,12} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z^2 * y^-1 * z^-3, z^2 * y^3 * x * z * y^-1 ] T39.12 : Triangle type {2,12,48} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-12, z^9 * y * x * z^4 * y^-1 * z^-1 * x ] T39.13 : Triangle type {2,12,48} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, z^3 * y * x * y^-1 * z^-3 * x, y^12 ] T39.14 : Triangle type {2,14,91} Group order 182 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-1 * x * z^3 * y * z^-2 * x * y * z^-5 ] T39.15 : Triangle type {2,16,24} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^-6 * z^-1 * y * x, z^6 * y * z^-5 * x ] T39.16 : Triangle type {2,16,24} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, z * y * x * z * y * x * z * y * x * y^-1 * z^-5 * x ] T39.17 : Triangle type {2,28,84} Group order 168 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, z^-2 * y^10 * z^-3 * y^12 * z^-1 ] T39.18 : Triangle type {2,42,42} Group order 168 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-38 * z * y^-1 ] T39.19 : Triangle type {2,79,158} Group order 158 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^65 * y^-12 * z ] T39.20 : Triangle type {2,80,80} Group order 160 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-14 * y^11 * z^-1 * y^11 * z^-1 * y ] T39.21 : Triangle type {2,80,80} Group order 160 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^66 * y^-13 ] T39.22 : Triangle type {2,156,156} Group order 156 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^64 * y^-12 * z ] T39.23 : Triangle type {3,3,6} Group order 456 Action chiral Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, y * x * z * y^-1 * z^-1 * x * z * y * x^-2 * z * y * x * z * y * x * z ] T39.24 : Triangle type {3,3,79} Group order 237 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^2 * y^-1 * z^-2 * x^-1 * z^3 * y^-1 * z^-1 * x^-1 ] T39.25 : Triangle type {3,4,10} Group order 240 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, x^-1 * y * z^-3 * x^-1 * y^-1 * z^-3 ] T39.26 : Triangle type {3,4,12} Group order 228 Action chiral Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, z * y^-1 * z^-1 * x^-1 * y^-1 * z^-2 * x^-1 * y * x * z^2 * y * x ] T39.27 : Triangle type {3,9,9} Group order 171 Action chiral Defining relators: [ x^3, x * y * z, z^-1 * y^2 * x^-1 * y * x * y^-1, y * z^-1 * y * x^-1 * z^3 ] T39.28 : Triangle type {3,9,9} Group order 171 Action chiral Defining relators: [ x^3, x * y * z, z^-2 * y * x * y^-1 * z^-1, z^-1 * x^-1 * y * x^-1 * z * y^2 ] T39.29 : Triangle type {3,9,9} Group order 171 Action chiral Defining relators: [ x^3, x * y * z, y * z^-1 * y * x^-1 * y^-1 * z^-1 ] T39.30 : Triangle type {3,40,120} Group order 120 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-29 * z * y^-1 * z * y^-7 * z ] T39.31 : Triangle type {3,117,117} Group order 117 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-28 * z * y^-1 * z * y^-6 * z^2 ] T39.32 : Triangle type {4,4,21} Group order 168 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^2, z^-15 * x^-1 * y^-1 * x * z * y * z^-3 ] T39.33 : Triangle type {4,4,40} Group order 160 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y^-1 * z^-1 * y * x * z * x^-1, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T39.34 : Triangle type {4,4,40} Group order 160 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * y^-1 * z^-1 ] T39.35 : Triangle type {4,4,40} Group order 160 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^33 * y * x * z^6 ] T39.36 : Triangle type {4,4,40} Group order 160 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-12 * x * z * y * z^-6 ] T39.37 : Triangle type {4,4,40} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^7 * y^-1 * z^-4 * x^-1 * y^-1 * z^-7 * x ] T39.38 : Triangle type {4,4,40} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^-12 * x * y^-1 * z^-7 ] T39.39 : Triangle type {4,4,78} Group order 156 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^26 * y * x^-1 * z^12 ] T39.40 : Triangle type {4,8,32} Group order 128 Action chiral Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, y^-1 * z^-3 * x^-1 * z^4 ] T39.41 : Triangle type {4,8,32} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, y * x^-1 * z^2 * y * x^-1 * z^7 * y^-1 * x * z^4 ] T39.42 : Triangle type {4,8,32} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^7 * y^-1 * z^-2 * x^-1 * z^6 ] T39.43 : Triangle type {4,9,9} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^2 * x^-1 * z^2, y * x * y^-1 * x * y^-1 * z^-1, z^2 * y^-6 * z ] T39.44 : Triangle type {4,10,60} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^10 ] T39.45 : Triangle type {4,12,30} Group order 120 Action chiral Defining relators: [ x * y * z, x^4, y^2 * x^2 * z^2, y^-1 * z^-1 * y * x * z * x^-1, (y * z^-1 * y)^2 ] T39.46 : Triangle type {4,12,30} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^3 * y^-1 * z^-2 * x^-1 * z^4 ] T39.47 : Triangle type {4,15,20} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, z^-2 * y * x * z^-1 * y ] T39.48 : Triangle type {4,27,108} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^9 * z^-2 * y^7 * z^-1 * y * z^-1 * y * z^-1 * y * z^-3 ] T39.49 : Triangle type {4,28,28} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * z * y^-5 * z * y^-1 * z * y^-2 * z ] T39.50 : Triangle type {4,28,28} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y^10 * z^-2 * y^7 * z^-1 * y * z^-1 * y * z^-1 * y * z^-3 ] T39.51 : Triangle type {4,28,28} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-24 * z * y^-2 * z ] T39.52 : Triangle type {4,104,104} Group order 104 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^7 * z^-2 * y^7 * z^-1 * y * z^-1 * y * z^-1 * y * z^-3 ] T39.53 : Triangle type {4,104,104} Group order 104 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y^8 * z^-2 * y^7 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T39.54 : Triangle type {6,10,10} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, y^3 * x * y^-1 * z^-1 ] T39.55 : Triangle type {6,32,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, z * y^-1 * z^5 * x^-1 * z^5 * y^-1 * z^3 ] T39.56 : Triangle type {6,48,48} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^6, y^-2 * z^5 * x^-1 * z^5 * y^-1 * z^3 ] T39.57 : Triangle type {6,48,48} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y * z^-1 * y^3 * z^-3 ] T39.58 : Triangle type {7,15,15} Group order 105 Action reflexible [n] Defining relators: [ x * y * z, y * x^2 * z, z * x^-2 * y * x^-1, z * y^-1 * z^3 * y^-2 * z * y^-6 * z ] T39.59 : Triangle type {7,91,91} Group order 91 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, y^-3 * z * y^-4 * z^4 * y^-1 ] T39.60 : Triangle type {7,91,91} Group order 91 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z * y^-1 * z * y^-4 * x * y^-4 * z ] T39.61 : Triangle type {7,91,91} Group order 91 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-7, z^2 * y^-1 * z * y^-4 * x * y^-4 * z ] T39.62 : Triangle type {8,8,14} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^2 * y * z^-1 * x^-1 * y^-1 * z^-4 * x^-1 * y^-1 * x * z^4 ] T39.63 : Triangle type {8,8,14} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^9 * y^-1 * x^-1 * z^4 ] T39.64 : Triangle type {8,8,52} Group order 104 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^2 * y^-1 * z^-1 * x^-1 * z^3 * y^-1 * z^-1 * x * z^4 ] T39.65 : Triangle type {8,8,52} Group order 104 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, y^-1 * z^-1 * x * z * y^-1 * x * z^3 * y^-1 * z^-1 * x * z^4 ] T39.66 : Triangle type {8,16,48} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * y * x^-1 * z^3 ] T39.67 : Triangle type {8,16,48} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, (x * z^-2)^2, z^-3 * x^-1 * z * y * z^-1 ] T39.68 : Triangle type {8,16,48} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, (x * z^-2)^2, z^2 * y * x^-1 * z^3 ] T39.69 : Triangle type {8,16,48} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z * y * z^-1, x^8 ] T39.70 : Triangle type {8,24,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, z^-1 * y * z^-1 * y * z^-2 ] T39.71 : Triangle type {8,24,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, z^-1 * y^2 * x^-1 * y^3 ] T39.72 : Triangle type {8,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, y * x^-2 * z * x^-1, y^-1 * z^5 * y^-4 * z * y^-1 ] T39.73 : Triangle type {8,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^8, y^4 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T39.74 : Triangle type {9,30,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^9, z^-5 * y^4 * z^-1 ] T39.75 : Triangle type {9,30,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^9, y^-5 * x * z^4 * y^-1 ] T39.76 : Triangle type {12,12,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, y^-1 * x^4 * y^-3 ] T39.77 : Triangle type {12,12,24} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, y^-1 * x^4 * y^-3 ] T39.78 : Triangle type {12,12,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * z * y^-1, z * y^-1 * z * x^-1 * z^3 ] T39.79 : Triangle type {12,12,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T39.80 : Triangle type {12,16,16} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, y * z^-1 * y * z^-1 * y * x^2 * z^-1 * y * z^-1 ] T39.81 : Triangle type {12,16,16} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * y^-1 * z^-1, y^6 * z^-2 ] T39.82 : Triangle type {14,84,84} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^2 * y^-5 * x^5 * y^-1 * x^2 ] T39.83 : Triangle type {14,84,84} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * x^-3 * z^2, y^-5 * x^5 * y^-1 ] T39.84 : Triangle type {14,84,84} Group order 84 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^3 * y^-3 * x^3 * y^-3 * x^5 ] T39.85 : Triangle type {21,28,84} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^5 * x^-1 * z^3, x^-6 * y^4 ] T39.86 : Triangle type {21,28,84} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-5 * x^3 * y^-3 * z * y^-1 * x * y^-2 ] T39.87 : Triangle type {21,28,84} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^2 * y^-5 * x * y^-1 * x * y^-1 * x^8 * y^-1 * x^3 ] T39.88 : Triangle type {21,28,84} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-2 * z^4 * x^-6 ] T39.89 : Triangle type {21,28,84} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-5 * z^2, y^-1 * z * y^-1 * z^5 * y^-4 ] T39.90 : Triangle type {27,81,81} Group order 81 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-27 ] T39.91 : Triangle type {27,81,81} Group order 81 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * x * y^-4, x^-1 * z^4 * x^-4 * z^2 ] T39.92 : Triangle type {27,81,81} Group order 81 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * x * y^-4, x^-1 * z^3 * x^-6 ] T39.93 : Triangle type {27,81,81} Group order 81 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-1 * x * z^-4 * x^2 * z^-5 * y * z^-4 ] T39.94 : Triangle type {27,81,81} Group order 81 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, y^3 * x^-5 * y^5 * x^-1 * y ] T39.95 : Triangle type {27,81,81} Group order 81 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^-6 * x^2 * y^-1 * z^3 * y^-2 ] T39.96 : Triangle type {27,81,81} Group order 81 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, z * x^-1 * z^4 * x^-2 * z^4 ] T39.97 : Triangle type {27,81,81} Group order 81 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^8 * y^-1 * x * y^-5 * x * y^-4 * x * y^-2 ] T39.98 : Triangle type {27,81,81} Group order 81 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^5 * y^-3, z * x^-1 * z^4 * x^-2 * z^4 ] T39.99 : Triangle type {28,28,42} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, y * x^-3 * y * x^-1 * z ] T39.100 : Triangle type {28,28,42} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, z * y^-1 * x * z, z^-1 * y * x^-1 * y^-2, x^-1 * z * x^-1 * z * x^-6 ] T39.101 : Triangle type {28,28,42} Group order 84 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^-4 * x * z^-5 * x * z^-1 * y * z^-1 * y * z^-1 ] T39.102 : Triangle type {40,80,80} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^2 * x^-5 * y^3 * z^-1 * y^2 ] T39.103 : Triangle type {40,80,80} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^-1 * z^5 * y^-4 ] T39.104 : Triangle type {40,80,80} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, y * x^-1 * y, z^22 * x^-1 * z^4 ] T39.105 : Triangle type {40,80,80} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^2 * y^-2, x^-1 * z * x^-1 * z * x^-1 * z^4 * x^-2 * z^4 ] T39.106 : Triangle type {40,80,80} Group order 80 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^40, y * z^-1 ] T39.107 : Triangle type {40,80,80} Group order 80 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-11 * z^2 * x^-8 ] T39.108 : Triangle type {40,80,80} Group order 80 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-2 * z^2 * x^-7 ] T39.109 : Triangle type {79,79,79} Group order 79 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^34 * x^-1 * y^5, x * z^-1 ] T39.110 : Triangle type {79,79,79} Group order 79 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-18 * x^4 * y^-3 * x * y^-2 ] T39.111 : Triangle type {79,79,79} Group order 79 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-1 * x^6 * y^-1 * x * y^-5 * x * y^-4 * x * y^-2 ] T39.112 : Triangle type {79,79,79} Group order 79 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^5 * x^-4 * y^5 * x^-1 * y * x^-1 ] T39.113 : Triangle type {79,79,79} Group order 79 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^-3 * z * y^-3 * x^5 * y^-1 * x * y^-1 ] T39.114 : Triangle type {79,79,79} Group order 79 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-1 * y * x^-5 * y^3 * z^-1 * y^2 ] T39.115 : Triangle type {79,79,79} Group order 79 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^3, y^-5 * x * y^-4 ] T39.116 : Triangle type {79,79,79} Group order 79 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^4, z^4 * x^-1 * z^4 ] T39.117 : Triangle type {79,79,79} Group order 79 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^7 * x^-1 * z^4 ] T39.118 : Triangle type {79,79,79} Group order 79 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * y^-4, x^-1 * z^4 * x^-5 * z ] T39.119 : Triangle type {79,79,79} Group order 79 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^-3 * z^4 * x^-6 ] T39.120 : Triangle type {79,79,79} Group order 79 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-1 * z^3 * x^-6, y^-1 * z^5 * y^-2 * z^2 ] T39.121 : Triangle type {79,79,79} Group order 79 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^5 * z^-2 * y^6 * z^-1 * y^3 ] T39.122 : Triangle type {79,79,79} Group order 79 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^3 * z^-3, y^-2 * z * y^-3 * x^4 * y^-2 ] Genus 40 T40.1 : Triangle type {2,3,12} Group order 936 Action chiral Defining relators: [ x^2, y^3, x * y * z, z^12, x * z^3 * y * x * z^2 * y^-1 * z^-1 * x * z^2 * y^-1 * z^-1, z^-1 * x * z * y * x * z * y * x * z * y * x * z^2 * y^-2 * z^-1 * x * z * y^-1 * z^-1 ] T40.2 : Triangle type {2,4,30} Group order 360 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y * x * y^-2 * z^3 * y^-1 * z^-2 ] T40.3 : Triangle type {2,4,82} Group order 328 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-74 * x * y * z^-7 ] T40.4 : Triangle type {2,4,160} Group order 320 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-72 * x * y^-1 * z^-7 ] T40.5 : Triangle type {2,6,6} Group order 468 Action chiral Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * y^-1 * z * y^-3 * z^-1 * y * z^-1 * y^2, z^-1 * x * z * y^-1 * z * y^2 * z^-1 * x * z * y^-1 * z^-1 ] T40.6 : Triangle type {2,6,6} Group order 468 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, z * y^-1 * z^2 * y * x * z * y * z^-2 * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x ] T40.7 : Triangle type {2,6,12} Group order 312 Action chiral Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, x * y^-1 * z * y^-2 * z^-4, y * x * z * y * x * y^-1 * z^-2 * x * z^2 ] T40.8 : Triangle type {2,6,12} Group order 312 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, x * z * y * x * y^-2 * z^-1 * y * x * y^-1 * z^-1 ] T40.9 : Triangle type {2,6,16} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z^2 * y^-2 * z^-1 * x * y^-1, z^-6 * x * z^2 * y * z^-1 * x * y * z^-1 * x * z * y^-1 * z^-2 ] T40.10 : Triangle type {2,6,42} Group order 252 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, x * z * y^-2 * z^-2 * y, z^-1 * x * z^5 * y * x * z * y * x * y^-1 * z^-4 ] T40.11 : Triangle type {2,6,42} Group order 252 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^15 * y * x * z^8 * y * x * z * y * z^-9 * x * z^6 ] T40.12 : Triangle type {2,6,42} Group order 252 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^31 * y * z^-8 * x * z^2 ] T40.13 : Triangle type {2,6,120} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-14 * x * z^15 * y * z^-1 * x * z^7 * y^-1 * z^-1 ] T40.14 : Triangle type {2,7,8} Group order 336 Action reflexible [m] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^-7, z^8, (z * y^-1 * z)^3 ] T40.15 : Triangle type {2,7,8} Group order 336 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^-7, y * x * z * y^2 * x * y^-1 * z^-1, z^8 ] T40.16 : Triangle type {2,9,18} Group order 234 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y^-9, z^2 * y^-3 * z^4, x * z * y * z^-1 * y * x * y^-1 * z^2 * y^-1 * z^-2 ] T40.17 : Triangle type {2,9,36} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y^-9, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^3 * y^-1 * z^-4 ] T40.18 : Triangle type {2,10,22} Group order 220 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^7 * y * x * z^3 * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z^5 ] T40.19 : Triangle type {2,12,18} Group order 216 Action chiral Defining relators: [ x^2, x * y * z, x * y^-4 * z^-2 * y * z^-1, z^2 * y^-3 * z^-1 * x * z^2 ] T40.20 : Triangle type {2,12,18} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-12, z^10 * y * x * y * z^-4 * x * z^2 ] T40.21 : Triangle type {2,12,18} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^5 * y * x * z^3 * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z^3 ] T40.22 : Triangle type {2,12,96} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-12, z^-9 * x * z^4 * y^-1 * z^-2 ] T40.23 : Triangle type {2,18,90} Group order 180 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^3 * y * z^-4 * x * z^2, y^-7 * z^3 * y^-5 * z^3 ] T40.24 : Triangle type {2,22,88} Group order 176 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^-11 * z^3 * y^-5 * z^3 ] T40.25 : Triangle type {2,30,30} Group order 180 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^7 * z^-1 * y * z^-1 ] T40.26 : Triangle type {2,30,30} Group order 180 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, z^-3 * y^10 * z^-3 * y^14 ] T40.27 : Triangle type {2,34,85} Group order 170 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^3 * y * z^-2 * x * z * y^-1 * z^-2 * x, y^-6 * z^3 * y^-6 * z^2 ] T40.28 : Triangle type {2,42,84} Group order 168 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-16 * y^11 * z^-1 * y^11 * z^-1 * y ] T40.29 : Triangle type {2,81,162} Group order 162 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^67 * y^-12 * z ] T40.30 : Triangle type {2,82,82} Group order 164 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^14 * z^-68 ] T40.31 : Triangle type {2,160,160} Group order 160 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^66 * y^-12 * z ] T40.32 : Triangle type {3,3,6} Group order 468 Action chiral Defining relators: [ x^3, x * y * z, y^3, z^6, (y * x^-1 * z)^3, z^2 * y^-1 * z^-1 * x^-1 * z^2 * y * x, x * z * y * x * z * y * x^-1 * y * x * z^-1 * x * z^-1 ] T40.33 : Triangle type {3,3,42} Group order 252 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^3 * y * z^-1 * x * z^5 ] T40.34 : Triangle type {3,4,5} Group order 360 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^2 * y^-1 * x^-1 * z^2, (x * z * y)^2 ] T40.35 : Triangle type {3,4,5} Group order 360 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z * x^-1 * y^-1 * x * y^-1 * x, z^2 * y^-1 * x^-1 * z^2, (x^-1 * z * y * z^-1 * y)^2 ] T40.36 : Triangle type {3,6,6} Group order 234 Action chiral Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, z * y * x^-1 * y^-1 * x * y^-1 * z * y^-1 ] T40.37 : Triangle type {3,6,6} Group order 234 Action chiral Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, x^-1 * y^-1 * z^-1 * y * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1 * x^-1 * z ] T40.38 : Triangle type {3,6,6} Group order 234 Action chiral Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^6, x * z * y * z^-1 * x^-1 * y^-1 * x * z^2 * y * z^-1 ] T40.39 : Triangle type {3,6,6} Group order 234 Action chiral Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y * z^-2 * x^-1 * y^-2 * z, y * z^-1 * y^2 * x^-1 * z * y^-1 * z^2 ] T40.40 : Triangle type {3,6,6} Group order 234 Action chiral Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * x^-1 * y^-1 * z^-2 * y * z^-1 * y ] T40.41 : Triangle type {3,6,15} Group order 180 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^2 * y * x^-1 * z^2 ] T40.42 : Triangle type {3,6,15} Group order 180 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, y * x^-1 * y * x^-1 * z^3 ] T40.43 : Triangle type {3,6,28} Group order 168 Action chiral Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^6, y * z^-1 * y * x * y^-1 * z^-1, y * z^-2 * y * x^-1 * z^3 ] T40.44 : Triangle type {3,12,12} Group order 156 Action chiral Defining relators: [ x^3, x * y * z, (y * z^-1)^2, z^-2 * x^-1 * y^-1 * x * y^-2 * z^-1 ] T40.45 : Triangle type {3,12,12} Group order 156 Action chiral Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^-1 * z * y * x^-1 * y^-3, z^-1 * y * z^-1 * y^2 * z^-2 * y ] T40.46 : Triangle type {3,12,12} Group order 156 Action chiral Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * y * z^-1 * x^-1 * y^-1 * z^-1 * y ] T40.47 : Triangle type {3,12,24} Group order 144 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * y^2 * z^-2, z^-1 * x^-1 * z * y * x * z^2 * y ] T40.48 : Triangle type {3,12,24} Group order 144 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2 ] T40.49 : Triangle type {3,16,16} Group order 144 Action reflexible [n] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * z * y^-1, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, y^2 * z^-2 * y^5 * z^-3 * y^4 ] T40.50 : Triangle type {3,16,16} Group order 144 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, z^-1 * y^2 * z^-1 * y^6 * z^-2 * y^3 * z^-1 ] T40.51 : Triangle type {3,22,33} Group order 132 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^4 * y^-3 * z * y^-1 * z ] T40.52 : Triangle type {3,41,123} Group order 123 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-30 * z * y^-1 * z * y^-7 * z ] T40.53 : Triangle type {3,42,42} Group order 126 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-31 * z * y^-1 * z * y^-7 * z ] T40.54 : Triangle type {3,42,42} Group order 126 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^29 * y^-3 * z * y^-7 * z ] T40.55 : Triangle type {3,42,42} Group order 126 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-2 * y * z^-1 * y^3 * z^-1 * y * z^-3 * y ] T40.56 : Triangle type {3,120,120} Group order 120 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-29 * z * y^-1 * z * y^-8 ] T40.57 : Triangle type {4,4,15} Group order 180 Action reflexible [n] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-3 * x^-1 * z^2 * y^-1 * z^-3 ] T40.58 : Triangle type {4,4,15} Group order 180 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, y * x^-1 * y * x^-1 * z^3 ] T40.59 : Triangle type {4,4,41} Group order 164 Action reflexible [n] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^-4 * x^-1 * y^-1 * x * z^-3 * y ] T40.60 : Triangle type {4,4,41} Group order 164 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-28 * x^-1 * y^-1 * z^-12 ] T40.61 : Triangle type {4,4,80} Group order 160 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^33 * y * x^-1 * z^6 ] T40.62 : Triangle type {4,6,12} Group order 156 Action chiral Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, x * z * y^2 * z^-2 ] T40.63 : Triangle type {4,6,12} Group order 156 Action chiral Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^-3 * x^-1 * y * z^-2, y * x * z^2 * y * z^-1 * x * y^-1 * z^-1 * x^-1 * z ] T40.64 : Triangle type {4,6,12} Group order 156 Action chiral Defining relators: [ x * y * z, x^4, y^2 * x^2 * z^2, y^6, z^-2 * y * x * z * y ] T40.65 : Triangle type {4,6,12} Group order 156 Action chiral Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, y^-1 * z^-1 * x^-1 * y^-1 * x * z^2 * x^-1 ] T40.66 : Triangle type {4,6,24} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, y * x^-1 * z * y * z^-1 * y * z^-1 * x * z, z^-4 * x^-1 * z^3 * y^-1 ] T40.67 : Triangle type {4,6,24} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * x^-1 * z^2, y^6 ] T40.68 : Triangle type {4,6,24} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^4 * y^-1 * z^-3 * x^-1 * z^4 ] T40.69 : Triangle type {4,6,24} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, x^-1 * z^5 * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-3 ] T40.70 : Triangle type {4,7,7} Group order 168 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * y^-1 * z, (y * z^-1 * y)^2, y^3 * x^-1 * y^-1 * x * z ] T40.71 : Triangle type {4,7,7} Group order 168 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (y^-1 * x)^3, (z^-1 * x)^3 ] T40.72 : Triangle type {4,8,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * z * y, z^-3 * x^-1 * y * z^-2 ] T40.73 : Triangle type {4,12,60} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^3 * y^-1 * z^-2 * x * z^4 ] T40.74 : Triangle type {4,15,30} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * z * y^-1, y * z^-3 * y * z^-4 * y^2 * z^-4 ] T40.75 : Triangle type {4,28,56} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, y^-2 * z * y^-9 * z * y^-1 ] T40.76 : Triangle type {4,54,108} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^9 * z^-2 * y^7 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T40.77 : Triangle type {5,21,105} Group order 105 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^3 * z^-1 * y^8 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T40.78 : Triangle type {5,22,22} Group order 110 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^-5, y^-3 * z * y^-12 * z * y^-1 * z * y^-2 * z ] T40.79 : Triangle type {5,100,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z^3 * y^-1 * z * y^-1 * z * y^-1 * z * y^-7 * z * y^-2 ] T40.80 : Triangle type {5,100,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z^3 * y^-1 * z * y^-1 * z * y^-1 * z * y^-10 ] T40.81 : Triangle type {6,6,6} Group order 156 Action chiral Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, z^6, y^-1 * x * y^-1 * x^2 * y^-2 * x ] T40.82 : Triangle type {6,6,6} Group order 156 Action chiral Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, y^6, z^6, y * x^-1 * y * x^-1 * y * x * z ] T40.83 : Triangle type {6,6,8} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z * y^-1 * x^2 * z^2, y^6 ] T40.84 : Triangle type {6,6,8} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, (x * y^-1 * x)^2, z^8 ] T40.85 : Triangle type {6,6,8} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^6, y^6, z^8 ] T40.86 : Triangle type {6,6,8} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, (y * z^-1)^2, x^6, (x * y^-1 * x)^2, y^6, z^-1 * y^2 * x * z^-1 * x, z^8 ] T40.87 : Triangle type {6,6,21} Group order 126 Action reflexible [n] Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z * x^-1 * y^-1 * x * z * x^-1, z^2 * y * x * z^2 ] T40.88 : Triangle type {6,6,21} Group order 126 Action reflexible [n] Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * z, x^6, (y^-1 * x)^3 ] T40.89 : Triangle type {6,6,21} Group order 126 Action reflexible [n] Defining relators: [ x * y * z, x * z^-1 * y * z^-1, x^6, (y^-1 * x)^3 ] T40.90 : Triangle type {6,6,21} Group order 126 Action reflexible [n] Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, x^6, (x * y^-1 * x)^2, z^-2 * y * x * z^-2 ] T40.91 : Triangle type {6,6,21} Group order 126 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^2 * y * z^-1 * x * z^3 ] T40.92 : Triangle type {6,6,21} Group order 126 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^10 * y^-1 * x * y * x^-1 * z^9 ] T40.93 : Triangle type {6,6,21} Group order 126 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^9 * y * x * y^-1 * z^-3 * x * z^7 ] T40.94 : Triangle type {6,6,60} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^10 * y^-1 * z^-4 * x^-1 * y * z^-1 * x^-1 * z^3 ] T40.95 : Triangle type {6,10,12} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, x^6, y^10 ] T40.96 : Triangle type {6,17,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, z^2 * y^-1 * z * y^-1 * z * y^-1 * z * y^-8 * z ] T40.97 : Triangle type {6,18,18} Group order 108 Action chiral Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, y^3 * x^-1 * y * z^-1 * y ] T40.98 : Triangle type {6,18,18} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^6, z^-2 * y^4 * x^-1 * y^4 * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T40.99 : Triangle type {6,18,18} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, (y * z^-1 * y)^2, z^-1 * y^2 * x^-1 * y^-3 ] T40.100 : Triangle type {6,18,18} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y * z^-1 * y * z^-2, z^-1 * y^2 * x^-1 * y^-3 ] T40.101 : Triangle type {6,18,18} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, z^-2 * y^2 * z^-2, y * x^-3 * z * x^-2 ] T40.102 : Triangle type {6,18,18} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^6, y^-1 * z * y^-12 * z * y^-1 * z^2 ] T40.103 : Triangle type {6,96,96} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^6, y^-2 * z^5 * x^-1 * z^5 * y^-4 ] T40.104 : Triangle type {9,9,9} Group order 117 Action chiral Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, x * z * y * x^-1 * y^-1 * z * y ] T40.105 : Triangle type {9,9,18} Group order 108 Action reflexible [n] Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, (y^-1 * x)^3, x * z * y^-1 * x * z^-2 ] T40.106 : Triangle type {9,9,18} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, y^-1 * x^3 * y^-2, (y^-1 * x)^3, (z^-1 * x)^3 ] T40.107 : Triangle type {9,11,99} Group order 99 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-9, y^-2 * z * y^-4 * x * y^-4 ] T40.108 : Triangle type {9,12,12} Group order 108 Action reflexible [n] Defining relators: [ x * y * z, x^-1 * y^-1 * x * z^-1, x^4 * y^-1 * z^-1, y * z^-1 * y^3 * z^-3 * y * z^-1 * y^2 ] T40.109 : Triangle type {9,12,12} Group order 108 Action chiral Defining relators: [ x * y * z, z * y^-1 * x^2 * y^-2, z^-1 * y * x^2 * z^-2, z^-2 * x^2 * z * y^-1 ] T40.110 : Triangle type {9,12,12} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^-9, y^-12 ] T40.111 : Triangle type {9,12,12} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, y * x^-3 * z * x^-2, x^-9 ] T40.112 : Triangle type {9,90,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^9, y * z^-3 * y * x^-1 * y^5 ] T40.113 : Triangle type {9,90,90} Group order 90 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^9, y * z^-4 * y^4 * z^-1 ] T40.114 : Triangle type {10,10,11} Group order 110 Action reflexible [n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-2, z^-2 * x^-1 * y^-1 * z^-1, x^10 ] T40.115 : Triangle type {10,10,11} Group order 110 Action reflexible [n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-2, y^-1 * z * x^-1 * z^2, x * y^-1 * x^5 * y^-3 ] T40.116 : Triangle type {10,10,11} Group order 110 Action reflexible [n] Defining relators: [ x * y * z, z * y * x * z, y * z^-1 * x^2 * z^-1 * y, x^10 ] T40.117 : Triangle type {10,10,11} Group order 110 Action reflexible [n] Defining relators: [ x * y * z, x * z^-1 * y * z^-1, y * x^-1 * y^-1 * x * z^2, x^-1 * y^2 * x^-4 * y * x^-2 ] T40.118 : Triangle type {10,10,11} Group order 110 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^10, z^6 * y^-1 * x^-1 * z^4 ] T40.119 : Triangle type {10,45,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x * y^-1 * x^8 * z^-1, y^-7 * z^2 ] T40.120 : Triangle type {10,45,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x * y^-1 * x^8 * z^-1, z * y^-4 * x^-1 * z^4 ] T40.121 : Triangle type {10,45,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x * y^-1 * x^8 * z^-1, y * z^-8 ] T40.122 : Triangle type {11,88,88} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x^-11 ] T40.123 : Triangle type {11,88,88} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, (x^-2 * z^4)^2 ] T40.124 : Triangle type {11,88,88} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, z^4 * x^-2 * z^4 ] T40.125 : Triangle type {11,88,88} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, x^-1 * z * x^-1 * z^4 * x^-3 * z^3 ] T40.126 : Triangle type {11,88,88} Group order 88 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-11 ] T40.127 : Triangle type {12,12,48} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, z * y * z^-2 * x^-1 * z^4 ] T40.128 : Triangle type {15,18,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^-1 * y^4 * x^-5 * y^2 * x^-4 ] T40.129 : Triangle type {15,18,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^4 * z^-4, y^-2 * x^5 * y^-4 ] T40.130 : Triangle type {15,30,30} Group order 90 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^4 * y^-1 * z^-1, (z^-1 * y)^3 ] T40.131 : Triangle type {15,30,30} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^4 * y^-1 * z^-1, y^4 * z^-2 ] T40.132 : Triangle type {15,30,30} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, x^-4 * y^-1 * x * z, y^2 * x^-3 * y^4 ] T40.133 : Triangle type {15,30,30} Group order 90 Action reflexible [m,n] Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^2 * z^-1, x^-3 * y * x^-9 * z * x^-2 ] T40.134 : Triangle type {15,30,30} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-3 * y^4, z^-1 * x * z^-1 * x^5 * z^-4 ] T40.135 : Triangle type {15,30,30} Group order 90 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-15 ] T40.136 : Triangle type {17,85,85} Group order 85 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-1 * z^3 * x^-4 * z^2, y^-2 * z^4 * x * y^-4 ] T40.137 : Triangle type {17,85,85} Group order 85 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * x * y^-2, x^-1 * z * x^-1 * z * x^-1 * z^4 * x^-2 * z^4 ] T40.138 : Triangle type {17,85,85} Group order 85 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-4 * z, x^9 * z^-4 * x * z^-1 * x^3 ] T40.139 : Triangle type {17,85,85} Group order 85 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^17 ] T40.140 : Triangle type {17,85,85} Group order 85 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, y^-1 * z^9 ] T40.141 : Triangle type {17,85,85} Group order 85 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^2 * x^-1 * z^4 * x^-2 * z^4 ] T40.142 : Triangle type {17,85,85} Group order 85 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, z^6 * x^-1 * z^4 ] T40.143 : Triangle type {17,85,85} Group order 85 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y^-1 * z^5 * y^-4, x^-1 * z^4 * x^-5 * z ] T40.144 : Triangle type {18,18,45} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z^-1 * x^-1 * y * x^-1 * y * z^-2 ] T40.145 : Triangle type {18,18,45} Group order 90 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-2 * x * z^2, z^2 * y^-1 * z^2 * x^-1 * z^4 ] T40.146 : Triangle type {21,84,84} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-2 * z * y^-2 * x^6 * y^-3 ] T40.147 : Triangle type {21,84,84} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^-5 * x^4 * z^-4 * x * z^-1 * x * z^-2 ] T40.148 : Triangle type {21,84,84} Group order 84 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^9 * z^-1 * x^7 * y^-1 * x^4 ] T40.149 : Triangle type {22,22,44} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * x^-1 * z^2, y^4 * x^-1 * y * x^-2 * y * z^-1 * y^3 ] T40.150 : Triangle type {22,22,44} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * x^2 * z^-2, y^-3 * x^2 * y^-3 ] T40.151 : Triangle type {22,22,44} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * y^-2, z^-2 * x * z^-1 * x * z^-3 ] T40.152 : Triangle type {22,22,44} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^3 * z^-1 * y, x^5 * z^-1 * x * z^-1 ] T40.153 : Triangle type {22,22,44} Group order 88 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-2 * x^-1 * z * y^-1, z^5 * x^-1 * z * x^-1 * z^4 ] T40.154 : Triangle type {28,42,84} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-10 * z^2 * y^-3 ] T40.155 : Triangle type {28,42,84} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, z^5 * x^-1 * z^4 ] T40.156 : Triangle type {28,42,84} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * x^-2 * z^2, y^2 * x^-5 * y * z^-3 * y^3 ] T40.157 : Triangle type {28,42,84} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^16 * z^-1 * x^8 * y^-1 * x^3 ] T40.158 : Triangle type {28,42,84} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-6 * x^3 * z^-9 ] T40.159 : Triangle type {41,82,82} Group order 82 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x * y^-6 * x * y^-1 * x * y^-1 * x^8 * y^-1 * x * y^-1 * x ] T40.160 : Triangle type {41,82,82} Group order 82 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^3 * z^-2 * x^10 ] T40.161 : Triangle type {41,82,82} Group order 82 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x * y^-3 * x^5 * z^-1 * x^2 ] T40.162 : Triangle type {41,82,82} Group order 82 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, y^-1 * z^5 * y^-3 * z ] T40.163 : Triangle type {41,82,82} Group order 82 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6 * z^-2, y^-1 * z * y^-1 * z^5 * y^-3 * z ] T40.164 : Triangle type {41,82,82} Group order 82 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-4 * z^5 * y^-1 * z^3 * y^-1 ] T40.165 : Triangle type {41,82,82} Group order 82 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4 * y^-2, z^-4 * x * z^-5 * y * z^-1 * y * z^-2 ] T40.166 : Triangle type {41,82,82} Group order 82 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^5 * x^-1 * z^3, x^-8 * y^2 ] T40.167 : Triangle type {41,82,82} Group order 82 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-1 * y * z^-5 * y * z^-5 * y * z^-1 * y * z^-2 ] T40.168 : Triangle type {41,82,82} Group order 82 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^2 * y^-4 * x^7 ] T40.169 : Triangle type {41,82,82} Group order 82 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-5 * z^2, y^-2 * z^3 * y^-1 * x * y^-4 ] T40.170 : Triangle type {41,82,82} Group order 82 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, z^-3 * x^6 * z^-4 * x * z^-1 * x * z^-2 ] T40.171 : Triangle type {41,82,82} Group order 82 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-6 * z * y^-8 * x^2 * y^-5 ] T40.172 : Triangle type {41,82,82} Group order 82 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * y^-2 * z^2, y^-5 * x^5 * y^-1 ] T40.173 : Triangle type {41,82,82} Group order 82 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^2 * x^-1 * z^4 * x^-2 * z^4 ] T40.174 : Triangle type {41,82,82} Group order 82 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * x^-2 * z^2, y^-2 * z * y^-3 * x^4 * y^-2 ] T40.175 : Triangle type {41,82,82} Group order 82 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * x^-4 * z^2, y^-2 * z^4 * x * y^-4 ] T40.176 : Triangle type {41,82,82} Group order 82 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * z * x^-1 * z * x^-1 * z^4 * x^-4 * z^2 ] T40.177 : Triangle type {41,82,82} Group order 82 Action reflexible [m] Defining relators: [ x * y * z, y * x^-1 * y, z^22 * x^-2 * z^4 ] T40.178 : Triangle type {41,82,82} Group order 82 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^41, y * z^-1 ] T40.179 : Triangle type {42,42,42} Group order 84 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-14 * x^2 * y^-6 ] T40.180 : Triangle type {42,42,42} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-1 * z^2 * x^-7, y^-1 * z^5 * y^-1 * z^3 ] T40.181 : Triangle type {81,81,81} Group order 81 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-1 * y^2, x * z^-2 * x^6 * z^-4 * x * z^-1 * x * z^-2 ] T40.182 : Triangle type {81,81,81} Group order 81 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^7 * y^-1, z^6 * x^-1 * z^4 ] T40.183 : Triangle type {81,81,81} Group order 81 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * z^3, x * y^-5 * x^7 ] T40.184 : Triangle type {81,81,81} Group order 81 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^35 * x^-1 * y^5, x * z^-1 ] T40.185 : Triangle type {81,81,81} Group order 81 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-4 * z * y^-3 * x^2 * y^-5 ] Genus 41 T41.1 : Triangle type {2,3,16} Group order 768 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, x * z^3 * y * x * y^-1 * z^-3 * x * y^-1 * z^-1, z^4 * y * z^-1 * x * z * y * x * z^-1 * x * y^-1 * z^-2 * x * z^7 ] T41.2 : Triangle type {2,3,16} Group order 768 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, x * z^3 * y * z^-1 * x * z^2 * y^-1 * z^-2, x * z * y * x * z * y * x * z * y * x * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 ] T41.3 : Triangle type {2,4,6} Group order 960 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^6, z^2 * y * z^-1 * y * z^-1 * y * z^-1 * x * z * y^-1 * z * y^-1 ] T41.4 : Triangle type {2,4,8} Group order 640 Action chiral Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z^-1 * x * z^2 * y * z^-1 * x * z^2 * y^-1 * z^-2 ] T41.5 : Triangle type {2,4,8} Group order 640 Action chiral Defining relators: [ x^2, x * y * z, y^4, z^8, y * x * z^2 * y^-2 * z^-3 * y * z^-1 ] T41.6 : Triangle type {2,4,8} Group order 640 Action chiral Defining relators: [ x^2, x * y * z, y^4, z^8, (z^-1 * y)^5, x * z * y * x * z * y^-1 * z^2 * y^-1 * z^2 * y^-1 * z^-1 * y ] T41.7 : Triangle type {2,4,8} Group order 640 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y^-1 * z * y^-1 * z * y^-1 * z * y * x * z * y^2 * z^-1 * x * y^-1 * z * y^-1 * z^-1 * y * z^-1 * x ] T41.8 : Triangle type {2,4,8} Group order 640 Action chiral Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * z^-2 * x * y^-1 * z^-3 * x, y * z^-1 * y * z^-1 * y * x * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-2 ] T41.9 : Triangle type {2,4,8} Group order 640 Action chiral Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * z^-2 * x * y^-1 * z^-3 * x, z * y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z * y^-1 * z ] T41.10 : Triangle type {2,4,8} Group order 640 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y^-1 * z * y^-1 * z * y^-1 * z * y * x * z * y^2 * z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * x ] T41.11 : Triangle type {2,4,12} Group order 480 Action chiral Defining relators: [ x^2, x * y * z, y^4, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z^-4 * x * y^-1 * z^-2 * y * z^-1 * y ] T41.12 : Triangle type {2,4,12} Group order 480 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^-12, y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z * y^-1 * z^-2 ] T41.13 : Triangle type {2,4,12} Group order 480 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, x * z * y^-1 * z * y^-2 * z^-2 * y * z^-1 * y ] T41.14 : Triangle type {2,4,12} Group order 480 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, y * z^-1 * y * x * z * y^2 * z^-1 * x * z^3, z * y * z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1 * x ] T41.15 : Triangle type {2,4,20} Group order 400 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z^-3 * x * z^7 * y^-1 * x * z^2 * y^-1 * z^-4 * x * y^-1 * z^-1 ] T41.16 : Triangle type {2,4,20} Group order 400 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z * y * x * y^-1 * z^-1 * x, z^-2 * x * y^-1 * z^3 * y^-1 * z * y^-1 * z * y^-2 * z^-1 * y * z^-5 * y ] T41.17 : Triangle type {2,4,24} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^2 * y^-2 * z^-3 * y, z^-8 * x * z^8 * y * x * z * y^-1 * z^-5 ] T41.18 : Triangle type {2,4,24} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^-2 * y * z^-1 * x * y^-1 * z^-2 * y * z^-2, z^-4 * x * z^5 * y^-1 * z^-2 ] T41.19 : Triangle type {2,4,24} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y^-2 * z^-3 * y, z^-4 * x * z^5 * y^-1 * z^-2 ] T41.20 : Triangle type {2,4,24} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, x * z * y * z^-1 * x * z^6 * y^-1 * z^-2 ] T41.21 : Triangle type {2,4,24} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-10 * x * z^7 * y * x * z^2 * y^-1 * z^-3 ] T41.22 : Triangle type {2,4,24} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-2 * z^-4 * y, z * y * z^-4 * x * z^4 * y^-1 * z^-1 * x ] T41.23 : Triangle type {2,4,24} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-2 * z^-4 * y, x * z^3 * y * z^-1 * x * z^4 * y^-1 * z^-2 ] T41.24 : Triangle type {2,4,24} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, y^-1 * z * y * x * z * y * x * y^-1 * z * y^-1 * z^-1 * x * z, x * z^5 * y^-1 * z^-2 * x * z * y^-1 * z^-2 ] T41.25 : Triangle type {2,4,36} Group order 360 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, x * z^5 * y * x * z^2 * y * x * z^7 * y^-1 * z^-1 ] T41.26 : Triangle type {2,4,44} Group order 352 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-29 * x * z^6 * y * z^-1 * x * z * y^-1 * z^-5 ] T41.27 : Triangle type {2,4,84} Group order 336 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-76 * x * y * z^-7 ] T41.28 : Triangle type {2,4,164} Group order 328 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-74 * x * y^-1 * z^-7 ] T41.29 : Triangle type {2,5,6} Group order 600 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^-5, z^6, x * z^2 * y^-1 * z * y^-1 * z^2 * y^-1 * z^-2 ] T41.30 : Triangle type {2,5,6} Group order 600 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^-5, z^6, (y * z^-1)^4, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T41.31 : Triangle type {2,5,20} Group order 320 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^-5, z * y^2 * z^-1 * y^2 * z^-1 * y * x * y^-1, z * y * z^-2 * y^2 * z^-2 * x * y^-1 ] T41.32 : Triangle type {2,5,20} Group order 320 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^-5, z * y * x * y^-1 * z^-1 * x, (y * z^-2 * y * z^-1)^2 ] T41.33 : Triangle type {2,6,6} Group order 480 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^6, z^6, (y * z^-1 * y * z^-1 * y)^2, z^-1 * y * x * z * y^2 * z^-1 * x * y^-1 * z^-1 ] T41.34 : Triangle type {2,6,8} Group order 384 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-1)^4, z^8, x * z * y^-1 * z * y^2 * z^-1 * x * y^-1 * z^-1 ] T41.35 : Triangle type {2,6,8} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z^8, z^-1 * x * z * y^-2 * z * y^-1 * z^-2 ] T41.36 : Triangle type {2,6,8} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z * y * z^-1 * x * y^-1 * z^-2 * x, z^8 ] T41.37 : Triangle type {2,6,8} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, z^8, (y * z^-1 * y)^4 ] T41.38 : Triangle type {2,6,8} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^8, x * z^3 * y * z^-1 * x * z^2 * y^-1 * z^-2 ] T41.39 : Triangle type {2,6,8} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z^8, x * z * y^-3 * z^-2 * y^2, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1 ] T41.40 : Triangle type {2,6,8} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z^8, x * z * y^-3 * z^-2 * y^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T41.41 : Triangle type {2,6,8} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y^-1 * z * y^-1 * z * y^-1 * z^-2 * x * z ] T41.42 : Triangle type {2,6,8} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1)^4, (y * z^-3)^2, z^8, z * y * x * z * y^2 * z^-2 * y * x ] T41.43 : Triangle type {2,6,8} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, y^-1 * z * y^-1 * z * y^-1 * z^-2 * x * z, z * y * x * z * y^2 * z^-2 * y * x ] T41.44 : Triangle type {2,6,8} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1)^4, (y * z^-3)^2, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T41.45 : Triangle type {2,6,8} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, y * z^-1 * x * z * y^2 * z^-1 * x * y^-1 * z^-1, z * y * z^-1 * y * x * y^-1 * z^-2 * y * x ] T41.46 : Triangle type {2,6,33} Group order 264 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, z^5 * y * x * y * x * z * y^-1 * z^-2 * x ] T41.47 : Triangle type {2,6,123} Group order 246 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-15 * x * z^15 * y * z^-1 * x * y^-1 * z^-8 ] T41.48 : Triangle type {2,8,8} Group order 320 Action chiral Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-1 * y * z^-1, y^8, z^-1 * y * z^-1 * y^3 * z^-3 * y ] T41.49 : Triangle type {2,8,8} Group order 320 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z * y^-1 * z * y^-1 * z * y^-2 * z^-1 * x * z * y^-2 * z^-1 * x ] T41.50 : Triangle type {2,8,8} Group order 320 Action chiral Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^8, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z ] T41.51 : Triangle type {2,8,8} Group order 320 Action chiral Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^8, z * y * z^-1 * y * x * y^-1 * z^-2 * y * x ] T41.52 : Triangle type {2,8,8} Group order 320 Action chiral Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^8, z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T41.53 : Triangle type {2,8,8} Group order 320 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z * y^-1 * z * y^-1 * z * y^-2 * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x ] T41.54 : Triangle type {2,8,16} Group order 256 Action chiral Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z * y^-1 * z * y^-2 * z^-2 * x * z, z^-2 * y * x * y^-1 * z^2 * y^-1 * z^-1 ] T41.55 : Triangle type {2,8,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-1 * x * z^8 * y * z^-6 ] T41.56 : Triangle type {2,8,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, (y * z^-1 * y^2)^2, x * z^9 * y^-1 * x * z * y^-1 * z^-4 ] T41.57 : Triangle type {2,8,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, z^-1 * x * z * y * x * y^-1 * z^-4 ] T41.58 : Triangle type {2,8,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, z^2 * y * z^-1 * x * y^-1 * z^-2 * x * z ] T41.59 : Triangle type {2,8,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, z * y * z^-2 * x * y^-1 * z^-3 * x ] T41.60 : Triangle type {2,8,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T41.61 : Triangle type {2,8,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^8, (y * z^-3)^2, y^-1 * z * y^-3 * z^-1 * y * x * z, z^-1 * x * z * y * x * y^-1 * z^-4 ] T41.62 : Triangle type {2,8,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, z * y * z^-2 * x * y^-1 * z^-3 * x ] T41.63 : Triangle type {2,8,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-1)^4, z^-2 * x * y^-2 * z^-3 * y, x * z^3 * y^-1 * z^-4 ] T41.64 : Triangle type {2,8,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y, z^-2 * x * y^-2 * z^-3 * y, x * z^3 * y^-1 * z^-4 ] T41.65 : Triangle type {2,8,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^8, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, x * z^3 * y^-1 * z^-4 ] T41.66 : Triangle type {2,8,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, x * z^3 * y^-1 * z^-4 ] T41.67 : Triangle type {2,8,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, (y * z^-1 * y^2)^2, z^-2 * x * y^-3 * z^-5 ] T41.68 : Triangle type {2,8,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z * y^-1 * z^-1, y^8, z^-2 * x * y^-3 * z^-5 ] T41.69 : Triangle type {2,8,24} Group order 240 Action chiral Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, x * z^2 * y^-2 * z * y^-1 * z^-2 ] T41.70 : Triangle type {2,8,24} Group order 240 Action chiral Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^2 * y * x * y^-1 * z^-2 * x ] T41.71 : Triangle type {2,8,56} Group order 224 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^16 * y * x * y^-1 * z^-1 * x * y^-1 * z^-4 * x * z^4 ] T41.72 : Triangle type {2,8,56} Group order 224 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-3 * x * z^5 * y * z^-2 * x * z^7 * y * x * z^2 * y^-1 * z^-2 * x * z^2 * y^-1 * z^-1 ] T41.73 : Triangle type {2,12,12} Group order 240 Action chiral Defining relators: [ x^2, x * y * z, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, x * y^-4 * z * y^-2 * z^-1 ] T41.74 : Triangle type {2,12,12} Group order 240 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^-1 * z * y^2 * z^-1 * x * y^-1 * z^-1, y^12 ] T41.75 : Triangle type {2,12,12} Group order 240 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (y * z^-2 * y)^2, z^-1 * x * z * y^2 * x * y^-1 * z^-1 ] T41.76 : Triangle type {2,12,12} Group order 240 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (y * z^-2 * y)^2, x * z * y^-3 * z * y^-1 * z^-2, z^-1 * y * x * y^-2 * z^-1 * y * z^-2, x * y^-1 * z * y^-2 * z^-2 * y * z^-1 ] T41.77 : Triangle type {2,14,14} Group order 224 Action reflexible [n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-1 * y * z^-2, y^-14 ] T41.78 : Triangle type {2,16,48} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^5 * z^-1 * y * z^-1, z^4 * y * z^-1 * x * z^6 ] T41.79 : Triangle type {2,16,48} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-5 * z^2 * y^-7 * z^2, z^4 * y * z^-1 * x * z^6 ] T41.80 : Triangle type {2,16,48} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^5 * z^-1 * y * z^-1, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x ] T41.81 : Triangle type {2,16,48} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-5 * z^2 * y^-7 * z^2, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x ] T41.82 : Triangle type {2,20,20} Group order 200 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, y * z^-1 * y * z^-1 * y^2 * z^-1 * y^9 * z^-3 * y ] T41.83 : Triangle type {2,20,20} Group order 200 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-5 * z^-1 * y^4, y^-1 * z^2 * y^-1 * z^4 * y^-9 * z * y^-1 * z ] T41.84 : Triangle type {2,20,20} Group order 200 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^-1 * z^-1 * x * z * y * x * y^-5 * z^-5 * x ] T41.85 : Triangle type {2,24,24} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^2 * z^-10 * y^9 * z^-2 * y ] T41.86 : Triangle type {2,24,24} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-2 * y * z^-1, x * y^-1 * z * y^-2 * z^-4, y^8 * z^-1 * y^2 * z^-1 ] T41.87 : Triangle type {2,24,24} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z^2 * y^-1 * z^-3, y^7 * z^-2 * y * z^-2 ] T41.88 : Triangle type {2,24,24} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-1 * y * z^-1, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, y^-8 * z * y^-2 * z ] T41.89 : Triangle type {2,24,24} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, x * z^3 * y^-1 * z^-4, y^9 * z^-1 * y * z^-1 ] T41.90 : Triangle type {2,24,24} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-4 * z^-1 * y^3, y^-1 * z^10 * y^-1 * z * y^-10 * z ] T41.91 : Triangle type {2,24,24} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^2 * z^-1 * y^10 * z^-1 * y^7 * z^-2 * y ] T41.92 : Triangle type {2,24,24} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y * z^-1 * y * z^-1 * y^4 * z^-1 * y * z^-1 * y ] T41.93 : Triangle type {2,24,24} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, x * z^3 * y^-1 * z^-4, z^-1 * y^6 * z^-1 * y^2 * z^-2 ] T41.94 : Triangle type {2,36,36} Group order 180 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^-2 * z^-1 * y * z^-1, z^-2 * y * z^-1 * y * z^-1 * y^7 * z^-5 ] T41.95 : Triangle type {2,44,44} Group order 176 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-17 * y^11 * z^-1 * y^14 ] T41.96 : Triangle type {2,83,166} Group order 166 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^68 * y^-14 ] T41.97 : Triangle type {2,84,84} Group order 168 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^15 * z^-68 * y ] T41.98 : Triangle type {2,164,164} Group order 164 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^14 * z^-67 * y ] T41.99 : Triangle type {3,3,8} Group order 384 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z^8, y * x * z * y * x^-1 * z * y^-1 * x * z ] T41.100 : Triangle type {3,3,8} Group order 384 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-1 * x * y^-1 * x * z * y^-1 * x, z^8 ] T41.101 : Triangle type {3,3,8} Group order 384 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z * y^-1 * z^-1 * x^-1 * z * y * x, z^8, x^-1 * z * x^-1 * z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T41.102 : Triangle type {3,4,4} Group order 480 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^4, z^4, z^-1 * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * y^-1 ] T41.103 : Triangle type {3,4,12} Group order 240 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, (x * z * y)^2, y * z^-2 * x^-1 * z^3 ] T41.104 : Triangle type {3,4,12} Group order 240 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, (y * z^-1)^2, x^-1 * z * y^-1 * z^-2 * x * z^-4 ] T41.105 : Triangle type {3,5,5} Group order 300 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^-5, z^2 * y^-1 * x^-1 * z^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T41.106 : Triangle type {3,5,5} Group order 300 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^-5, z^2 * y^-1 * x^-1 * z^2, (x^-1 * z * y)^2, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1 ] T41.107 : Triangle type {3,6,6} Group order 240 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^6, z^6, y * x^-1 * y * x^-1 * y^-1 * x * z, y * z^-1 * y * x^-1 * y^-1 * z * y ] T41.108 : Triangle type {3,6,12} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^6, z^-1 * y^2 * x^-1 * y^3, z^2 * y * x^-1 * z * y^-1 * x, y * z^-1 * x^-1 * y^-1 * x * z * y * z^-1 ] T41.109 : Triangle type {3,8,8} Group order 192 Action chiral Defining relators: [ x^3, x * y * z, (x^-1 * z * y)^2, y * z^-1 * y * x^-1 * y^-1 * z^-2 ] T41.110 : Triangle type {3,8,8} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, (x^-1 * z * y)^2, (z^-1 * y)^3, y^3 * x^-1 * z^3, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T41.111 : Triangle type {3,8,8} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, (x^-1 * z * y)^2, y^3 * x^-1 * z^3, z * y^2 * x^-1 * y^-1 * z * y^-1 ] T41.112 : Triangle type {3,8,8} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, (z^-1 * y)^3, y^3 * x^-1 * z^3, z^-2 * y * x^-1 * z * y^2 ] T41.113 : Triangle type {3,8,8} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3 * x^-1 * z^3, z * y^2 * x^-1 * y^-1 * z * y^-1, z^-2 * y * x^-1 * z * y^2 ] T41.114 : Triangle type {3,8,8} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y^8, y^-1 * z * y^2 * x * z * y * x^-1 ] T41.115 : Triangle type {3,8,8} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, (z^-1 * y)^3, y^8 ] T41.116 : Triangle type {3,8,8} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y * z^-1 * y * x^-1 * y^-1 * z^-2, y^8 ] T41.117 : Triangle type {3,8,8} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^8, y * z^-1 * y^3 * x^-1 * y^-1 * z^4 ] T41.118 : Triangle type {3,8,8} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, (z^-1 * y)^3, y * z^-1 * y * x^-1 * y^-1 * z^2, y^2 * x^-1 * y^-1 * x * z * y^2 ] T41.119 : Triangle type {3,8,8} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T41.120 : Triangle type {3,8,8} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, (y * z^-1 * y)^2, (y * z^-2)^2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y^8 ] T41.121 : Triangle type {3,8,8} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^3 * x^-1 * z^3, y^8 ] T41.122 : Triangle type {3,33,33} Group order 132 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, y * z^-2 * y^5 * z^-2 * y ] T41.123 : Triangle type {3,123,123} Group order 123 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-30 * z * y^-1 * z * y^-6 * z^2 ] T41.124 : Triangle type {4,4,4} Group order 320 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, x^-1 * z * y * x^2 * z * y * x^-1, y * z^-1 * x^-1 * y^-1 * x * z * y^-1 * z ] T41.125 : Triangle type {4,4,4} Group order 320 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, y * x * z^-1 * x^-1 * y^-1 * z^-1 * x^-1, y^-2 * z^-1 * x^-1 * z * y^-1 * z ] T41.126 : Triangle type {4,4,4} Group order 320 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * z^-1 * x * z^-2 * y * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x * z * y ] T41.127 : Triangle type {4,4,4} Group order 320 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x * z ] T41.128 : Triangle type {4,4,4} Group order 320 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * z^-1 * x * z^-2 * y * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T41.129 : Triangle type {4,4,4} Group order 320 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, y * z^-1 * y * z^-1 * y * x * z * y * x * z ] T41.130 : Triangle type {4,4,4} Group order 320 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x^-1 * z ] T41.131 : Triangle type {4,4,6} Group order 240 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^6, y * z^-1 * x^-2 * z^2 * x^-1, z * x^-1 * y * x^-1 * z^2 * y^-1 ] T41.132 : Triangle type {4,4,6} Group order 240 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^6, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z^2 * y * x^-1 * y^-1 * z * x^-1 ] T41.133 : Triangle type {4,4,6} Group order 240 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, z^-1 * x^-1 * y * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 ] T41.134 : Triangle type {4,4,6} Group order 240 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (x * z * y)^2, z^6, z^-3 * x^-1 * z^2 * y^-1, z * x^-1 * y * x^2 * y^-1 * z^-1 * x ] T41.135 : Triangle type {4,4,6} Group order 240 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (x * z * y)^2, z^6, z^-3 * x^-1 * z^2 * y^-1, z * x^-1 * y * x^2 * y^-1 * z * y^-1 ] T41.136 : Triangle type {4,4,10} Group order 200 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^4, y * x^-1 * y^-1 * x * z^-2, y^-1 * z^-1 * y * x * z * x^-1, y^-1 * z^-5 * x^-1 * z^4 ] T41.137 : Triangle type {4,4,10} Group order 200 Action chiral Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, z^-3 * x^-1 * z * y^-1 * z^-1, z * x^-1 * y * x^2 * y^-1 * z^-1 * x^-1 ] T41.138 : Triangle type {4,4,10} Group order 200 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z * x^-1 * y * x^-1 * y^2 * x, z^10 ] T41.139 : Triangle type {4,4,10} Group order 200 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^3 * y^-1 * z^2 * x^-1 * y * z^-2 * x * z ] T41.140 : Triangle type {4,4,12} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, (x * z^-1 * y)^2, z^2 * y * z^-3 * x^-1 * y * x * y^-1 * x * z^4 ] T41.141 : Triangle type {4,4,12} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (y * z^-1)^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z^12 ] T41.142 : Triangle type {4,4,12} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y^-1 * z * y * x^-1 * y^-1 * z^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z * y * z^-1 * x^-1 * z^3 ] T41.143 : Triangle type {4,4,12} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y^-1 * z * y * x^-1 * y^-1 * z^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z^-3 * x^-1 * z^2 * y^-1 ] T41.144 : Triangle type {4,4,12} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, z^-3 * x^-1 * z^2 * y^-1 ] T41.145 : Triangle type {4,4,12} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z * x^-1 * y * x^-1 * y^2 * x, z * y * x^-1 * y^-1 * x * z^3 ] T41.146 : Triangle type {4,4,12} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-2 * z^2 * x^-1, y * z^-5 * x * z^6 ] T41.147 : Triangle type {4,4,12} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, (x * z^-2)^2, y^-1 * z^-6 * x^-1 * z^5 ] T41.148 : Triangle type {4,4,12} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-3 * x^-1 * z^2 * y, (x * z^-1)^4 ] T41.149 : Triangle type {4,4,12} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, z^-1 * x^-1 * z * y^-1 * x * z^2 * y^-1 ] T41.150 : Triangle type {4,4,12} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-3 * x^-1 * z^2 * y^-1, (x * z^-1)^4 ] T41.151 : Triangle type {4,4,12} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, z^-1 * x^-1 * z * y^-1 * x * z^2 * y ] T41.152 : Triangle type {4,4,12} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-2 * y * x^-1 * z * y^2, z^12 ] T41.153 : Triangle type {4,4,12} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, x * z^3 * y * z^-1 * x^-1 * y^-1 * x * y^-1 * x * y^-1 * z^-4 ] T41.154 : Triangle type {4,4,12} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, y * x * z * y * x * z^3 ] T41.155 : Triangle type {4,4,12} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * x^-1 * y^-1 * x * z * y * z^-1 ] T41.156 : Triangle type {4,4,12} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, y * z^-1 * x^-1 * y^-1 * x * z^3 ] T41.157 : Triangle type {4,4,12} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z * y * x^2 * z * y^-1, x^-1 * y * z^-2 * y * z^-1 * x^-1 * z, z^-6 * x * z^4 * y * z^-1 ] T41.158 : Triangle type {4,4,12} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-2)^2, z * y^-1 * z^-5 * x^-1 * y * z^-4 * x ] T41.159 : Triangle type {4,4,12} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y^-1 * z^-1 * x^-2 * z^2 * x^-1, z^-7 * x * y * z^-4 ] T41.160 : Triangle type {4,4,18} Group order 180 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z * x^-1 * y * x^-1 * y^2 * x, z^-3 * x * z * y * x * z * y^-1 * z^-2 ] T41.161 : Triangle type {4,4,22} Group order 176 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^10 * y^-1 * z^-3 * x^-1 * z * y * z^-6 * x ] T41.162 : Triangle type {4,4,42} Group order 168 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-29 * x^-1 * y^-1 * z^-12 ] T41.163 : Triangle type {4,4,82} Group order 164 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-28 * x^-1 * y * z^-12 ] T41.164 : Triangle type {4,6,6} Group order 192 Action chiral Defining relators: [ x * y * z, x^4, (y^-1 * x)^3, y^6, x^-1 * z * y * x^-1 * y^-1 * z^-1 ] T41.165 : Triangle type {4,6,6} Group order 192 Action reflexible [n] Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * y^-2, y^6 ] T41.166 : Triangle type {4,6,6} Group order 192 Action chiral Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x^-1 * y^-1 * z^-1, z^6, y * z^-1 * y * x^-1 * y^-1 * z^2, y * x^-1 * y * x^2 * z^2 * x^-1 ] T41.167 : Triangle type {4,6,6} Group order 192 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x * y^-1 * z^-1, z^6, z^-2 * y * x^-1 * y * z^-1 * y ] T41.168 : Triangle type {4,6,6} Group order 192 Action chiral Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x * z * y, (y * z^-2)^2, z^6 ] T41.169 : Triangle type {4,6,6} Group order 192 Action chiral Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (x * z * y)^2, z^6, y * z^-1 * y * x^-1 * y^-1 * z^2, z^-2 * y * x^-1 * y * z^-1 * y ] T41.170 : Triangle type {4,6,6} Group order 192 Action reflexible [n] Defining relators: [ x * y * z, x^4, y * x * y^-1 * x * z * y, y^6 ] T41.171 : Triangle type {4,6,6} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^6, (z^-1 * x)^3, z * y^-1 * z^-1 * x * z * y^-1, y * x^-1 * y * x^-1 * y^-1 * z^-2 ] T41.172 : Triangle type {4,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x * y^-1 * z^-1, z^6, z^-1 * y^2 * x^-1 * y^3 ] T41.173 : Triangle type {4,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^2 * x^-1 * z^2, y^6, y * x * z^-1 * x^-1 * y^-1 * x * z ] T41.174 : Triangle type {4,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x * y^-1 * x * y^-1 * z^-1, y^6, z^-1 * x * z^-1 * x * z * y^-1 ] T41.175 : Triangle type {4,6,6} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y^-1 * x)^3, y^6, y * z^-1 * y * x^-1 * z * y, z^-1 * x * z^-1 * x^-1 * y^-1 * z^-1 * y, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^2 ] T41.176 : Triangle type {4,6,6} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, z * y^-1 * x * z, y^6, y^-1 * z^-1 * x * y^-1 * z^-1 * x^-1 * y^-1 * z * y^-2 * z^-1 * x ] T41.177 : Triangle type {4,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^6, y * z^-1 * y * x^-1 * y^-1 * z^2, y^2 * z^-1 * x^-1 * z * y^-1 * z ] T41.178 : Triangle type {4,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * y^-1 * z, y^6 ] T41.179 : Triangle type {4,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * z * y, z^6, y * z^-1 * y * x^-1 * y^2 * z^-1 ] T41.180 : Triangle type {4,6,6} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (y * z^-2)^2, z^6, z^-1 * y^2 * x^-1 * y^3, y * z^-1 * y * x^-1 * y * x * z ] T41.181 : Triangle type {4,6,6} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^6, (x * z * y)^2, z^2 * y * x^-1 * z * y^-1, (z^-1 * x)^3 ] T41.182 : Triangle type {4,6,6} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (x * z * y)^2, (y * z^-2)^2, z^6, z^-1 * y^2 * x^-1 * y^3 ] T41.183 : Triangle type {4,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^6, (y * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1, y * x^-1 * y * x^2 * z^2 * x^-1 ] T41.184 : Triangle type {4,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-1 * y^-1 * x * z * y, y^6 ] T41.185 : Triangle type {4,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * z * y, (z^-1 * y)^3 ] T41.186 : Triangle type {4,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * y^-1 * z^-1, z^6, y * z^-1 * y * x^-1 * y^2 * z^-1 ] T41.187 : Triangle type {4,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * y)^3 ] T41.188 : Triangle type {4,8,8} Group order 160 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y^-2 * z^-1 * x^-1 * z * y^-1 * z ] T41.189 : Triangle type {4,8,8} Group order 160 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z * y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x^-1 ] T41.190 : Triangle type {4,8,8} Group order 160 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, z^-1 * y * z^-1 * x^-1 * z * y^-2, y^8 ] T41.191 : Triangle type {4,8,8} Group order 160 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y^-1 * z * y * x^-1 * z * y^-1 * z ] T41.192 : Triangle type {4,8,8} Group order 160 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y^2 * z^-1 * x^-1 * z * y^-1 * z, y^8 ] T41.193 : Triangle type {4,8,8} Group order 160 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z * y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * x ] T41.194 : Triangle type {4,8,8} Group order 160 Action chiral Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, x * z^-1 * x^-2 * z * y^-1 * z^-1, y^8 ] T41.195 : Triangle type {4,8,8} Group order 160 Action chiral Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^-1 * x * z^-1 * x^-1 * y * z^-1 * x ] T41.196 : Triangle type {4,16,16} Group order 128 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * z * y * z^-1, y * z^-1 * y * x^-1 * z * y^-1 * z ] T41.197 : Triangle type {4,16,16} Group order 128 Action reflexible [n] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x * y^-2)^2, x^-1 * z * y * x * z * y ] T41.198 : Triangle type {4,16,16} Group order 128 Action reflexible [n] Defining relators: [ x * y * z, x^4, z * x^-1 * y^-1 * x * y^-1 * z, z * y^-2 * x * z * x^-1, x^-1 * z * y * x^-1 * y^-1 * z^-1 ] T41.199 : Triangle type {4,16,16} Group order 128 Action chiral Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, x^-1 * z * y * x^-1 * y^-1 * z^-1 ] T41.200 : Triangle type {4,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, (y^-4 * z * y^-1 * z * y^-1)^2 ] T41.201 : Triangle type {4,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, z^-2 * y^3 * z^-2 * y ] T41.202 : Triangle type {4,16,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y^-1 * z^-1 * y * x * z * x^-1, y^2 * z^-1 * y^2 * z^-3 ] T41.203 : Triangle type {4,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^4 * z^-3 ] T41.204 : Triangle type {4,16,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^4 * z^-3 ] T41.205 : Triangle type {4,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, z^-1 * y^4 * z^-3 ] T41.206 : Triangle type {4,16,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, z * y^2 * x * z * x^-1, y^5 * z^-1 * y * z^-1 ] T41.207 : Triangle type {4,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, (y * z^-2 * y)^2 ] T41.208 : Triangle type {4,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y^-5 * z * y^-3 * z^2 * y^-3 * z * y^-1 ] T41.209 : Triangle type {4,16,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * x^-1 * z^2, y^5 * z^-1 * y * z^-1 ] T41.210 : Triangle type {4,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, z^-1 * x * y^-1 * x * z * y, z * y^2 * x * z * x^-1, y^5 * z^-1 * y * z^-1 ] T41.211 : Triangle type {4,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, y^5 * z^-1 * y * z^-1 ] T41.212 : Triangle type {4,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * z^2 * y^-1, z^-1 * y^4 * z^-3 ] T41.213 : Triangle type {4,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, y^3 * x^-1 * z^3, (y * z^-1 * y^2)^2 ] T41.214 : Triangle type {4,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, (y * z^-1 * y^2)^2 ] T41.215 : Triangle type {4,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * z^2 * y^-1, z^-1 * y^4 * z^-3 ] T41.216 : Triangle type {4,16,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * z^2 * y^-1, z^-2 * y^3 * z^-2 * y ] T41.217 : Triangle type {4,16,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, (y^-4 * z * y^-1 * z * y^-1)^2 ] T41.218 : Triangle type {4,16,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * y * z^-1 * y * z^-3 ] T41.219 : Triangle type {4,16,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * x^-1 * z^2, z^-2 * y^3 * z^-2 * y ] T41.220 : Triangle type {4,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^4 * x^-1 * y^-3 * z, z^2 * y * z^-1 * x^-1 * z^4 ] T41.221 : Triangle type {4,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z * y^-1 * z^-2 * x^-1 * z^4, y^4 * x^-1 * y^-3 * z ] T41.222 : Triangle type {4,16,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, (y * z^-1 * y^2)^2, z^-4 * x^-1 * y * z^-3 ] T41.223 : Triangle type {4,16,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^5 * z^-1 * y * z^-1, z^-4 * x^-1 * y * z^-3 ] T41.224 : Triangle type {4,20,30} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^7 * z^-1 * y * z^-1 ] T41.225 : Triangle type {4,24,24} Group order 120 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * y^2 * z^-2 ] T41.226 : Triangle type {4,24,24} Group order 120 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, z^-1 * y^2 * x^-1 * y * z^-1 * y ] T41.227 : Triangle type {4,56,56} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-24 * z * y^-1 * z * y^-1 ] T41.228 : Triangle type {4,56,56} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y^10 * z^-2 * y^7 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T41.229 : Triangle type {5,5,10} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^-5, y^-5, (x * z * y)^2, z * y^-1 * z^-1 * x * z^2 ] T41.230 : Triangle type {5,5,10} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, x^-5, y^-5, z^-1 * y * x^-2 * y^2 * z^-1 ] T41.231 : Triangle type {5,5,10} Group order 160 Action reflexible [m,n] Defining relators: [ x * y * z, x^-5, y^-5, (x * z * y)^2, y^-1 * z^-2 * x * z^2 ] T41.232 : Triangle type {5,5,10} Group order 160 Action reflexible [m,n] Defining relators: [ x * y * z, (x * y^-1)^2, x^-5, y^-5, y^-1 * z^-2 * x * z^2 ] T41.233 : Triangle type {6,10,15} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x^-1 * y^-1 * x * z * y, y^-3 * x^-1 * z^2 ] T41.234 : Triangle type {6,12,12} Group order 120 Action chiral Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^6, y * z^-1 * y * x^-1 * y^-1 * z^-2 ] T41.235 : Triangle type {6,34,51} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-4 * x * y^-5 ] T41.236 : Triangle type {7,14,14} Group order 112 Action chiral Defining relators: [ x * y * z, (x * z^-1)^2, z^-2 * x^-1 * y^2 ] T41.237 : Triangle type {7,14,14} Group order 112 Action chiral Defining relators: [ x * y * z, z * y * x^-1 * z * y^-1, (x * y^-1 * x)^2 ] T41.238 : Triangle type {7,14,14} Group order 112 Action chiral Defining relators: [ x * y * z, (y * z^-1)^2, y^2 * x^2 * z * y, x^-7 ] T41.239 : Triangle type {8,8,8} Group order 128 Action chiral Defining relators: [ x * y * z, z * x^-1 * y^-1 * x * y^-1 * z, z^-1 * x * y^-1 * x * z * y, z * y^2 * x * z * x^-1 ] T41.240 : Triangle type {8,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^-1 * z * y * x * y^-1 * z^-1, x^8 ] T41.241 : Triangle type {8,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x * z^-1 * x, x^8 ] T41.242 : Triangle type {8,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^8 ] T41.243 : Triangle type {8,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * x^2 * z^-1 * y, x^8 ] T41.244 : Triangle type {8,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, (x * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1 ] T41.245 : Triangle type {8,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, (x * z^-1 * y)^2 ] T41.246 : Triangle type {8,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * y * x^2 * z^-1 * y, y^-1 * x * y^-1 * x * z^2 ] T41.247 : Triangle type {8,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, (x * z^-1)^2, (x * y^-1 * x)^2, z^-1 * x^-1 * y^-1 * x * z * y, z * x^-3 * y^-3 ] T41.248 : Triangle type {8,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, z^-2 * x^-1 * z * y, z * x^-3 * y^-3 ] T41.249 : Triangle type {8,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^2 * z^-1 * y, z^-1 * x^-1 * y * x^-1 * y * x * y^-1 ] T41.250 : Triangle type {8,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, z^-2 * x^-1 * z * y, (x * y^-1 * x)^2, z * y * x^2 * z * y^-1 ] T41.251 : Triangle type {8,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, (x * z * y^-1)^2, (x * z * y)^2, (y * z^-2)^2, y * x^-3 * y^-1 * z * y ] T41.252 : Triangle type {8,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, z^-2 * x^-1 * z * y, (x * y^-1 * x)^2, z^-1 * y * x^2 * z^-1 * y ] T41.253 : Triangle type {8,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * y * x^2 * z^-1 * y, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1 ] T41.254 : Triangle type {8,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, (x * z^-1 * y)^2, (x^-1 * z * y)^2, (x * z * y)^2 ] T41.255 : Triangle type {8,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y, (x * z^-1 * y)^2, (x^-1 * z * y)^2 ] T41.256 : Triangle type {8,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * y * x^2 * z^-1 * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, (x * z * y^-1)^2 ] T41.257 : Triangle type {8,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, x^8 ] T41.258 : Triangle type {8,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, x^-1 * z * y * x * y^-1 * z^-1, x^8 ] T41.259 : Triangle type {8,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z * y^-1 * x^2 * z * y^-1, z^-1 * x^-1 * y^-1 * x * z * y, x^8 ] T41.260 : Triangle type {8,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^8 ] T41.261 : Triangle type {8,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * y^2 * x * z^-1 * x, z^-1 * x^-3 * y * z^-2 ] T41.262 : Triangle type {8,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, (x * z * y)^2 ] T41.263 : Triangle type {8,8,8} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, (x * z * y)^2 ] T41.264 : Triangle type {8,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, y^-1 * x * y^-1 * x * z^2, z^-1 * y^2 * x * z^-1 * x ] T41.265 : Triangle type {8,8,8} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, y^-1 * x * y^-1 * x * z^2, z * y^2 * x^-1 * z * x^-1 ] T41.266 : Triangle type {8,8,12} Group order 120 Action chiral Defining relators: [ x * y * z, x^-1 * y * x^-1 * y^-1 * z^-1, z^2 * x^-1 * z * y^-1 ] T41.267 : Triangle type {8,8,12} Group order 120 Action chiral Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, y^-1 * z^-1 * x^2 * z^-1 * x^-1 ] T41.268 : Triangle type {8,8,28} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^3 * y * z^-1 * x^-1 * y^-1 * z^-3 * x * y^-1 * x^-1 * z^4 ] T41.269 : Triangle type {8,8,28} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^5 * y^-1 * z^-3 * x * y^-1 * x * z^4 ] T41.270 : Triangle type {8,48,48} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^-1 * z^6 * y^-1 * z^4 ] T41.271 : Triangle type {8,48,48} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^8, y * z^-1 * y * z^-9 ] T41.272 : Triangle type {8,48,48} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^-1 * z^6 * y^-5 ] T41.273 : Triangle type {8,48,48} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^8, y * z^-1 * y * z^-5 * y^4 ] T41.274 : Triangle type {10,20,20} Group order 100 Action chiral Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * y * x^-1 * y^-1 * z, y^-1 * x^4 * y^-3 ] T41.275 : Triangle type {10,20,20} Group order 100 Action chiral Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z^-1 * x^-1 * z * y^-1, x^10 ] T41.276 : Triangle type {10,20,20} Group order 100 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^10, y^-1 * z * y^-4 * z^4 ] T41.277 : Triangle type {10,20,20} Group order 100 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^-1 * y^-1 * x^2 * z * x^-1, x^10 ] T41.278 : Triangle type {10,20,20} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * x^3 * z^-1 * x^-1, x^2 * y^-1 * x^2 * y^-3 ] T41.279 : Triangle type {10,20,20} Group order 100 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^10, y^-2 * z * y^-1 * z * y^-1 * x * z * y^-1 * z * y^-1 ] T41.280 : Triangle type {12,16,48} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, z^-2 * y * z^-1 * y * z^-3 ] T41.281 : Triangle type {12,16,48} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * y^2 * z^-3, x^12 ] T41.282 : Triangle type {12,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, (y * z^-1)^2, x^-12 ] T41.283 : Triangle type {12,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-1 * z^-1, y^-1 * z^-1 * x^-1 * z * y^-1, x^-4 * y * x^-1 * y ] T41.284 : Triangle type {12,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, (y * z^-1)^2, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * y^-1 * z, (x * z * y)^2, x^-4 * y * x^-1 * y ] T41.285 : Triangle type {12,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^3 * z^-2, z^-1 * x^4 * y^-2 * z^-1 ] T41.286 : Triangle type {12,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x * y^-1 * x^3 * y^-3, x * z^-1 * x^3 * z^-3 ] T41.287 : Triangle type {12,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^12 ] T41.288 : Triangle type {12,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^-12 ] T41.289 : Triangle type {12,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * y^-1 * z^-1, x * y^-1 * x^3 * y^-1 * z^-2 ] T41.290 : Triangle type {12,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^12 ] T41.291 : Triangle type {12,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, z^-1 * y^4 * z^-3 ] T41.292 : Triangle type {16,16,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z * y^-1 * z^-1 * x^-1 * z^3 ] T41.293 : Triangle type {16,16,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * z^-1 * x, z^-1 * y^3 * z^-1 * y, z^-3 * x^-1 * z^2 * y^-1 ] T41.294 : Triangle type {16,16,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * z^-1 * x, z^-1 * y^3 * z^-1 * y, z * y^-1 * z^-1 * x^-1 * z^3 ] T41.295 : Triangle type {16,16,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-3 * x^-1 * z^2 * y^-1, z^2 * y^-1 * z * x^-1 * z^4 ] T41.296 : Triangle type {18,30,45} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^-2 * y^3 * x^-9 * y^2 * x^-4 ] T41.297 : Triangle type {18,30,45} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, z^-3 * x * z^-1 * x^9 * z^-1 ] T41.298 : Triangle type {22,44,44} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^3 * x^-7 * y^2 * z^-1 * y^2 ] T41.299 : Triangle type {22,44,44} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^4 * z^-1 * y^6 * z^-1 * y^4 ] T41.300 : Triangle type {22,44,44} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^6 * x^-2 * z^2, x^-6 * y^4 ] T41.301 : Triangle type {22,44,44} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, x^-2 * z^4 * x^-6 ] T41.302 : Triangle type {22,44,44} Group order 88 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^10 * z^-1 * x^7 * y^-1 * x^4 ] T41.303 : Triangle type {42,84,84} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-4 * x^4 * y^-1 * z^3 * y^-2 ] T41.304 : Triangle type {42,84,84} Group order 84 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * x^-3 * z^2, (x * y^-4)^2 ] T41.305 : Triangle type {42,84,84} Group order 84 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^42, y * z^-1 ] T41.306 : Triangle type {83,83,83} Group order 83 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^36 * x^-1 * y^5, x * z^-1 ] T41.307 : Triangle type {83,83,83} Group order 83 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-20 * x^3 * y^-3 * x * y^-2 ] T41.308 : Triangle type {83,83,83} Group order 83 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-2 * x^6 * y^-1 * x * y^-5 * x * y^-4 * x * y^-2 ] T41.309 : Triangle type {83,83,83} Group order 83 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x * y^-13 * x * y^-2 ] T41.310 : Triangle type {83,83,83} Group order 83 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^-1 * x * y^-5 * x^5 * y^-1 * x * y^-1 ] T41.311 : Triangle type {83,83,83} Group order 83 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x * y^-5 * x^7 ] T41.312 : Triangle type {83,83,83} Group order 83 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^3, y^-5 * x^5 * y^-1 ] T41.313 : Triangle type {83,83,83} Group order 83 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^5 * x^-1 * z^3, x^-7 * y^3 ] T41.314 : Triangle type {83,83,83} Group order 83 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, z^5 * x^-1 * z^4 ] T41.315 : Triangle type {83,83,83} Group order 83 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^5 * y^-3, z^6 * x^-1 * z^4 ] T41.316 : Triangle type {83,83,83} Group order 83 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-6 * x^2 * z^-5 * y * z^-4 ] T41.317 : Triangle type {83,83,83} Group order 83 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^4 * x^-2 * z^-5 * y * z^-1 * y^2 ] T41.318 : Triangle type {83,83,83} Group order 83 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, y^-2 * z^5 * y^-2 * z^2 ] T41.319 : Triangle type {83,83,83} Group order 83 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^-2 * z * x^-1 * z^4 * x^-6 ] Genus 42 T42.1 : Triangle type {2,4,45} Group order 360 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-28 * x * z^9 * y^-1 * x * z * y^-1 * z^-5 ] T42.2 : Triangle type {2,4,86} Group order 344 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-78 * x * y * z^-7 ] T42.3 : Triangle type {2,4,168} Group order 336 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-76 * x * y^-1 * z^-7 ] T42.4 : Triangle type {2,5,10} Group order 410 Action chiral Defining relators: [ x^2, x * y * z, y^-5, z^2 * y * z^-1 * y^2 * z^-1 * y * z^-1 * x ] T42.5 : Triangle type {2,5,10} Group order 410 Action chiral Defining relators: [ x^2, x * y * z, y^-5, z * y * z^-2 * y^2 * z^-2 * x * y^-1, (y * z^-2 * y * z^-1)^2, z * y * z^-1 * y * x * y^-1 * z^-4 * x ] T42.6 : Triangle type {2,6,44} Group order 264 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^17 * y * x * z^8 * y * x * z * y * z^-9 * x * z^6 ] T42.7 : Triangle type {2,8,8} Group order 328 Action chiral Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, (y * z^-1)^4, z^-1 * x * z * y^3 * x * y^-1 * z^-1 * y ] T42.8 : Triangle type {2,8,30} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, x * z^3 * y * x * z^3 * y * z^-1 * x * y^-1 * z^-2 * x * y^-1 * z^-2 ] T42.9 : Triangle type {2,8,30} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^12 * y * x * z * y^-1 * z^-11 * x * z^4 ] T42.10 : Triangle type {2,10,105} Group order 210 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^3 * y * z^-2 * x * z^15 ] T42.11 : Triangle type {2,14,16} Group order 224 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^2 * x * y^-10 * z^-1 * y, z^4 * y * x * z^3 * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z^2 ] T42.12 : Triangle type {2,26,91} Group order 182 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^4 * y * z^-3 * x * z^2 * y^-1 * z^-3, y^-2 * z^3 * y^-4 * z^4 ] T42.13 : Triangle type {2,44,88} Group order 176 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^-11 * z^3 * y^-6 * z * y^-1 ] T42.14 : Triangle type {2,45,45} Group order 180 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-41 * z * y^-1 ] T42.15 : Triangle type {2,58,87} Group order 174 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-1 * y^10 * z^-3 * y^13 * z^-1 ] T42.16 : Triangle type {2,85,170} Group order 170 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^69 * y^-14 * z ] T42.17 : Triangle type {2,86,86} Group order 172 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^16 * z^-70 ] T42.18 : Triangle type {2,168,168} Group order 168 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^15 * z^-69 ] T42.19 : Triangle type {3,43,129} Group order 129 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-32 * z * y^-1 * z * y^-7 * z ] T42.20 : Triangle type {3,44,44} Group order 132 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^31 * y^-3 * z * y^-7 * z ] T42.21 : Triangle type {3,126,126} Group order 126 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-31 * z * y^-1 * z * y^-8 ] T42.22 : Triangle type {4,4,43} Group order 172 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^36 * y * x * z^6 ] T42.23 : Triangle type {4,4,84} Group order 168 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-29 * x^-1 * y * z^-12 ] T42.24 : Triangle type {4,8,18} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-1 * z * x^-1 * y^-2, z * y^2 * x^-1 * z * y^-1 * z, z^4 * y^-1 * x * z^4 ] T42.25 : Triangle type {4,8,18} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^6 * y * x * z^6 * y * x * z^4 ] T42.26 : Triangle type {4,20,60} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-2 * x^-1 * z^3, y^7 * z^-1 * y * z^-1 ] T42.27 : Triangle type {4,29,116} Group order 116 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^-10 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-3 * z^3 * y^-1 * z^2 ] T42.28 : Triangle type {4,30,30} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, y^2 * z^-1 * y * z^-3 * y^2 * z^-3 * y^2 * z^-1 ] T42.29 : Triangle type {4,30,30} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-1 * z * y^-2 * z^2 * y^-1 * z * y^-10 * z * y^-5 * z * y^-5 ] T42.30 : Triangle type {4,112,112} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^10 * z^-2 * y^7 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T42.31 : Triangle type {5,5,5} Group order 205 Action chiral Defining relators: [ x * y * z, x^-5, y^-5, z^2 * y^-1 * x^-1 * z^2, z^-1 * y * x^-2 * y^2 * z^-1, x * z^-1 * y * x^-1 * z * x^-1 * y ] T42.32 : Triangle type {5,5,5} Group order 205 Action chiral Defining relators: [ x * y * z, x^-5, y^-5, z^2 * y^-1 * x^-1 * z^2, z^-1 * y * x^-2 * y^2 * z^-1, y^-1 * z^-1 * x^-2 * z^2 * x^-1 ] T42.33 : Triangle type {5,22,110} Group order 110 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, z^-3 * y * z^-1 * y^8 * z^-1 * y * z^-1 * y * z^-1 * y * z^-3 ] T42.34 : Triangle type {5,105,105} Group order 105 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-5, y * z^-1 * y * z^-1 * y^8 * z^-1 * y * z^-1 * y * z^-1 * y * z^-3 ] T42.35 : Triangle type {5,105,105} Group order 105 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y * z^-1 * y * z^-1 * y^8 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T42.36 : Triangle type {6,6,22} Group order 132 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-9 * x^-1 * y * x^-1 * y^-1 * x * z^4 * y^-1 * z^-6 ] T42.37 : Triangle type {6,10,20} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^-1 * z^2 * y^-1 * z * x^-1 * y^-1 * x^-1 * y^-1 * z^3 ] T42.38 : Triangle type {6,27,27} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^2 * x^-1 * z^2, x^6, y^-1 * z * y^-1 * z^2 * y^-1 * z * y^-2 ] T42.39 : Triangle type {6,51,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-4 * x * y^-4 * z ] T42.40 : Triangle type {7,15,105} Group order 105 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, y * z^-4 * x * y^4 * z^-1 * y * z^-1 * y^3 ] T42.41 : Triangle type {7,16,16} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^-7, y^-16 ] T42.42 : Triangle type {7,98,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, y^-2 * z^4 * x^-2 * z^4 * y^-4 ] T42.43 : Triangle type {7,98,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, z^-1 * y * z^-1 * y * z^-5 * y^4 * z^-1 ] T42.44 : Triangle type {7,98,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, z^2 * y^-3 * z^5 * y^-1 * z * y^-1 * z ] T42.45 : Triangle type {8,8,15} Group order 120 Action reflexible [n] Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * z, z * x^-3 * y^-3, x^8 ] T42.46 : Triangle type {8,8,15} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^3 * y * x^-1 * y * x^-1 * y * x^-1 * z^3 * y * z^-1 * x^-1 * z^4 ] T42.47 : Triangle type {8,13,104} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, z * y^-1 * z * y^-1 * z * y^-4 * x^-1 * z^4 ] T42.48 : Triangle type {8,14,14} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^8, y^-14 ] T42.49 : Triangle type {8,96,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, y * z^-1 * y * z^-5 * x * z^-4 ] T42.50 : Triangle type {8,96,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, y * z^-1 * y * z^-5 * y^3 * z^-1 ] T42.51 : Triangle type {9,9,13} Group order 117 Action reflexible [n] Defining relators: [ x * y * z, z * x^-2 * y^-2, z^-2 * x^-1 * y^-1 * z^-1, x^-9 ] T42.52 : Triangle type {12,32,32} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * y^-1 * z^-1, y * z^-1 * y * z^-1 * y * z^-3 ] T42.53 : Triangle type {13,91,91} Group order 91 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-6 * z, x^13 ] T42.54 : Triangle type {13,91,91} Group order 91 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-4 * x^-1 * z^3, x^13 ] T42.55 : Triangle type {13,91,91} Group order 91 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * y^-3 * x^-1 * z^3, x^13 ] T42.56 : Triangle type {13,91,91} Group order 91 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-4 * x * y^-3, z^-3 * x^5 * z^-4 ] T42.57 : Triangle type {13,91,91} Group order 91 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-4, z^-1 * y * z^-1 * x^5 * z^-4 ] T42.58 : Triangle type {13,91,91} Group order 91 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y^-3 * x^3 * y^-4, z^3 * y^-2 * x^-5 * z^2 ] T42.59 : Triangle type {15,90,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-1 * z^2 * x^-7 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T42.60 : Triangle type {15,90,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x * y^-1 * x * y^-2 * x^6 * y^-3 ] T42.61 : Triangle type {15,90,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, x^2 * y^-2 * x^5 * y^-4 ] T42.62 : Triangle type {18,45,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, x^2 * y^-2 * x^6 * y^-3 ] T42.63 : Triangle type {18,45,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^-2 * y * x^-9 * y^2 * x^-1 * y * x^-1 * y * x^-1 ] T42.64 : Triangle type {18,45,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^-2 * x * z^-1 * x * z^-1 * x^9 * z^-1 ] T42.65 : Triangle type {22,88,88} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^8 * x^-1 * z^4 ] T42.66 : Triangle type {22,88,88} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, (x^-2 * z^4)^2 ] T42.67 : Triangle type {22,88,88} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-4 * x * y^-10 * x * y^-2 ] T42.68 : Triangle type {22,88,88} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^5 * z^-1 * x^12 * z^-1 * x * z^-1 * x * z^-1 ] T42.69 : Triangle type {22,88,88} Group order 88 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^-3 * z^4 * x^-6 ] T42.70 : Triangle type {29,87,87} Group order 87 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^4 * z^-2 * y^2 * x^-1 * y^7 ] T42.71 : Triangle type {29,87,87} Group order 87 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * x^-3 * z^2, y^-5 * x * y^-4 ] T42.72 : Triangle type {29,87,87} Group order 87 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^10 * y^-1 * x * y^-5 * x * y^-4 * x * y^-2 ] T42.73 : Triangle type {29,87,87} Group order 87 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * y^-4, x^-2 * z^3 * x^-6 ] T42.74 : Triangle type {29,87,87} Group order 87 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^3 * x^-4 * y^6 ] T42.75 : Triangle type {29,87,87} Group order 87 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * z^3 * y^-1 * x * y^-4, x^-1 * z^4 * x^-4 * z^2 ] T42.76 : Triangle type {29,87,87} Group order 87 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^-1 * z * y^-1 * z * y^-3 * x^3 * y^-5 ] T42.77 : Triangle type {29,87,87} Group order 87 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-7 * y * z^-10 ] T42.78 : Triangle type {29,87,87} Group order 87 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^16 * y^-1 * x^7 * z^-1 * x^5 ] T42.79 : Triangle type {29,87,87} Group order 87 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-6 * z^2, y^-1 * z * y^-1 * z^5 * y^-3 * z ] T42.80 : Triangle type {29,87,87} Group order 87 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-1 * z^3 * x^-6, y^-1 * z^2 * y^-2 * x * y^-4 ] T42.81 : Triangle type {29,87,87} Group order 87 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^-2 * z * y^-1 * z^5 * x^3 * y^-3 ] T42.82 : Triangle type {29,87,87} Group order 87 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-5 * z^3 * x^-7 ] T42.83 : Triangle type {29,87,87} Group order 87 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^3 * z^-2 * x^6 * z^-1 * x^4 ] T42.84 : Triangle type {43,86,86} Group order 86 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-12 * z * y^-9 ] T42.85 : Triangle type {43,86,86} Group order 86 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-21 * x^3 * y^-3 * x * y^-2 ] T42.86 : Triangle type {43,86,86} Group order 86 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * x^-2 * z^2, y^-2 * x^9 * y^-2 ] T42.87 : Triangle type {43,86,86} Group order 86 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-1 * x^2 * y^-1 * x * y^-10 * x * y^-2 ] T42.88 : Triangle type {43,86,86} Group order 86 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^-2 * z^2 * x^-7 ] T42.89 : Triangle type {43,86,86} Group order 86 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-6 * x^5 * y^-2 ] T42.90 : Triangle type {43,86,86} Group order 86 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-1 * z * x^-1 * z^4 * x^-5 * z ] T42.91 : Triangle type {43,86,86} Group order 86 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^5 * x^-1 * z^3, y * x^-5 * y^3 * z^-1 * y ] T42.92 : Triangle type {43,86,86} Group order 86 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^5 * x^-1 * z^-5 * y * z^-1 * y * z^-1 ] T42.93 : Triangle type {43,86,86} Group order 86 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-1 * z^2 * x^-7, y^-1 * z^5 * y^-2 * z^2 ] T42.94 : Triangle type {43,86,86} Group order 86 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^8 * y^-1 * x^9 * z^-1 * x * z^-1 * x * z^-1 ] T42.95 : Triangle type {43,86,86} Group order 86 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4 * y^-2, z^-3 * y^2 * z^-5 * y * z^-1 * y * z^-1 * y * z^-1 ] T42.96 : Triangle type {43,86,86} Group order 86 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^-5 * z * y^-1 * z * y^-10 ] T42.97 : Triangle type {43,86,86} Group order 86 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x * z^-4 * x^2 * z^-4 * x * z^-1 * x * z^-1 * x ] T42.98 : Triangle type {43,86,86} Group order 86 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-5 * z^2, y^-2 * z^2 * y^-2 * x * y^-4 ] T42.99 : Triangle type {43,86,86} Group order 86 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * z^5 * y^-3 * z, x^-1 * z^4 * x^-6 ] T42.100 : Triangle type {43,86,86} Group order 86 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^2 * z^-3 * x^3 * z^-4 * x * z^-1 * x^3 ] T42.101 : Triangle type {43,86,86} Group order 86 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z * x^-1 * z * x^-1 * z^4 * x^-2 * z^4 ] T42.102 : Triangle type {43,86,86} Group order 86 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6 * z^-2, y^-1 * z * y^-1 * z^5 * x * y^-4 ] T42.103 : Triangle type {43,86,86} Group order 86 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^-2 * z^3 * y^-1 * x * y^-4 ] T42.104 : Triangle type {43,86,86} Group order 86 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^43, y * z^-1 ] T42.105 : Triangle type {44,44,44} Group order 88 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, z^-1 * y * x^-1 * y^-2, y^-1 * z * y^-1 * z^2 * y^-3 * x * y^-4 ] T42.106 : Triangle type {44,44,44} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2, y^-3 * x^2 * y^-3 ] T42.107 : Triangle type {85,85,85} Group order 85 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^37 * x^-1 * y^5, x * z^-1 ] T42.108 : Triangle type {85,85,85} Group order 85 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-1 * z^3 * x^-4 * z^2, y^-1 * z^2 * y^-2 * x * y^-4 ] T42.109 : Triangle type {85,85,85} Group order 85 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z * y^-1 * z * y^-1 * z^9 ] T42.110 : Triangle type {85,85,85} Group order 85 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-20 * x^4 * y^-3 * x * y^-2 ] T42.111 : Triangle type {85,85,85} Group order 85 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^7 * y^-1, y^-2 * z^5 * y^-1 * z^3 ] T42.112 : Triangle type {85,85,85} Group order 85 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-6 * z, y^-2 * z * y^-1 * z^5 * y^-4 ] T42.113 : Triangle type {85,85,85} Group order 85 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^4, x^-1 * z^4 * x^-6 ] T42.114 : Triangle type {85,85,85} Group order 85 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-1 * x^8 * y^-1 * x * y^-5 * x * y^-4 * x * y^-2 ] Genus 43 T43.1 : Triangle type {2,3,9} Group order 1512 Action chiral Defining relators: [ x^2, y^3, x * y * z, z^-4 * x * y * z^-4, z * y * x * z * y * z^-1 * x * z^2 * y * x * y^-1 * z^-2 * x * z, z^-2 * x * z * y * x * z * y * x * z^2 * y * x * z^2 * y^2 * z^-1 * x * z^2 * y^-1 * z^-1 ] T43.2 : Triangle type {2,3,9} Group order 1512 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^-4 * x * y * z^-4, z^-1 * x * z^3 * y * z^-1 * x * z^2 * y * z^-2 * x * z * y^-1 * z^-1 ] T43.3 : Triangle type {2,3,12} Group order 1008 Action chiral Defining relators: [ x^2, y^3, x * y * z, z * y * z^-3 * x * y^-1 * z^-4 * x, z * y * x * z * y^-1 * z^-2 * x * z * y * x * z * y * x * z * y * x * z^2 * y * x * z * y^-2 * z^-2 * x * z * y^-1 * z^-1 * x ] T43.4 : Triangle type {2,3,20} Group order 720 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z * y * x * z * y * x * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z ] T43.5 : Triangle type {2,4,8} Group order 672 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^8, (y * z^-2 * y * z^-1)^2, x * z * y * z^-1 * x * z^2 * y * x * z * y^-1 * z^-2 ] T43.6 : Triangle type {2,4,8} Group order 672 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^3 * y * z^-1 * x * z^2 * y^-1 * z^-2 ] T43.7 : Triangle type {2,4,88} Group order 352 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-80 * x * y * z^-7 ] T43.8 : Triangle type {2,4,88} Group order 352 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-30 * x * z^5 * y * z^-1 * x * y^-1 * z^-6 ] T43.9 : Triangle type {2,4,172} Group order 344 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-78 * x * y^-1 * z^-7 ] T43.10 : Triangle type {2,6,9} Group order 378 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-4 * x * y * z^-4, x * z * y * x * y^-1 * z * y^-3 * z^-1 * y^2 * z^-1 * y ] T43.11 : Triangle type {2,6,9} Group order 378 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-4 * x * y * z^-4, x * z * y * x * z * y * x * y^-2 * z^-1 * y * x * z * y ] T43.12 : Triangle type {2,6,9} Group order 378 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-4 * x * y * z^-4, z * y * x * y^-1 * z * y^-2 * z^-1 * y * x * y^-2 * z^-1 * x ] T43.13 : Triangle type {2,6,12} Group order 336 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^3 * y^2 * x * z^2, x * z^2 * y * x * z * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-2 ] T43.14 : Triangle type {2,6,21} Group order 294 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^2 * y * x * y^-2 * z * y^-1 * z^-2 * x ] T43.15 : Triangle type {2,6,24} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, x * z^3 * y^-1 * z^-4 ] T43.16 : Triangle type {2,6,24} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^3 * y^-1 * z^-4 ] T43.17 : Triangle type {2,6,24} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z * y * z^-1 * x * y^-1 * z^-2 * x, (y * z^-3)^2 ] T43.18 : Triangle type {2,6,24} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^-1 * x * z * y^-2 * z * y^-1 * z^-2 ] T43.19 : Triangle type {2,6,45} Group order 270 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, x * z * y * x * z^5 * y * x * y^-1 * z^-1 * x * z * y^-1 * z^-3 ] T43.20 : Triangle type {2,6,45} Group order 270 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-16 * x * z * y * x * z^15 * y * z^-1 * x * z^7 * y^-1 * z^-2 ] T43.21 : Triangle type {2,6,129} Group order 258 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^33 * y * z^-7 * x * z^2 ] T43.22 : Triangle type {2,8,8} Group order 336 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^8, y * x * z * y^2 * x * y^-1 * z^-1, z * y * z^-1 * x * y^-1 * z^-2 * x, z^8, z^-1 * y^2 * z^-1 * y^2 * z^-2 * y * z^-1 ] T43.23 : Triangle type {2,8,8} Group order 336 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, y^8, z^8, (y * z^-2 * y^2)^2 ] T43.24 : Triangle type {2,8,12} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z * y^-1 * z^-1, y^8, (y^-1 * z)^6 ] T43.25 : Triangle type {2,8,12} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z * y^-1 * z^-1, y^8, y^-1 * z * y * z^-2 * y * x * y^-1 * z^3 * y^-1 * z ] T43.26 : Triangle type {2,10,20} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, z * y * z^-1 * y^2 * z^-1 * x * y^-1, z * y * z^-1 * x * y^-1 * z^-2 * x ] T43.27 : Triangle type {2,12,15} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y * x * y^-3 * z^-1 * x * z^2 ] T43.28 : Triangle type {2,12,36} Group order 216 Action chiral Defining relators: [ x^2, x * y * z, z^2 * y * x * y^-1 * z^-2 * x, x * y^-4 * z^-2 * y * z^-1, y^12 ] T43.29 : Triangle type {2,12,36} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^4 * y * x * z^4 * y * x * y^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z ] T43.30 : Triangle type {2,12,36} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-12, z^-14 * x * z^2 * y^-1 * z^-1 ] T43.31 : Triangle type {2,15,30} Group order 210 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z * y * z^-1 * x * y^-1 * z^-1 * x * z, y^-2 * z^3 * y^-6 * z^3 * y^-1 ] T43.32 : Triangle type {2,24,48} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, z^3 * y * x * y^-1 * z^-3 * x, y^9 * z^-1 * y * z^-1 ] T43.33 : Triangle type {2,24,48} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^3 * y^-4 * z^5 ] T43.34 : Triangle type {2,87,174} Group order 174 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^70 * y^-16 ] T43.35 : Triangle type {2,88,88} Group order 176 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-18 * y^11 * z^-1 * y^13 * z^-1 ] T43.36 : Triangle type {2,88,88} Group order 176 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^17 * z^-70 * y ] T43.37 : Triangle type {2,172,172} Group order 172 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^16 * z^-69 * y ] T43.38 : Triangle type {3,3,6} Group order 504 Action chiral Defining relators: [ x^3, x * y * z, y^3, z^6, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T43.39 : Triangle type {3,3,6} Group order 504 Action chiral Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, y * x * y^-1 * x * y^-1 * x * z * y * z^-1 * x^-1 * y^-1 * x * z * y * x * y^-1 * x * z ] T43.40 : Triangle type {3,3,10} Group order 360 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z * y * x^-1 * y * x^-1 * y^-1 * x * y^-1 * x ] T43.41 : Triangle type {3,4,6} Group order 336 Action chiral Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^6, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * z * y * z^-2 * x * z^-1 * x * z^2 * y^-1 * z^-1 ] T43.42 : Triangle type {3,4,6} Group order 336 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^6, y * z^-2 * x^-1 * y * z^-2, y * z^-1 * x^-1 * y^-1 * x * z * y * z^-1 ] T43.43 : Triangle type {3,4,6} Group order 336 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^6, y * z^-2 * x^-1 * y * z^-2, (x * y^-1 * z^-1 * y)^2 ] T43.44 : Triangle type {3,4,12} Group order 252 Action chiral Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, x^-1 * z * y * z^-2 * x^-1 * z * x^-1 * z * y * x * z * y^-1 * z^-1 ] T43.45 : Triangle type {3,8,24} Group order 168 Action chiral Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y^-1 * x * z^2 * y, y^8 ] T43.46 : Triangle type {3,9,9} Group order 189 Action chiral Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, x^-1 * y * x^-1 * y * x^-1 * y^-1 * z * y^-1 * z^-1, y^-9 ] T43.47 : Triangle type {3,9,9} Group order 189 Action chiral Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y^-1 * z^-1 ] T43.48 : Triangle type {3,9,9} Group order 189 Action chiral Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y * x * z * y * x^-1 * y^-1 * z * y^-1 * z ] T43.49 : Triangle type {3,16,48} Group order 144 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^3 * z^-2 * y^6 * z^-4 * y ] T43.50 : Triangle type {3,21,21} Group order 147 Action chiral Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^2 * y^-2 * x * y^-1 * z * y^-1 ] T43.51 : Triangle type {3,24,24} Group order 144 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, (y * z^-1 * y)^2, (y * z^-2)^2, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T43.52 : Triangle type {3,24,24} Group order 144 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, (z^-1 * y)^3, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^3 * x^-1 * z^3 ] T43.53 : Triangle type {3,24,24} Group order 144 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, (z^-1 * y)^3, z^-1 * y^4 * z^-3 ] T43.54 : Triangle type {3,24,24} Group order 144 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^4 * z^-3 ] T43.55 : Triangle type {3,44,132} Group order 132 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-33 * z * y^-1 * z * y^-7 * z ] T43.56 : Triangle type {3,45,45} Group order 135 Action chiral Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, z^-3 * y^3 * z^-1 * y^5 * z^-2 * y ] T43.57 : Triangle type {3,45,45} Group order 135 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-34 * z * y^-1 * z * y^-7 * z ] T43.58 : Triangle type {3,129,129} Group order 129 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-32 * z * y^-1 * z * y^-8 ] T43.59 : Triangle type {4,4,4} Group order 336 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, (z^-1 * x)^3, x * z * y * x^-1 * y^-1 * z^-1 * y ] T43.60 : Triangle type {4,4,4} Group order 336 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, z * x^-1 * z * x^-1 * y^-1 * z * y^-1, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x ] T43.61 : Triangle type {4,4,44} Group order 176 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^13 * y * z^-1 * x^-1 * y * z^-6 * x ] T43.62 : Triangle type {4,4,44} Group order 176 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^13 * y * z^-1 * x^-1 * y * z^-6 * x^-1 ] T43.63 : Triangle type {4,4,44} Group order 176 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^44 ] T43.64 : Triangle type {4,4,86} Group order 172 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^36 * y * x^-1 * z^6 ] T43.65 : Triangle type {4,6,12} Group order 168 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^-1 * y * z^-2, z^-1 * x^-1 * z * y * x * z * y^-1 * z^-1 ] T43.66 : Triangle type {4,6,12} Group order 168 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-2)^2, z^-3 * x^-1 * y * z^-2, x^-1 * z * y^2 * x * y^-2 * z^-1 ] T43.67 : Triangle type {4,8,10} Group order 160 Action chiral Defining relators: [ x * y * z, x^4, z * y * x^-1 * y^-2, (x * z * y^-1)^2, y^-1 * z^-2 * x^-1 * z^3 ] T43.68 : Triangle type {4,8,10} Group order 160 Action chiral Defining relators: [ x * y * z, x^4, (x * y^-1)^2, (y * z^-1 * y)^2, y^-1 * z^-2 * x^-1 * z^3, y^8 ] T43.69 : Triangle type {4,8,10} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^-1 * x^-1 * z * y * x^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-3 ] T43.70 : Triangle type {4,8,10} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, z^-4 * x^-1 * z * y * x * y^-1 * z^-3 ] T43.71 : Triangle type {4,9,18} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * y^-3, y^9 ] T43.72 : Triangle type {4,12,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * y * z^-2, y^-12 ] T43.73 : Triangle type {4,12,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^-2 * z * x^-1 * y^-3 ] T43.74 : Triangle type {4,12,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^3 * x^-1 * y^-2 * z, y * z^-1 * y^2 * z^-1 * y^2 * x^-1 * y^2 * z^-3 ] T43.75 : Triangle type {4,12,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y * z^-1 * y^7 * z^-3 ] T43.76 : Triangle type {4,12,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^3 * x^-1 * y^-1 * z * y, x^-1 * z^5 * y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * z^-2 ] T43.77 : Triangle type {4,12,12} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * y^-1 * z^-1 ] T43.78 : Triangle type {4,12,12} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z * y ] T43.79 : Triangle type {4,12,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, z * y^2 * x^-1 * z * x^-1, (x * z^-1 * y)^2, y^-1 * z * y * x^-1 * y^-3 ] T43.80 : Triangle type {4,12,33} Group order 132 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^6 * y * x * z^4 ] T43.81 : Triangle type {4,30,60} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^-6 * z * y^-4 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-3 * z^3 * y^-1 * z * y^-1 ] T43.82 : Triangle type {4,58,116} Group order 116 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^-6 * z^3 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-3 * z^3 * y^-1 * z * y^-1 ] T43.83 : Triangle type {6,6,6} Group order 168 Action chiral Defining relators: [ x * y * z, x^6, y^-1 * x * y^-1 * x * z^-1 * x, y^-1 * z * y^-1 * x * y^-1 * z ] T43.84 : Triangle type {6,6,6} Group order 168 Action chiral Defining relators: [ x * y * z, z^-1 * x^-2 * y * z^-1, z * x^-2 * y^-2, y^2 * x^-1 * z^2, y * x * y^-1 * x * y^-1 * x * z * y * x * z ] T43.85 : Triangle type {6,6,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, y^6, z * y^-1 * z^-1 * x * z * y^-1 ] T43.86 : Triangle type {6,6,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y * x * y^-1 * x * y^-1 * z^-1, y^6 ] T43.87 : Triangle type {6,6,12} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, z * x^-1 * y^-1 * x * z * x^-1 ] T43.88 : Triangle type {6,6,12} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-2 * y^-2, z^-2 * x^-1 * z * y^-1, x^6 ] T43.89 : Triangle type {6,6,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, x^6, y^6, z^-1 * y^2 * x^-1 * y^3 ] T43.90 : Triangle type {6,6,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^-2 * x^2 * z^-2, y^6, z^-1 * y^2 * x^-1 * y^3 ] T43.91 : Triangle type {6,6,12} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, z * y * x^2 * z^-1 * x^-1 ] T43.92 : Triangle type {6,6,12} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, z^2 * x^-1 * z * y^-1, x^6 ] T43.93 : Triangle type {6,8,8} Group order 144 Action reflexible [n] Defining relators: [ x * y * z, x^6, z^-1 * y * x^2 * z * y^-1, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, y^8 ] T43.94 : Triangle type {6,8,8} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, x^6, x^-2 * y^-1 * x^2 * y^-1 * z^2 ] T43.95 : Triangle type {6,8,8} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, x^6, y * x^-3 * z * x^-2, y^8 ] T43.96 : Triangle type {6,9,18} Group order 126 Action chiral Defining relators: [ x * y * z, y * x^-2 * y^2, x^-1 * z * x^-1 * y^-1 * z, z^-3 * x^2 * z^-3, x^-1 * z^2 * y * x * y^-1 * z^-2 ] T43.97 : Triangle type {6,9,18} Group order 126 Action chiral Defining relators: [ x * y * z, y^2 * x * z^-1, x^6, z^-3 * x^-1 * y * z^-2, x^-1 * z^2 * y * x * y^-1 * z^-2 ] T43.98 : Triangle type {6,10,30} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x^-1 * y^-1 * x * z * y, y * x^-3 * z * x^-2, y^2 * x^-2 * y * z^-2 ] T43.99 : Triangle type {6,12,20} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6, z^5 * y * x * z^4 ] T43.100 : Triangle type {6,15,15} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y^-1 * z * y^-1 * x * z * y^-1 ] T43.101 : Triangle type {6,36,36} Group order 108 Action chiral Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, z^-2 * y^2 * z^-1 * y ] T43.102 : Triangle type {6,36,36} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^6, y^6 * x^-1 * y^4 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y ] T43.103 : Triangle type {6,36,36} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y * x^-3 * z * x^-2, z * y^-1 * z * x^-1 * y^-1 * z^2 ] T43.104 : Triangle type {6,36,36} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^6, y^-13 * x * z * y^-1 * z * y^-2 ] T43.105 : Triangle type {9,12,36} Group order 108 Action chiral Defining relators: [ x * y * z, z^-1 * x^2 * y^-1, y^-1 * x^3 * z^-1 * x^-1, y^-1 * z^4 * y^-1 * z^2 * y^-4 ] T43.106 : Triangle type {9,12,36} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-9, y^-3 * z * y^-4 * x * y^-4 ] T43.107 : Triangle type {9,12,36} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-1 * z, x^-9 ] T43.108 : Triangle type {9,12,36} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2, y * x^-3 * y^3 ] T43.109 : Triangle type {9,33,99} Group order 99 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-9, y^-2 * z * y^-6 * z^2 ] T43.110 : Triangle type {9,33,99} Group order 99 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-9, z * y^-1 * z * y^-4 * z^4 ] T43.111 : Triangle type {10,10,10} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, x * z^-1 * x^-1 * z * y ] T43.112 : Triangle type {12,12,18} Group order 108 Action reflexible [n] Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, y * z^-1 * x^2 * z * y, y * x^-3 * y * z^-1 * x^-1 ] T43.113 : Triangle type {12,12,18} Group order 108 Action chiral Defining relators: [ x * y * z, z * y * x^-1 * y * x, y * x^3 * z^2, z^3 * x^-1 * z^2 * y^-1 ] T43.114 : Triangle type {12,12,18} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, z^3 * y^-1 * z^-1 * x * z^4 ] T43.115 : Triangle type {12,12,18} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x * y^-1 * z^-3 * x * y^-1 * x * y^-1 * z^-3 ] T43.116 : Triangle type {12,32,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^12 ] T43.117 : Triangle type {12,32,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-4, x^12 ] T43.118 : Triangle type {12,48,48} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, x^12 ] T43.119 : Triangle type {12,48,48} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^-5 * z * y, y * z^-1 * y^3 * z^-3 ] T43.120 : Triangle type {15,15,15} Group order 105 Action chiral Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * z * x^-1, z^-1 * x^3 * z^-2, y^-3 * x^3 * y^-3 ] T43.121 : Triangle type {16,24,48} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^2 * z^-2, x^-7 * z * y ] T43.122 : Triangle type {16,24,48} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^-2 * z * x^-10 * y * x^-3 ] T43.123 : Triangle type {16,24,48} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * y * z^-2, x^-7 * z * y ] T43.124 : Triangle type {16,24,48} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, x^2 * z^-2 * x^4 * z^-4 ] T43.125 : Triangle type {24,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x * z^-1 * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^3 ] T43.126 : Triangle type {24,24,24} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, y^3 * x^-1 * y * z^-1 * y ] T43.127 : Triangle type {30,45,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^11 * y^-1 * x * y^-1 * x * y^-5 * x * y^-5 ] T43.128 : Triangle type {30,45,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, z^-5 * x^3 * z^-4 ] T43.129 : Triangle type {30,45,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x * y^-1 * x^7 * y^-2, z * y^-4 * x^-1 * z^4 ] T43.130 : Triangle type {30,45,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^-14 * y * x^-1 * y * x^-8 * y * x^-5 ] T43.131 : Triangle type {30,45,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^-1 * y * x^-8 * z * x^-1 * z * x^-1 * z * x^-1 * z ] T43.132 : Triangle type {30,45,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^5 * x^-2 * z^7 ] T43.133 : Triangle type {44,88,88} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, y^-1 * z^9 ] T43.134 : Triangle type {44,88,88} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, z^-1 * x^6 * z^-4 * x * z^-1 * x * z^-2 ] T43.135 : Triangle type {44,88,88} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-2 * x * y^-8 * z * y^-1 * x * y^-2 ] T43.136 : Triangle type {44,88,88} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^21 * x^-2 * y^7 ] T43.137 : Triangle type {44,88,88} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-3 * x * z^-4 * x^3 * z^-9 ] T43.138 : Triangle type {44,88,88} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * z^5 * y^-2 * z^2, x^-6 * y^4 ] T43.139 : Triangle type {44,88,88} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-2 * x^9 * y^-1 * x * y^-1 ] T43.140 : Triangle type {44,88,88} Group order 88 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^9 * x^-2 * z^3 ] T43.141 : Triangle type {44,88,88} Group order 88 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^44, y * z^-1 ] T43.142 : Triangle type {44,88,88} Group order 88 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^10 * z^-1 * x^7 * z^-1 * x^4 ] T43.143 : Triangle type {87,87,87} Group order 87 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^38 * x^-1 * y^5, x * z^-1 ] T43.144 : Triangle type {87,87,87} Group order 87 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * x^-3 * z^2, y^2 * x^-4 * y^5 ] T43.145 : Triangle type {87,87,87} Group order 87 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, z * x^-1 * z^4 * x^-2 * z^4 ] T43.146 : Triangle type {87,87,87} Group order 87 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-2 * x * y^-1 * x * y^-10 * x * y^-2 ] T43.147 : Triangle type {87,87,87} Group order 87 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z * y^-1 * z * y^-1 * z^9 ] Genus 44 T44.1 : Triangle type {2,4,90} Group order 360 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-82 * x * y * z^-7 ] T44.2 : Triangle type {2,4,176} Group order 352 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-80 * x * y^-1 * z^-7 ] T44.3 : Triangle type {2,6,6} Group order 516 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, y * x * z * y * x * z^2 * y * z^-1 * x * z * y * z^-1 * y * z^-1 * x * z * y^-1 * z^2 ] T44.4 : Triangle type {2,6,46} Group order 276 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-24 * x * z^5 * y^-1 * z^-16 ] T44.5 : Triangle type {2,6,132} Group order 264 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^17 * y * x * z^15 * y * z^-8 * x * z^2 ] T44.6 : Triangle type {2,8,60} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^12 * y * x * z * y * x * z^15 ] T44.7 : Triangle type {2,10,24} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^3 * y * x * z * y * x * z * y * x * y * x * y^-1 * z^-7 * x * y^-1 * z^-3 * x * z^3 ] T44.8 : Triangle type {2,10,110} Group order 220 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^-2 * x * z^6 * y^-1 * x * y^-1 * z^-8 * x * z^2 * y^-1 * z^-1 ] T44.9 : Triangle type {2,18,99} Group order 198 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y * z^-3 * x * y * z^-5 ] T44.10 : Triangle type {2,46,92} Group order 184 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-20 * y^11 * z^-1 * y^13 * z^-1 ] T44.11 : Triangle type {2,89,178} Group order 178 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^71 * y^-16 * z ] T44.12 : Triangle type {2,90,90} Group order 180 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^18 * z^-72 ] T44.13 : Triangle type {2,176,176} Group order 176 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^17 * z^-71 ] T44.14 : Triangle type {3,6,6} Group order 258 Action chiral Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, y * x * z * y * x^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 ] T44.15 : Triangle type {3,6,6} Group order 258 Action chiral Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y * z^-1 * y * z^-1 * y * z^-2 * y^2 * z^-1 * y * z^-1 * y * z^-1 ] T44.16 : Triangle type {3,46,46} Group order 138 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^33 * y^-3 * z * y^-7 * z ] T44.17 : Triangle type {3,132,132} Group order 132 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-33 * z * y^-1 * z * y^-6 * z^2 ] T44.18 : Triangle type {4,4,45} Group order 180 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^4, y * x^-1 * y^-1 * x * z^-2, y^-1 * z^-1 * y * x * z * x^-1, y * z^-2 * x * z^6 ] T44.19 : Triangle type {4,4,45} Group order 180 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^45 ] T44.20 : Triangle type {4,4,88} Group order 176 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^31 * y^-1 * z^-4 * x * z^8 ] T44.21 : Triangle type {4,6,14} Group order 168 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^-4 * x^-1 * z^3 * y * x^-1 * y * x * z * y * z^-3 ] T44.22 : Triangle type {4,8,36} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^6 * y * x * z^6 * y * x^-1 * z^4 ] T44.23 : Triangle type {4,12,66} Group order 132 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^6 * y * x^-1 * z^4 ] T44.24 : Triangle type {4,60,60} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, z * y^-3 * z^2 * y^-1 * z * y^-10 * z * y^-5 * z * y^-5 ] T44.25 : Triangle type {5,23,115} Group order 115 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-2 * z^4 * y^-1 * z^2 ] T44.26 : Triangle type {5,24,24} Group order 120 Action reflexible [n] Defining relators: [ x * y * z, y * x^2 * z, x * y^-1 * x * z^-1, y^10 * z^-1 * y * z^-1 * y^7 * z^-4 ] T44.27 : Triangle type {5,24,24} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^-5, y^-1 * z * y^-1 * z * y^-1 * z * y^-6 * z * y^-3 * z * y^-1 * z * y^-5 ] T44.28 : Triangle type {5,110,110} Group order 110 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y * z^-2 * y * z^-1 * y^8 * z^-1 * y * z^-1 * y * z^-1 * y * z^-3 ] T44.29 : Triangle type {5,110,110} Group order 110 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-5, z^-5 * y^8 * z^-1 * y * z^-1 * y * z^-1 * y * z^-3 ] T44.30 : Triangle type {6,6,23} Group order 138 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^-23 ] T44.31 : Triangle type {6,6,66} Group order 132 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^6 * y * z^-3 * x * y^-1 * x * y^-1 * z^-3 * x * z^7 ] T44.32 : Triangle type {6,10,60} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^-1 * z^2 * y^-3 * x^-1 * y^-1 * z^3 ] T44.33 : Triangle type {6,12,30} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z * y^-1 * z^-2 * x^-1 * z * y^-1 * x^-1 * z^4 ] T44.34 : Triangle type {6,15,20} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y * x * y^-1 * x * y^-1 * z^-1, y^2 * x^-2 * y * z^-1 * y ] T44.35 : Triangle type {6,54,54} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^-3 * z * y^-1 * z * y^-1 * z * y^-4 * x * y^-6 ] T44.36 : Triangle type {8,8,30} Group order 120 Action reflexible [n] Defining relators: [ x * y * z, z^-1 * x^3 * y^-1 * z^-1, z * y^-1 * x^2 * z^-1 * x ] T44.37 : Triangle type {8,8,30} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^3 * y * x^-1 * y * x^-1 * z^10 ] T44.38 : Triangle type {8,14,28} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, y * x^-2 * z * x^-1, y * z^-2 * y^3 * z^-2 * y * z^-2 * y * z^-2 ] T44.39 : Triangle type {8,26,104} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, y^-2 * z * y^-1 * z * y^-6 * z^2 ] T44.40 : Triangle type {9,99,99} Group order 99 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-9, y^-2 * z * y^-5 * z^3 ] T44.41 : Triangle type {9,99,99} Group order 99 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-9, y^-2 * z * y^-8 ] T44.42 : Triangle type {10,10,12} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^10, z^7 * y^-1 * x^-1 * z^4 ] T44.43 : Triangle type {10,10,55} Group order 110 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-2 * x^2 * y^-2, z^2 * y * z^-2 * x * z * y^-1 * x^-1 * z^4 ] T44.44 : Triangle type {10,10,55} Group order 110 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-2)^2, z * y * z^-4 * x * y^-1 * x * z^4 ] T44.45 : Triangle type {10,50,50} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^10, y^-1 * z * y^-5 * z^3 ] T44.46 : Triangle type {10,50,50} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^10, y^-1 * z * y^-7 * z ] T44.47 : Triangle type {12,96,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, z^-2 * x * z^-2 * x^4 * z^-4 ] T44.48 : Triangle type {23,92,92} Group order 92 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-2 * z^2 * y^-2 * x^3 * y^-2 * z^2 * y^-2 ] T44.49 : Triangle type {23,92,92} Group order 92 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^4 * x^-4 * y^5 * x^-1 * y^3 ] T44.50 : Triangle type {23,92,92} Group order 92 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x * z^-1 * x * z^-1 * x^7 * z^-2 ] T44.51 : Triangle type {23,92,92} Group order 92 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-1 * y^12 * x^-1 * y * x^-1 * y^3 ] T44.52 : Triangle type {23,92,92} Group order 92 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, x * z^-1 * x * z^-1 * x * z^-1 * x * z^-1 * x^5 * z^-4 ] T44.53 : Triangle type {23,92,92} Group order 92 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x^7 * y^-4 ] T44.54 : Triangle type {23,92,92} Group order 92 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * x^-5, y^-1 * z^2 * y^-2 * x^7 * y^-3 ] T44.55 : Triangle type {23,92,92} Group order 92 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^2 * z^-1 * x^6 * z^-3 ] T44.56 : Triangle type {23,92,92} Group order 92 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-16 * z * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T44.57 : Triangle type {23,92,92} Group order 92 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6 * z^-4, y^-1 * z * y^-2 * x^4 * y^-4 ] T44.58 : Triangle type {23,92,92} Group order 92 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-23 ] T44.59 : Triangle type {24,32,32} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-2 * x^2 * z * y^-1, z * x^-3 * z^3 ] T44.60 : Triangle type {24,32,32} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * z * x^-1 * y^-1 * z, x^-7 * z * y ] T44.61 : Triangle type {45,90,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^-16 * x^2 * y^-3 * z * y^-2 ] T44.62 : Triangle type {45,90,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, z^-1 * x * z^-1 * x^5 * z^-4 ] T44.63 : Triangle type {45,90,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x * y^-1 * x^6 * y^-3, z^-1 * x * z^-1 * x^5 * z^-4 ] T44.64 : Triangle type {45,90,90} Group order 90 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-10 * y^2 * x^-4 ] T44.65 : Triangle type {45,90,90} Group order 90 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^45, y * z^-1 ] T44.66 : Triangle type {46,46,46} Group order 92 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^15 * x^-2 * y^7 ] T44.67 : Triangle type {46,46,46} Group order 92 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^6 * x^-1 * y^5 * x^-1 * y^3 ] T44.68 : Triangle type {46,46,46} Group order 92 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, x^2 * y^-1 * x^8 * y^-3 ] T44.69 : Triangle type {46,46,46} Group order 92 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, z^-4 * x^2 * z^-4 ] T44.70 : Triangle type {89,89,89} Group order 89 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^39 * x^-1 * y^5, x * z^-1 ] T44.71 : Triangle type {89,89,89} Group order 89 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^17 * x^-1 * y^3 * x^-3 * y^7 ] T44.72 : Triangle type {89,89,89} Group order 89 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^2 * x^-4 * y^4 * x^-1 * y^4 * x^-1 * y^5 * x^-1 * y^2 ] T44.73 : Triangle type {89,89,89} Group order 89 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^15 * x^-1 * y^2 ] T44.74 : Triangle type {89,89,89} Group order 89 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-1 * y * x^-1 * y * x^-5 * y^7 ] T44.75 : Triangle type {89,89,89} Group order 89 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-2 * y * x^-5 * y^4 * x^-2 ] T44.76 : Triangle type {89,89,89} Group order 89 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^3, x^-1 * y * x^-5 * y^4 * x^-1 ] T44.77 : Triangle type {89,89,89} Group order 89 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^5 * x^-1 * z^3, y^-5 * x * y^-4 ] T44.78 : Triangle type {89,89,89} Group order 89 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^8 * x^-1 * z^4 ] T44.79 : Triangle type {89,89,89} Group order 89 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^-2 * z^5 * y^-4 ] T44.80 : Triangle type {89,89,89} Group order 89 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * z^4 * y^-4, x^-1 * z * x^-1 * z^4 * x^-4 * z^2 ] T44.81 : Triangle type {89,89,89} Group order 89 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^-3 * z * y^-3 * x^5 * y^-4 ] T44.82 : Triangle type {89,89,89} Group order 89 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^5 * x^-4 * z^2, y^-2 * z^4 * x * y^-4 ] T44.83 : Triangle type {89,89,89} Group order 89 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x * y^-5 * x^7 ] T44.84 : Triangle type {89,89,89} Group order 89 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^2 * z^-1 * x^9 * z^-2 * x^5 ] Genus 45 T45.1 : Triangle type {2,3,10} Group order 1320 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^10, z^2 * y * x * z^2 * y * x * z * y^2 * z^-1 * x * z * y^-1 * z^-1 * x, z * y * x * z * y * z^-1 * x * z * y * x * z * y * x * z * y^2 * z^-2 * x * z^3 ] T45.2 : Triangle type {2,3,10} Group order 1320 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^10, x * z * y * x * z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y * x * z^5 * y * x * z * y^2 * z^-3 * x * z^2 ] T45.3 : Triangle type {2,3,22} Group order 726 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, y * z^-21 * x ] T45.4 : Triangle type {2,3,28} Group order 672 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^3 * y * z^-1 * x * z * y * x * y^-1 * z^3 * y^-1 * z^-1 * x ] T45.5 : Triangle type {2,4,15} Group order 480 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-4)^2, z^-7 * x * y * z^-7 ] T45.6 : Triangle type {2,4,48} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^2 * y^-2 * z^-3 * y, z^-8 * x * z^8 * y * x * z^4 * y^-1 * z^-2 ] T45.7 : Triangle type {2,4,48} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-30 * x * z^7 * y * x * y * x * y^-1 * z^-8 ] T45.8 : Triangle type {2,4,48} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-38 * x * y * z^-9 ] T45.9 : Triangle type {2,4,48} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-10 * x * z^7 * y * z^-1 * x * y^-1 * z^-4 ] T45.10 : Triangle type {2,4,92} Group order 368 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-84 * x * y * z^-7 ] T45.11 : Triangle type {2,4,180} Group order 360 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-82 * x * y^-1 * z^-7 ] T45.12 : Triangle type {2,5,6} Group order 660 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^-5, z^6, z * y^2 * z^-1 * y^2 * z^-1 * y * x * y^-1, z^-1 * x * z * y * x * y^-1 * z^-2 * y * z^-1 * y ] T45.13 : Triangle type {2,5,6} Group order 660 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^-5, z^6, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (z^-1 * y)^5 ] T45.14 : Triangle type {2,6,14} Group order 336 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^-2 * x * y^-2 * z^-4, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T45.15 : Triangle type {2,8,10} Group order 320 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^2 * y^3 * x * z^2, z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y ] T45.16 : Triangle type {2,8,10} Group order 320 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, z^2 * y^3 * x * z^2, (y * z^-1)^4 ] T45.17 : Triangle type {2,8,32} Group order 256 Action chiral Defining relators: [ x^2, x * y * z, y^8, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, z * y * z^-2 * x * y^-1 * z^-1 * x * z^2 ] T45.18 : Triangle type {2,8,32} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^10 * y * x * z^2 * y * x * z * y * x * y * x * z^15 ] T45.19 : Triangle type {2,8,32} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^22 * y * z^-7 * x * z^2 ] T45.20 : Triangle type {2,8,32} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, y^8, (y * z^-1 * y^2)^2, z^-2 * x * z * y * x * z^5 * y^-1 * z^-2 * x * z^2 * y^-1 * z^-1 ] T45.21 : Triangle type {2,8,32} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-1 * x * z^8 * y^-1 * z^-1 * x * y^-1 * z^-4 ] T45.22 : Triangle type {2,8,32} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-1 * x * z^8 * y^-1 * z^-1 * x * z^2 * y^-1 * z^-2 ] T45.23 : Triangle type {2,8,32} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^8, (y * z^-1 * y^2)^2, z^-1 * x * z^8 * y * x * z * y^-1 * z^-4 ] T45.24 : Triangle type {2,8,120} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-4 * x * z^16 * y * x * y^-1 * z^-8 ] T45.25 : Triangle type {2,8,120} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-1 * x * z^17 * y * z^-2 * x * z^2 * y^-1 * z^-2 * x * z^2 * y^-1 * z^-1 ] T45.26 : Triangle type {2,11,22} Group order 242 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, y^-11 ] T45.27 : Triangle type {2,12,20} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z^-2 * y^3 * z^-3, z * y^-1 * z * y^-2 * z^-2 * x * y^-1 ] T45.28 : Triangle type {2,12,20} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z^-1 * x * y^-2 * z^-3, (z^-1 * y)^5 ] T45.29 : Triangle type {2,12,20} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^-20 ] T45.30 : Triangle type {2,14,105} Group order 210 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-3 * z^2 * y^-7 * z^2, z^-9 * y * z^4 * y^-1 * z^-2 ] T45.31 : Triangle type {2,15,15} Group order 240 Action reflexible [n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-1 * y^2 * z^-1, y^-15 ] T45.32 : Triangle type {2,15,15} Group order 240 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-4, y^-15 ] T45.33 : Triangle type {2,22,99} Group order 198 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^4 * y^-2 * z^5 ] T45.34 : Triangle type {2,32,96} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-5 * z^2 * y^-4 * z^4 * y^-1 ] T45.35 : Triangle type {2,32,96} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-3 * y^11 * z^-2 * y^14 * z^-1 ] T45.36 : Triangle type {2,38,95} Group order 190 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^3 * y * z^-4 * x * z^2, y^-7 * z * y^-6 * z^4 * y^-1 ] T45.37 : Triangle type {2,48,48} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z^2 * y^-1 * z^-3, y^7 * z^-1 * y * z^-1 * y * z^-1 ] T45.38 : Triangle type {2,48,48} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^2 * z^-10 * y^11 * z^-1 ] T45.39 : Triangle type {2,48,48} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^-1 * z * y^-32 * z * y^-13 ] T45.40 : Triangle type {2,48,48} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-21 * y^11 * z^-2 * y^13 * z^-1 ] T45.41 : Triangle type {2,48,48} Group order 192 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^-12 * z^2 * y^-8 * z^2 ] T45.42 : Triangle type {2,48,48} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^2 * z^-1 * y^10 * z^-1 * y^8 * z^-2 ] T45.43 : Triangle type {2,62,93} Group order 186 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, z^-4 * y^10 * z^-3 * y^12 * z^-2 ] T45.44 : Triangle type {2,91,182} Group order 182 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^72 * y^-18 ] T45.45 : Triangle type {2,92,92} Group order 184 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^19 * z^-72 * y ] T45.46 : Triangle type {2,180,180} Group order 180 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^18 * z^-71 * y ] T45.47 : Triangle type {3,3,5} Group order 660 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^2 * y^-1 * x^-1 * z^2, x^-1 * z * y * x^-1 * y^-1 * x * z * y * x^-1 * z, y^-1 * z^-1 * x^-1 * z * y * x * z * y * z^-1 * x^-1 ] T45.48 : Triangle type {3,3,5} Group order 660 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^2 * y^-1 * x^-1 * z^2, (x * z * y^-1 * z^-1)^2 ] T45.49 : Triangle type {3,3,11} Group order 363 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^5 * y^-1 * z^-1 * x^-1 * y * x * z^4 ] T45.50 : Triangle type {3,3,14} Group order 336 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-3 * x * z^3, z^-1 * x^-1 * z * y * x^-1 * z * y * x * y^-1 ] T45.51 : Triangle type {3,3,91} Group order 273 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, x * z^6 * x^-1 * z^-5 ] T45.52 : Triangle type {3,3,91} Group order 273 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, x * z^9 * y ] T45.53 : Triangle type {3,4,20} Group order 240 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, x^-1 * y * z^-3 * x * z^-4 ] T45.54 : Triangle type {3,8,12} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, z * y^2 * x^-1 * y^-1 * z^-1 * x, z^-3 * x^-1 * z^2 * y^-1 ] T45.55 : Triangle type {3,8,12} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, z * y^-1 * z^-1 * x * z * y^-1, y * x^-1 * y * x^-1 * y^-2 * z ] T45.56 : Triangle type {3,12,52} Group order 156 Action chiral Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y * z^-2 * x^-1 * z * y * z^-1 ] T45.57 : Triangle type {3,46,138} Group order 138 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-35 * z * y^-1 * z * y^-7 * z ] T45.58 : Triangle type {3,135,135} Group order 135 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-34 * z * y^-1 * z * y^-8 ] T45.59 : Triangle type {4,4,24} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, (y * z^-2)^2, z^4 * y * x^-1 * y^-1 * z^-1 * x * z * y * z^-3 * x^-1 ] T45.60 : Triangle type {4,4,24} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, y^-1 * z^-1 * y * x^-1 * z * y^-1 * z, z^4 * y * x^-1 * y^-1 * z^-1 * x * y^-1 * z^-4 * x ] T45.61 : Triangle type {4,4,24} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, y * z^-2 * x^-1 * z^3, y^-2 * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z ] T45.62 : Triangle type {4,4,24} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-3 * x^-1 * z^2 * y^-1, y^-2 * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z ] T45.63 : Triangle type {4,4,24} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^2, z^-18 * x * y * z^-5 ] T45.64 : Triangle type {4,4,24} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, y * x^-1 * y^-1 * x * z^-2, (x * z^-1 * y)^2, z^3 * y * z^-2 * x^-1 * y^-1 * x * y^-1 * x * z^4 ] T45.65 : Triangle type {4,4,24} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (y * z^-1)^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, y^-1 * z^-3 * x^-1 * z^8 ] T45.66 : Triangle type {4,4,24} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^12 * y^-1 * z^-4 * x * y^-1 * x * z * y^-1 * z^-4 * x^-1 ] T45.67 : Triangle type {4,4,24} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, z * y^-1 * z^-2 * x^-1 * z^8 ] T45.68 : Triangle type {4,4,24} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z^-1 * x^-1 * z^2 * y * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-5 ] T45.69 : Triangle type {4,4,24} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, z * y * z^-2 * x^-1 * z^8 ] T45.70 : Triangle type {4,4,24} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^-18 * x * y * z^-5 ] T45.71 : Triangle type {4,4,24} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z * y * x^2 * z * y^-1, x^-1 * y * z^-2 * y * z^-1 * x^-1 * z, z^-7 * x^-1 * z * y * z^-3 ] T45.72 : Triangle type {4,4,24} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-2)^2, z^-6 * x^-1 * y * x^-1 * y^-1 * z^-4 ] T45.73 : Triangle type {4,4,24} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-7 * x * y^-1 * z^-4 ] T45.74 : Triangle type {4,4,24} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, y^-1 * z^-1 * x^-2 * z^2 * x^-1, z^-7 * x * y^-1 * z^-4 ] T45.75 : Triangle type {4,4,46} Group order 184 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^46 ] T45.76 : Triangle type {4,4,90} Group order 180 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^32 * y^-1 * z^-4 * x * z^8 ] T45.77 : Triangle type {4,6,8} Group order 192 Action chiral Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, z * y^2 * x * z^2 ] T45.78 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, z * y^2 * x^-1 * z^2, (z^-1 * x)^3 ] T45.79 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, z * y^2 * x^-1 * z^2, y * z^-2 * x^-1 * z * x^-1 * z ] T45.80 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^6, z * y^2 * x^-1 * z^2, (z^-1 * x)^3, y * z^-1 * x^-2 * z^2 * x^-1 ] T45.81 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^6, z * y^2 * x^-1 * z^2, y * z^-1 * x^-2 * z^2 * x^-1, y * z^-2 * x^-1 * z * x^-1 * z ] T45.82 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, y^6, (y * z^-1 * y)^2, x^-1 * y^2 * x^2 * z * x^-1 * z ] T45.83 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, y^6, z^-1 * y^2 * x^-1 * y^3, x^-1 * y^2 * x^2 * z * x^-1 * z ] T45.84 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, y * z^-1 * y * x^-1 * z * y^-1 * z^-1 ] T45.85 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y^2 * x^-1 * y^3, x^-1 * z^2 * y * x * z^2 * y ] T45.86 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^6, x^-1 * z * y^2 * x * z * y^2 ] T45.87 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-1 * y)^2, x^-1 * z^2 * y * x * z * y^-1 * z^-1 ] T45.88 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, y * z^-1 * y * x^-1 * z^2 * y ] T45.89 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^6, x^-1 * z * y^2 * x * y^-1 * z^-1 * y ] T45.90 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^6, y^-1 * z^-1 * y * x * z^2, (z^-1 * x)^3 ] T45.91 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^6, y^-1 * z^-1 * y * x * z^2, y * z^-1 * x^-2 * z^2 * x^-1, y * x * z^-1 * x^-1 * z^3 ] T45.92 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^-1 * x * y^-1 * x * z^2, y^6, (z^-1 * x)^3 ] T45.93 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^8, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T45.94 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^8, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T45.95 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y^6, y^2 * x^-2 * z * y * x^-1 ] T45.96 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y^6, z^-1 * y^2 * x^-1 * y^3, x * z * y * x^2 * z * x^-1 * y^-1 ] T45.97 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, y^6, y * x^-1 * y * x^-1 * y^-1 * x * z ] T45.98 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, (x * y^-2)^2, y^6, z^8 ] T45.99 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * z^-1 * x^-1 * z^2, y^6, x^-1 * y^2 * x^-1 * y * x * z^-1 ] T45.100 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y^6, (x * z^-2)^2, x^-1 * y^2 * x^-1 * y * x * z^-1, z^8 ] T45.101 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, (x * z * y^-1)^2, y^6, x^-1 * y * x^-2 * z^3, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^2 * y^-1 * z * y ] T45.102 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^6, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T45.103 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y^6, y * z^-1 * x^-2 * z^2 * x^-1, z^8 ] T45.104 : Triangle type {4,6,8} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y, y^6, z^8, z^2 * y * x^-2 * z^3 * x^-1 ] T45.105 : Triangle type {4,8,72} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^4 * y * z^-4 * x^-1 * z^9 ] T45.106 : Triangle type {4,8,72} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^4 * y * z^-4 * x^-1 * z^6 * y^-1 * x * z^2 ] T45.107 : Triangle type {4,9,36} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, y^9 ] T45.108 : Triangle type {4,10,10} Group order 160 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^2 * y^-1 * x * z^2, y^3 * x * z^-1 * y, x^-1 * z * y * x * y^-1 * z^-1 ] T45.109 : Triangle type {4,10,10} Group order 160 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^2 * y^-1 * x * z^2, y^3 * x * z^-1 * y, x^-1 * z * y * x * z * y ] T45.110 : Triangle type {4,31,124} Group order 124 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^8 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-2 * y^3 ] T45.111 : Triangle type {4,32,32} Group order 128 Action chiral Defining relators: [ x * y * z, x^4, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, z^-2 * y^3 * z^-1 * y * z^-1 ] T45.112 : Triangle type {4,32,32} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^6 * z^-2 ] T45.113 : Triangle type {4,32,32} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-4 * z * y^-1 * z * y^-4 * z^3 * y^-1 * z ] T45.114 : Triangle type {4,32,32} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, z * y^-6 * z^2 * y^-1 * z^4 * y^-1 * z * y^-16 ] T45.115 : Triangle type {4,32,32} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-4 * z * y^-1 * z * y^-4 * z^4 * y^-1 ] T45.116 : Triangle type {4,32,32} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y^-5 * z * y^-3 * z * y^-6 ] T45.117 : Triangle type {4,32,32} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-2 * x^-1 * z * y^-1, y^-5 * z^4 * y^-7 ] T45.118 : Triangle type {4,32,32} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y^9 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-2 * y^3 ] T45.119 : Triangle type {4,32,32} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-4 * z * y^-1 * z * y^-5 * z * y^-2 * z ] T45.120 : Triangle type {4,120,120} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y^-6 * z * y^-4 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-3 * z^3 * y^-1 * z^2 ] T45.121 : Triangle type {4,120,120} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y^-11 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-3 * z^3 * y^-1 * z * y^-1 ] T45.122 : Triangle type {5,5,31} Group order 155 Action reflexible [n] Defining relators: [ x * y * z, x^-5, x^-1 * y * x^2 * z^2 ] T45.123 : Triangle type {5,5,31} Group order 155 Action reflexible [n] Defining relators: [ x * y * z, z * y * x * z, x^-5 ] T45.124 : Triangle type {6,6,7} Group order 168 Action chiral Defining relators: [ x * y * z, x^-1 * y * x^-1 * z^2, x^6, x^-1 * y^2 * x^-1 * y^2 * z^-1 ] T45.125 : Triangle type {6,6,7} Group order 168 Action chiral Defining relators: [ x * y * z, x^6, (y^-1 * x)^3, y^6, z * y^2 * x * y^-1 * z, (z^-1 * y)^3 ] T45.126 : Triangle type {6,12,60} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^2 * y^-1 * z^-3 * x * z^4 ] T45.127 : Triangle type {6,15,30} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, z^-2 * y * x * z^-1 * y ] T45.128 : Triangle type {6,19,114} Group order 114 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z^3 * y^-3 * x * y^-4 * z ] T45.129 : Triangle type {6,20,20} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^6, z^-1 * y^3 * z^-1 * y * z^-1 * x^-1 * y^3 * z^-1 * y^7 * z^-1 * y ] T45.130 : Triangle type {6,108,108} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y * z^-1 * y^4 * x^-1 * y^4 * z^-1 * y * z^-1 * y * z^-1 * y * z^-2 ] T45.131 : Triangle type {7,16,112} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, y * z^-4 * y^4 * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T45.132 : Triangle type {7,105,105} Group order 105 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, y * z^-4 * x * y^4 * z^-1 * y * z^-1 * y * z^-2 ] T45.133 : Triangle type {7,105,105} Group order 105 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, y^-2 * z * y^-1 * z * y^-1 * z * y^-6 * z^2 ] T45.134 : Triangle type {7,105,105} Group order 105 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-7, z^-5 * x * y^4 * z^-1 * y * z^-4 ] T45.135 : Triangle type {8,8,16} Group order 128 Action chiral Defining relators: [ x * y * z, z^-1 * y * x^2 * z^-1 * y, x * z * y^-1 * x * y^-1 * z^-1, z^-1 * y^2 * x * z^-1 * x ] T45.136 : Triangle type {8,8,16} Group order 128 Action reflexible [n] Defining relators: [ x * y * z, y^-1 * z^-1 * x^-1 * z^2, z^-1 * y * x^2 * z^-1 * y, x^8 ] T45.137 : Triangle type {8,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, (x * y^-1 * x)^2, x^8 ] T45.138 : Triangle type {8,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, y^-1 * x * y^-1 * x * z^2, x^8 ] T45.139 : Triangle type {8,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, (x * y^-1 * x)^2, z^-2 * y^2 * z^-2, x^8 ] T45.140 : Triangle type {8,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, x^8 ] T45.141 : Triangle type {8,8,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z^-1 * y^2 * x * z^-1 * x, z^-3 * x * y^-1 * x * z^2 * y^-1 * z^-1 ] T45.142 : Triangle type {8,8,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, (x * z^-1 * y)^2, z * y * z^-1 * x^-1 * y^-1 * x * z^4 ] T45.143 : Triangle type {8,8,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, z^2 * y^-1 * x * y^-1 * x * z^4 ] T45.144 : Triangle type {8,8,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^-9 * x^-1 * y * x * y^-1 * z^-5 ] T45.145 : Triangle type {8,8,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T45.146 : Triangle type {8,8,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^-1 * x^-1 * z * y * z^-1 * x^-1 * z * y * z^-1 * x^-1 * z^2 * y * z^-1 * x^-1 * y * z^-4 ] T45.147 : Triangle type {8,8,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^8, z * y^-1 * z^-1 * x * y^-1 * x * z^4 ] T45.148 : Triangle type {8,8,60} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^3 * y * z^-1 * x^-1 * y * z^-4 * x * z * y * z^-1 * x * z^2 ] T45.149 : Triangle type {8,8,60} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^3 * y * z^-1 * x^-1 * y * z^-4 * x^-1 * y * z^-1 * x^-1 * z^3 ] T45.150 : Triangle type {8,14,56} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^6 * z^-3 * y^3 * z^-1 * y ] T45.151 : Triangle type {8,14,56} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z * y^-1 * z * y^-1 * z * y^-4 * x^-1 * z^4 ] T45.152 : Triangle type {8,52,104} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, y^-2 * z * y^-1 * z * y^-8 ] T45.153 : Triangle type {8,52,104} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, y^-2 * z * y^-1 * z * y^-4 * z^4 ] T45.154 : Triangle type {9,9,39} Group order 117 Action chiral Defining relators: [ x * y * z, z * x^-2 * y^-2, z * x^-1 * y^-1 * x * z * x^-1, z * y^-2 * x * z^2 ] T45.155 : Triangle type {10,11,110} Group order 110 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^10, y^-2 * z * y^-4 * x * y^-4 ] T45.156 : Triangle type {10,12,12} Group order 120 Action reflexible [n] Defining relators: [ x * y * z, x^-3 * z * y, z * x^-2 * y * x, y^2 * z^-1 * y^3 * z^-1 * y^2 * z^-2 * y ] T45.157 : Triangle type {10,12,12} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^10, y^-4 * z * y^-6 * z ] T45.158 : Triangle type {10,100,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^10, y^-6 * x * y^-4 ] T45.159 : Triangle type {10,100,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^10, y^-1 * z * y^-6 * z^2 ] T45.160 : Triangle type {11,11,11} Group order 121 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^6 * y^-1 * x^-1 * z^4, y^-3 * z * y^-3 * x * y^-4 ] T45.161 : Triangle type {11,99,99} Group order 99 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * y^-4 * x^-2 * z^3, y^-1 * x * y^-4 * x^3 * y^-4 ] T45.162 : Triangle type {11,99,99} Group order 99 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * y^-3 * x^-2 * z^3, y^-5 * x^3 * y^-4 ] T45.163 : Triangle type {11,99,99} Group order 99 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-6 * z^3, x^11 ] T45.164 : Triangle type {11,99,99} Group order 99 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * y^-4 * z^4, x^11 ] T45.165 : Triangle type {11,99,99} Group order 99 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y^-6 * x * y^-3, x^11 ] T45.166 : Triangle type {14,49,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, y^5 * x^-6 * y^2 ] T45.167 : Triangle type {14,49,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-5 * z^2, x^14 ] T45.168 : Triangle type {14,49,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x^3 * z^-4, y^-3 * x^4 * y^-4 ] T45.169 : Triangle type {14,49,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^4, z^-1 * x * z^-2 * x^4 * z^-4 ] T45.170 : Triangle type {14,49,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-4 * x^-1 * z^3, x^14 ] T45.171 : Triangle type {14,49,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * x^-1 * z^3, y^-1 * x * y^-1 * x^7 * y^-5 ] T45.172 : Triangle type {15,15,35} Group order 105 Action chiral Defining relators: [ x * y * z, z^-1 * y * x^-1 * z * y, z^-1 * x^-1 * y^-1 * x * y^-2, (z^-1 * x)^3 ] T45.173 : Triangle type {15,15,35} Group order 105 Action reflexible [n] Defining relators: [ x * y * z, y * x^-2 * z^2, z^-2 * x^-1 * y^2 ] T45.174 : Triangle type {16,96,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-3 * y^4, x * z^-1 * x * z^-2 * x^5 * z^-3 ] T45.175 : Triangle type {16,96,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^-2 * y^4 * x^-7 * y * x^-1 * y * x^-1 ] T45.176 : Triangle type {16,96,96} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-2 * z * x^-10 * y * x^-3 ] T45.177 : Triangle type {16,96,96} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^2 * z^-2 * x^3 * z^-4, y^-2 * x^5 * y^-4 ] T45.178 : Triangle type {16,96,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, x * z^-1 * x * z^-1 * x * z^-2 * x^6 * z^-2 ] T45.179 : Triangle type {19,95,95} Group order 95 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x * z^-2 * x^4 * z^-3, y^-4 * x^2 * y^-1 * z^3 * y^-2 ] T45.180 : Triangle type {19,95,95} Group order 95 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^-4 * x * z^-2 * x^4 * z^-4 ] T45.181 : Triangle type {19,95,95} Group order 95 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * x^6 * y^-4, x * z^-1 * x * z^-2 * x^6 * z^-2 ] T45.182 : Triangle type {19,95,95} Group order 95 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^-4 * x^7 * y^-6 ] T45.183 : Triangle type {19,95,95} Group order 95 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-4, y^-4 * x^3 * y^-2 * z^2 * y^-2 ] T45.184 : Triangle type {19,95,95} Group order 95 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^-2 * y^2 * x^-9 * z^2 * x^-6 ] T45.185 : Triangle type {19,95,95} Group order 95 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^3 * z^-3, y^-5 * x^3 * y^-5 ] T45.186 : Triangle type {19,95,95} Group order 95 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-4 * z, z^4 * x^-8 * z^2 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T45.187 : Triangle type {19,95,95} Group order 95 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-2 * x^5 * z^-2, y * z^-5 * y^4 ] T45.188 : Triangle type {24,32,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x^-9 * y * x^-10 * y * x^-1 * y * x^-1 * y ] T45.189 : Triangle type {24,32,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * y^2 * z^-3, x * y^-1 * x^8 * y^-3 ] T45.190 : Triangle type {24,32,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^-8 * x^3 * z^-4 ] T45.191 : Triangle type {24,32,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, y * z^-1 * y^2 * x^-7 * y^4 ] T45.192 : Triangle type {24,48,48} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-10 * z * x^-7 * y^2 * x^-1 * z * x^-4 ] T45.193 : Triangle type {24,48,48} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^-9 * z * x^-2 * y ] T45.194 : Triangle type {24,48,48} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^2 * z^-1 * x * z^-2 * x^7 * z^-1 ] T45.195 : Triangle type {24,48,48} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^2 * z^-1 * x * y^-1 * x * y^-1 * x^5 * z^-1 * x ] T45.196 : Triangle type {31,93,93} Group order 93 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^-9 * y^6 * x^-3 * y^3 * x^-1 * y * x^-1 * y * x^-1 * y ] T45.197 : Triangle type {31,93,93} Group order 93 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-2 * x * y^-3 * x^4 * y^-4 ] T45.198 : Triangle type {31,93,93} Group order 93 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^7 * y^-1, z^3 * y^-4 * x * y^-4 * z ] T45.199 : Triangle type {31,93,93} Group order 93 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-7 * z^2, x^8 * z^-3 ] T45.200 : Triangle type {31,93,93} Group order 93 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * x^3 * y^-2, z^-4 * x * z^-11 ] T45.201 : Triangle type {31,93,93} Group order 93 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-2 * x^2 * z^-3 * x * z^-4 * x^3 * z^-6 ] T45.202 : Triangle type {31,93,93} Group order 93 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * y^-4 * z^4, x^2 * y^-3 * x^5 * y^-3 ] T45.203 : Triangle type {31,93,93} Group order 93 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^-8 * x^3 * y^-4 ] T45.204 : Triangle type {31,93,93} Group order 93 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^-5 * x^2 * y^-4 ] T45.205 : Triangle type {31,93,93} Group order 93 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, z^-2 * x * z^-1 * x^7 * z^-6 ] T45.206 : Triangle type {31,93,93} Group order 93 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-17 * y * x^-8 * z * x^-5 ] T45.207 : Triangle type {31,93,93} Group order 93 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-8 * z, x^2 * y^-3 * x^8 ] T45.208 : Triangle type {31,93,93} Group order 93 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-9 * y^3 * x^-5 ] T45.209 : Triangle type {31,93,93} Group order 93 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, z^2 * y^-1 * z * y^-4 * z^4 ] T45.210 : Triangle type {31,93,93} Group order 93 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^-1 * z * y^-1 * z * y^-4 * x * y^-4 ] T45.211 : Triangle type {32,32,48} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * z^-1 * x, y * x^-1 * y * x^-1 * y * z^-1 * y ] T45.212 : Triangle type {32,32,48} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z * y * x^-1 * z, z^-1 * x^-2 * y^-1 * x, y^-5 * x * y^-2 * z * y^-2 * z ] T45.213 : Triangle type {32,32,48} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * x^-2 * z^2, z^-1 * y * x^-1 * y^-2, y^-1 * x^4 * y^-3 ] T45.214 : Triangle type {32,32,48} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-3 * x^-1 * z^2 * y^-1, z * x^-1 * z^2 * x^-1 * z^4 ] T45.215 : Triangle type {32,32,48} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^8 * x^-2 * z^4 * x^-1 * z * x^-1 * z ] T45.216 : Triangle type {46,92,92} Group order 92 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-5 * x^3 * y^-5 ] T45.217 : Triangle type {46,92,92} Group order 92 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^22 * x^-1 * y^8 ] T45.218 : Triangle type {46,92,92} Group order 92 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, y^2 * z^-1 * y * z^-5 * x * z^-4 * y ] T45.219 : Triangle type {46,92,92} Group order 92 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^9 * y^-2, z^-4 * x^2 * z^-4 ] T45.220 : Triangle type {46,92,92} Group order 92 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^5 * x^-6 * y^3 ] T45.221 : Triangle type {46,92,92} Group order 92 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^2 * z^-1 * x * z^-1 * x * z^-1 * x^8 * z^-1 ] T45.222 : Triangle type {46,92,92} Group order 92 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-7 * y, z^-6 * x * z^-4 ] T45.223 : Triangle type {46,92,92} Group order 92 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^5 * y^-4, x^2 * z^-1 * x^6 * z^-3 ] T45.224 : Triangle type {46,92,92} Group order 92 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, x * z^-1 * x * z^-1 * x^5 * z^-4 ] T45.225 : Triangle type {46,92,92} Group order 92 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^10 * x^-2 * y^6 * z^-1 * y ] T45.226 : Triangle type {46,92,92} Group order 92 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^46, y * z^-1 ] T45.227 : Triangle type {91,91,91} Group order 91 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^40 * x^-1 * y^5, x * z^-1 ] T45.228 : Triangle type {91,91,91} Group order 91 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, z^-1 * x * z^-1 * x^6 * z^-5 ] T45.229 : Triangle type {91,91,91} Group order 91 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^9, z * y^-4 * z^4 ] T45.230 : Triangle type {91,91,91} Group order 91 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^5 * y^-1, z^3 * y^-1 * z * y^-10 * z^2 ] T45.231 : Triangle type {91,91,91} Group order 91 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^20 * x^-2 * y^9 ] T45.232 : Triangle type {91,91,91} Group order 91 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-4 * x * y^-4, x^8 * z^-3 ] T45.233 : Triangle type {91,91,91} Group order 91 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-4 * z, x^2 * z^-1 * x * z^-1 * x * z^-1 * x^11 * z^-1 ] T45.234 : Triangle type {91,91,91} Group order 91 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^-11 * x^2 * z^-6 ] T45.235 : Triangle type {91,91,91} Group order 91 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^10 * z^-1 * x^12 ] T45.236 : Triangle type {91,91,91} Group order 91 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^6 * z^-4, y^-2 * x^5 * y^-4 ] T45.237 : Triangle type {91,91,91} Group order 91 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^9 * z^-1, y^-5 * x * y^-4 ] Genus 46 T46.1 : Triangle type {2,3,8} Group order 2160 Action chiral Defining relators: [ x^2, y^3, x * y * z, z^8, z * y * z^-1 * x * z^2 * y * z^-2 * x * z * y * z^-1 * x * z * y^-1 * z^-3 * x ] T46.2 : Triangle type {2,3,8} Group order 2160 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^8, y * x * z^2 * y * x * z^2 * y * z^-1 * x * z * y * z^-1 * x * y^-1 * z^-2 * x * z^2 ] T46.3 : Triangle type {2,3,8} Group order 2160 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^8, y * x * z * y * x * z * y * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x * z ] T46.4 : Triangle type {2,3,36} Group order 648 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^8 * y * z^-1 * x * z^5 * y^-1 * z^-1 * x * z * y^-1 * z^-7 * x ] T46.5 : Triangle type {2,4,8} Group order 720 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^8, y^-1 * z^2 * y^-1 * z^2 * y^2 * z^-1 * x * y^-1 * z^2, (z^-2 * y * z^-1)^3 ] T46.6 : Triangle type {2,4,8} Group order 720 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^8, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (z^-1 * y)^5, z^2 * y * z^-1 * y * z^-2 * y * z^-2 * y * z^-1 * x ] T46.7 : Triangle type {2,4,8} Group order 720 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^8, z * y * z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1 * x, y * z^-1 * y * z^-2 * x * y^-1 * z^-3 * y * z^-1 ] T46.8 : Triangle type {2,4,9} Group order 648 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-4 * x * y * z^-4 ] T46.9 : Triangle type {2,4,9} Group order 648 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^-4 * x * y * z^-4, z * y * z^-1 * x * z * y^2 * z^-2 * x * z * y^-1, x * z * y * x * z * y * z^-1 * y * z^-3 * y * z^-1 ] T46.10 : Triangle type {2,4,12} Group order 540 Action chiral Defining relators: [ x^2, x * y * z, y^4, x * z^3 * y^-1 * z^-4, z^-1 * y * z^-2 * x * y^-1 * z^-3 * y * z^-1, z * y * x * z * y^-1 * z * y^2 * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x ] T46.11 : Triangle type {2,4,24} Group order 432 Action chiral Defining relators: [ x^2, x * y * z, y^4, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^-2 * x * z * y^-2 * z^-4 * y, x * z * y * z^-2 * x * z^5 * y^-1 * z^-2 ] T46.12 : Triangle type {2,4,94} Group order 376 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-86 * x * y * z^-7 ] T46.13 : Triangle type {2,4,184} Group order 368 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-84 * x * y^-1 * z^-7 ] T46.14 : Triangle type {2,6,8} Group order 432 Action chiral Defining relators: [ x^2, x * y * z, y^6, z^8, (z * y^-1 * z)^3, z * y^-1 * z * y^3 * z^-1 * x * z^2 ] T46.15 : Triangle type {2,6,8} Group order 432 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, (y * z^-1 * y * z^-1 * y)^2 ] T46.16 : Triangle type {2,6,8} Group order 432 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y ] T46.17 : Triangle type {2,6,12} Group order 360 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (z^-1 * y)^3, x * z^3 * y^-1 * z^-4 ] T46.18 : Triangle type {2,6,18} Group order 324 Action chiral Defining relators: [ x^2, x * y * z, y^6, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, z^3 * y^-2 * z * y^-1 * z^-1 * x ] T46.19 : Triangle type {2,6,18} Group order 324 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, z^-2 * x * z^8 * y * z^-2 * x * z * y^-1 * z^-3 ] T46.20 : Triangle type {2,6,18} Group order 324 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, x * z * y^-2 * z^-2 * y, z^-3 * x * z * y * z^-7 * x * y^-1 * x * z^3 * y^-1 * z^-1 ] T46.21 : Triangle type {2,6,18} Group order 324 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-3 * y)^2 ] T46.22 : Triangle type {2,6,18} Group order 324 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, z * y * z^-1 * x * y^-1 * z^-2 * x, (y * z^-1)^6 ] T46.23 : Triangle type {2,6,18} Group order 324 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-4 * x * z^5 * y^-1 * z^-2 ] T46.24 : Triangle type {2,6,18} Group order 324 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, z^-2 * x * z^6 * y * z^-6 * x * z^2 * y^-1 ] T46.25 : Triangle type {2,6,18} Group order 324 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T46.26 : Triangle type {2,6,18} Group order 324 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z * y^-2 * z * y^-2 * z * y^-1 * z^-2 * x ] T46.27 : Triangle type {2,6,18} Group order 324 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, x * z^2 * y^-1 * z^-3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y ] T46.28 : Triangle type {2,6,48} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, x * z * y^-2 * z^-2 * y, z^-3 * x * z^7 * y^-1 * z^-5 ] T46.29 : Triangle type {2,6,48} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^28 * y * z^-2 * x * z^6 * y * x * y^-1 * z^-8 * x * z ] T46.30 : Triangle type {2,6,48} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^29 * y * x * z^3 * y * x * z * y * x * y^-1 * z^-6 * x * z^5 ] T46.31 : Triangle type {2,6,138} Group order 276 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-19 * x * z^7 * y * z^-2 * x * z^5 * y * z^-1 * x * z^7 * y^-1 * z^-2 ] T46.32 : Triangle type {2,9,9} Group order 324 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, (z^-1 * y)^3, y^-9 ] T46.33 : Triangle type {2,9,9} Group order 324 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^-9, x * z * y^-3 * z^-1 * y * z^-2, y^-1 * z^2 * y^3 * x * z * y^-1 * z ] T46.34 : Triangle type {2,10,25} Group order 250 Action chiral Defining relators: [ x^2, x * y * z, x * z * y^3 * z^-3 ] T46.35 : Triangle type {2,10,25} Group order 250 Action chiral Defining relators: [ x^2, x * y * z, y * z^-2 * y^2 * z^-1 * x * z ] T46.36 : Triangle type {2,10,25} Group order 250 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^-3 * x * z * y * z^-3 * x * z^3 * y^-1 * z^-13 ] T46.37 : Triangle type {2,10,115} Group order 230 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^3 * y * z^-3 * x * y * z^-14 * x * z ] T46.38 : Triangle type {2,16,28} Group order 224 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^4 * x * y^-10 * z^-1 * y, z^-1 * x * z * y * x * z^3 * y * x * y^-1 * z^-1 * x * y^-1 * z^-4 ] T46.39 : Triangle type {2,18,36} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^2 * y * z^-4 * x * z^3 * y^-1 * z^-1 * x, (y^-6 * z^2 * y^-1)^2 ] T46.40 : Triangle type {2,18,36} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-6 * z^-1 * y^5, y^-1 * z^5 * y^-9 * z * y^-2 ] T46.41 : Triangle type {2,24,24} Group order 216 Action chiral Defining relators: [ x^2, x * y * z, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, x * y^-4 * z^-1 * y * z^-2, z^-1 * y^6 * z^-1 * y * z^-1 * y^2 ] T46.42 : Triangle type {2,33,66} Group order 198 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-3 * z^-1 * y^2, y * z^-6 * y^9 * z^-1 * y^2 * z^-13 * y ] T46.43 : Triangle type {2,93,186} Group order 186 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^73 * y^-18 * z ] T46.44 : Triangle type {2,94,94} Group order 188 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^20 * z^-74 ] T46.45 : Triangle type {2,184,184} Group order 184 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^19 * z^-73 ] T46.46 : Triangle type {3,3,4} Group order 1080 Action chiral Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * y * z^-1 * x^-1 * z * y * x * z * y^-1 * x * z * y ] T46.47 : Triangle type {3,3,4} Group order 1080 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * z * x^-1 * y^-1 * z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 * z^-1 * x * z^-1, z * y^-1 * z^-2 * x^-1 * z * y * x * y^-1 * z^-1 * x * z^-1 * x ] T46.48 : Triangle type {3,3,4} Group order 1080 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^4, z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x ] T46.49 : Triangle type {3,3,18} Group order 324 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^3, (y * x^-1 * z)^3, x * z * y^-1 * z^-1 * x^-1 * z^3 * y ] T46.50 : Triangle type {3,3,18} Group order 324 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-2 * x * z^2 * y * z^-1 * x * z^4 * y * z^-1 ] T46.51 : Triangle type {3,3,93} Group order 279 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z * y^-1 * z^-4 * x^-1 * z^5 ] T46.52 : Triangle type {3,4,6} Group order 360 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, (x * z * y)^2, z^6, y * x^-1 * y^-2 * x * z * y^-1 * z^-1 ] T46.53 : Triangle type {3,4,6} Group order 360 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, (y * z^-2)^2, z^6 ] T46.54 : Triangle type {3,4,6} Group order 360 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^6, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1 ] T46.55 : Triangle type {3,4,6} Group order 360 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^6, y^-1 * z * y * x^-1 * y^-1 * z^2 ] T46.56 : Triangle type {3,6,8} Group order 240 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^6, (y * z^-1 * y)^2, z * y * x * y^-1 * x * z^2 * y^-1 ] T46.57 : Triangle type {3,6,8} Group order 240 Action reflexible [m] Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * z^2, y^6, y * x^-1 * y^-2 * x * y^-1 * z * y ] T46.58 : Triangle type {3,6,12} Group order 216 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1, z^-4 * x^-1 * z^3 * y^-1 ] T46.59 : Triangle type {3,6,12} Group order 216 Action reflexible [m] Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, y^6, y * z^-1 * y * x * y^-1 * z^-1, z^2 * y^2 * x^-1 * z^3 ] T46.60 : Triangle type {3,6,12} Group order 216 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^6, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^-2, z^-3 * x^-1 * y^-1 * z * y ] T46.61 : Triangle type {3,6,12} Group order 216 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, (z^-1 * y)^3 ] T46.62 : Triangle type {3,6,62} Group order 186 Action chiral Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^6, z^-3 * x^-1 * y^-1 * z^-2 ] T46.63 : Triangle type {3,8,8} Group order 216 Action reflexible [n] Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y * z^-1 * x^-1 * y^-3, y^8 ] T46.64 : Triangle type {3,8,8} Group order 216 Action reflexible [n] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * z * y^-1, y^8 ] T46.65 : Triangle type {3,8,8} Group order 216 Action chiral Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * z * y, y^8 ] T46.66 : Triangle type {3,8,8} Group order 216 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * y * x^-1 * y^-1 * x * z, y^3 * x^-1 * z^3, y^8 ] T46.67 : Triangle type {3,8,8} Group order 216 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * z^3, y^8 ] T46.68 : Triangle type {3,18,18} Group order 162 Action chiral Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, y^3 * x^-1 * y^2 * z^-1 ] T46.69 : Triangle type {3,18,18} Group order 162 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * y^3 * z^-1 * y^6 * z^-1 * y * z^-2 * y^2 ] T46.70 : Triangle type {3,18,18} Group order 162 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, y * z^-3 * y^11 * z^-3 ] T46.71 : Triangle type {3,18,18} Group order 162 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * y^3 * z^-2 ] T46.72 : Triangle type {3,18,18} Group order 162 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^-1 * z * x^-1 * y^-1 * x * y^-1 * z^2 ] T46.73 : Triangle type {3,18,18} Group order 162 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (z^-1 * y)^3 ] T46.74 : Triangle type {3,18,18} Group order 162 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, z^-1 * y^3 * z^-2, x^-1 * z * y * x * y^-1 * z^-1 ] T46.75 : Triangle type {3,18,18} Group order 162 Action reflexible [m] Defining relators: [ x^3, x * y * z, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-2)^2, z^-2 * y * x^-1 * z * y^-2 ] T46.76 : Triangle type {3,18,18} Group order 162 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, y * x^-1 * y^-1 * x * z * y, y * z^-1 * y * z^-1 * y^2 * z^-1 * y^3 * z^-1 * y^3 * z^-1 * y^2 * z^-1 ] T46.77 : Triangle type {3,18,18} Group order 162 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, y^-1 * z * x^-1 * y^-1 * x * z^2 * y^-1 ] T46.78 : Triangle type {3,18,18} Group order 162 Action reflexible [m] Defining relators: [ x^3, x * y * z, y * x^-1 * y^-1 * x * z * y, (z^-1 * y)^3, y * z^-2 * x^-1 * z^3 ] T46.79 : Triangle type {3,18,18} Group order 162 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * x * y^-1 * x * y^-1 * z^-1, (y * z^-2)^2 ] T46.80 : Triangle type {3,18,18} Group order 162 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (y * z^-1 * y)^2, (y * x^-1 * z)^3 ] T46.81 : Triangle type {3,18,18} Group order 162 Action reflexible [m] Defining relators: [ x^3, x * y * z, (z^-1 * y)^3, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * z * y^-2, z * y * z^-1 * x^-1 * y^-3 ] T46.82 : Triangle type {3,18,18} Group order 162 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, (z^-1 * y)^3, y^5 * z^-1 * x^-1 * y^-2 * z * y * z^-1 * y ] T46.83 : Triangle type {3,47,141} Group order 141 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-36 * z * y^-1 * z * y^-7 * z ] T46.84 : Triangle type {3,48,48} Group order 144 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-37 * z * y^-1 * z * y^-7 * z ] T46.85 : Triangle type {3,48,48} Group order 144 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^35 * y^-3 * z * y^-7 * z ] T46.86 : Triangle type {3,48,48} Group order 144 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^3 * z^-2 * y^6 * z^-1 * y * z^-1 * y * z^-1 ] T46.87 : Triangle type {3,138,138} Group order 138 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-35 * z * y^-1 * z * y^-8 ] T46.88 : Triangle type {4,4,4} Group order 360 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * x^-1 * y^-1)^2, y^-1 * z^-1 * x * y^-1 * x * z * y^-1 * x, x^-1 * y^-1 * z * y^-1 * x * z * y^-1 * z ] T46.89 : Triangle type {4,4,12} Group order 216 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^4, y * x^-1 * y^-1 * x * z^-2, x * z * y * x^2 * z * x^-1 * y^-1 ] T46.90 : Triangle type {4,4,12} Group order 216 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^4, y * x^-1 * y^-1 * x * z^-2, z^-1 * x^-1 * y * x^2 * z * y * x, y * z^-1 * x * y^-1 * x * z^3 ] T46.91 : Triangle type {4,4,12} Group order 216 Action chiral Defining relators: [ x * y * z, x^4, y^4, x^-1 * y * x^-2 * y^-1 * z^-1 * y, z * x^-1 * y * x^-1 * z * x^-1 * z, z^-2 * x^-1 * y^-1 * x * z^2 * y^-1 ] T46.92 : Triangle type {4,4,47} Group order 188 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^47 ] T46.93 : Triangle type {4,4,92} Group order 184 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^33 * y^-1 * z^-4 * x * z^8 ] T46.94 : Triangle type {4,6,6} Group order 216 Action chiral Defining relators: [ x * y * z, x^4, (y^-1 * x)^3, y^6, (z^-1 * x)^3, y^-1 * z^-1 * x^-2 * z * y^-2 ] T46.95 : Triangle type {4,6,6} Group order 216 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-2 * x^-1 * z * y^-1, y^6, y^-1 * z^-1 * y * x * z * x^-1, z^6 ] T46.96 : Triangle type {4,6,6} Group order 216 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^2 * x^-1 * z * y^-1, y^6, (x * z^-1 * y)^2, z^6 ] T46.97 : Triangle type {4,6,6} Group order 216 Action reflexible [m] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^6, (y * z^-2)^2 ] T46.98 : Triangle type {4,6,6} Group order 216 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^6, z * y^2 * x^-1 * z * x^-1, (x * z^-1 * y)^2, z^6 ] T46.99 : Triangle type {4,6,6} Group order 216 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^6, z * y^2 * x^-1 * z * x^-1, (x * z * y)^2, z^6 ] T46.100 : Triangle type {4,6,6} Group order 216 Action reflexible [m] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^6, z^6, y * z^-1 * y * x^-1 * z^2 * y ] T46.101 : Triangle type {4,6,6} Group order 216 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^6, z^-2 * y * x^-1 * z * y^-2 ] T46.102 : Triangle type {4,6,6} Group order 216 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^6, x^-1 * z * y^2 * x * y^-1 * z^-1 * y, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T46.103 : Triangle type {4,6,6} Group order 216 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-1 * y)^2, z^6, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T46.104 : Triangle type {4,6,6} Group order 216 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y^-1 * x)^3, y^6, y * z^-1 * y * x^-1 * z * y, (z^-1 * x)^3 ] T46.105 : Triangle type {4,6,12} Group order 180 Action chiral Defining relators: [ x * y * z, x^4, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, z^-2 * y * x * z * y ] T46.106 : Triangle type {4,12,24} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y * z^-1 * x^-1 * z^2, y^-2 * z * x^-1 * y^-3 ] T46.107 : Triangle type {4,12,24} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^7 * y^-1 * x * z^4 ] T46.108 : Triangle type {4,12,24} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^3 * x^-1 * y^-1 * z * y, x^-1 * z^5 * y^-1 * z^-1 * x^-1 * y^-1 * x * y^-1 * z^-3 ] T46.109 : Triangle type {4,14,28} Group order 140 Action chiral Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, x * z^-1 * x^-2 * z * y^-1 * z^-1, z * y^-3 * x * z^2 * y^-1 ] T46.110 : Triangle type {4,16,16} Group order 144 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y^2 * x^-1 * y^-1 * z^-1 * y ] T46.111 : Triangle type {4,62,124} Group order 124 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^7 * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-2 * y^2 * z^-1 ] T46.112 : Triangle type {5,6,30} Group order 150 Action reflexible [m] Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^6 ] T46.113 : Triangle type {5,24,120} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, z^2 * y^-3 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-2 * z^4 * y^-1 * z^2 ] T46.114 : Triangle type {5,25,25} Group order 125 Action chiral Defining relators: [ x * y * z, x^-5, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z * y^-1 * x * y^-2, y^-1 * z^-1 * y * x * z * x^-1 ] T46.115 : Triangle type {5,25,25} Group order 125 Action chiral Defining relators: [ x * y * z, x^-5, z^-1 * x^-1 * y^-1 * x * z * y, y^-3 * x * y^-1 * z, y^-1 * z^-1 * y * x * z * x^-1 ] T46.116 : Triangle type {5,25,25} Group order 125 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-5, y * z^-1 * y^6 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-1 * y^4 ] T46.117 : Triangle type {5,115,115} Group order 115 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, z^3 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-2 * z^4 * y^-1 * z^2 ] T46.118 : Triangle type {5,115,115} Group order 115 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z^2 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-2 * z^4 * y^-1 * z * y^-1 ] T46.119 : Triangle type {6,6,9} Group order 162 Action chiral Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, y^6, z^-1 * y^2 * x * y^-1 * z^-1 ] T46.120 : Triangle type {6,6,9} Group order 162 Action reflexible [n] Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * z^-1 * x^-1, y^6, y^-1 * z^-1 * y * x * z * x^-1 ] T46.121 : Triangle type {6,6,9} Group order 162 Action chiral Defining relators: [ x * y * z, x^6, x^-1 * y * x^2 * z^-2, y^6, y^-1 * z^-1 * y^2 * z^-1 * x ] T46.122 : Triangle type {6,6,9} Group order 162 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^4 * y^-1 * x^-1 * z^4 ] T46.123 : Triangle type {6,6,9} Group order 162 Action reflexible [m] Defining relators: [ x * y * z, z * y^-1 * x * z, x^6, y^6, y^2 * z^-1 * y * x^-1 * y^-1 * z^-1 * x * z ] T46.124 : Triangle type {6,6,9} Group order 162 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * x^-2 * z^2, x^-1 * y * x^-1 * y * z^-1, y^6, y^2 * z^-1 * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T46.125 : Triangle type {6,6,9} Group order 162 Action reflexible [m] Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z^-1 * x^-1 * y^-1 * x * z * y ] T46.126 : Triangle type {6,6,9} Group order 162 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z * x^-1 * y^-1 * x * z * x^-1, z^-3 * x^-1 * z^2 * y^-1 ] T46.127 : Triangle type {6,6,9} Group order 162 Action reflexible [m,n] Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, z^-1 * y * x^2 * z^-1 * y, z^3 * y * z^-2 * x * z^3 ] T46.128 : Triangle type {6,6,9} Group order 162 Action reflexible [m,n] Defining relators: [ x * y * z, x^6, (x * y^-1 * x)^2, (x * y^-2)^2, z^-2 * x^-2 * y^-1 * z * y^-1 ] T46.129 : Triangle type {6,6,9} Group order 162 Action reflexible [m,n] Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, x^6, (x * y^-1 * x)^2, z^3 * x^-1 * z^2 * y^-1 ] T46.130 : Triangle type {6,6,9} Group order 162 Action reflexible [m,n] Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, x^-1 * y * x^-2 * y^-2 * z, z^4 * y^-1 * x^-1 * z^4 ] T46.131 : Triangle type {6,6,9} Group order 162 Action reflexible [m,n] Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, (y^-1 * x)^3 ] T46.132 : Triangle type {6,6,9} Group order 162 Action reflexible [m,n] Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, z^-1 * y^2 * x^2 * z^-1 * x^-1 * y^-1 ] T46.133 : Triangle type {6,6,9} Group order 162 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * z^-1 * x * z, x^6, (y^-1 * x)^3 ] T46.134 : Triangle type {6,6,9} Group order 162 Action reflexible [m] Defining relators: [ x * y * z, (y * z^-1)^2, x^6, y^-1 * z^-1 * x^2 * z^-1 * x, (y^-1 * x)^3 ] T46.135 : Triangle type {6,6,24} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T46.136 : Triangle type {6,6,24} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^2 * y * x * z^-1 * x^-1 ] T46.137 : Triangle type {6,6,24} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^6, y^6, z^3 * y * x^-1 * z^4 ] T46.138 : Triangle type {6,6,24} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z * y * x^2 * z^2, y^6 ] T46.139 : Triangle type {6,6,24} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, z^-1 * y * x^-1 * y^-2, x^6, z * y * z^-2 * x^-1 * z^4 ] T46.140 : Triangle type {6,6,24} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^24 ] T46.141 : Triangle type {6,6,24} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^-12 * x * y^-1 * z^-3 * x * z * y * z^-6 ] T46.142 : Triangle type {6,6,69} Group order 138 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^6 * y^-1 * z^-4 * x * y^-1 * x * y^-1 * z^-3 * x * z^7 ] T46.143 : Triangle type {6,8,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y^2 * x^2 * z^-1 * y, (z^-1 * y)^3 ] T46.144 : Triangle type {6,8,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, x^6, x^-1 * z * y * x^-1 * z * x^-1 * z ] T46.145 : Triangle type {6,8,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, x^6, y^8, y * x^-1 * z * y * x^-1 * z^3 ] T46.146 : Triangle type {6,8,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, x^6, y^8, y * x^-1 * z * y * x^-1 * z^3 ] T46.147 : Triangle type {6,8,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, (y * z^-1)^2, x^6, z^-1 * x^-1 * y^-1 * x * y^-1 * z^-1, z^-1 * x * z^-1 * x^-1 * z * y * x ] T46.148 : Triangle type {6,8,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, z * y * x^-1 * y^-2, x^6, z * y^-1 * x^2 * z * y^-1 ] T46.149 : Triangle type {6,14,21} Group order 126 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-3 * x^-1 * z^2 * y^-1, y^-4 * z^3 ] T46.150 : Triangle type {6,20,30} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, y^-3 * x^-1 * z^2, z^-1 * x * z^-1 * x * z * y^-1 ] T46.151 : Triangle type {6,20,30} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^-1 * z^2 * y^-3 * z^4 ] T46.152 : Triangle type {6,38,57} Group order 114 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y * z^-3 * y^4 * z^-3 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T46.153 : Triangle type {8,12,24} Group order 120 Action chiral Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x * y^-1 * x^2 * z * y^-1, x * z^-1 * x^2 * z^-2 ] T46.154 : Triangle type {8,12,24} Group order 120 Action chiral Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x * z^-1 * x^-1 * y * z^-1, x^8 ] T46.155 : Triangle type {8,28,28} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^8, z * y^-9 * x * z * y^-1 * z * y^-1 ] T46.156 : Triangle type {9,36,36} Group order 108 Action reflexible [n] Defining relators: [ x * y * z, x * y^-1 * x * z^-1, x^4 * z * y, y^6 * z^-1 * y * z^-2 * y^2 ] T46.157 : Triangle type {9,36,36} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * x^2 * z^-2, x^2 * y^-1 * x^2 * y^-3 ] T46.158 : Triangle type {9,36,36} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-3 * y^-1 * x^2, x^-9 ] T46.159 : Triangle type {9,36,36} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-9, y^-1 * z * y^-1 * z * y^-4 * z^4 ] T46.160 : Triangle type {12,18,36} Group order 108 Action chiral Defining relators: [ x * y * z, y^2 * x^2 * z^2, x * z^-1 * x^2 * z^-2, y^3 * x^-1 * y * z^-1 * y ] T46.161 : Triangle type {12,18,36} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * y^-4 * x^-1 * z^4, x^4 * y^-4 * x^2 * z^-4 * x^2 ] T46.162 : Triangle type {12,18,36} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, y^2 * x * z^-1, z^-2 * x^-1 * z * y^-1, x^2 * y^-1 * x * y^-1 * x^4 * y^-1 * z^-1 * x * y^-1 * x ] T46.163 : Triangle type {12,18,36} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, y * x^-2 * y^2, z^-2 * x^-1 * z * y^-1, z^-3 * x^2 * z^-3 ] T46.164 : Triangle type {14,16,16} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x * z * y^-1 * z * y^-1 * x^2 * z * y^-1 * z * y^-1 ] T46.165 : Triangle type {15,21,35} Group order 105 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x^3 * z^-4, x^2 * y^-4 * x^3 * y^-3 ] T46.166 : Triangle type {18,18,18} Group order 108 Action reflexible [n] Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, x^-4 * y * x^-1 * z, y^3 * x^-1 * y * z^-1 * y ] T46.167 : Triangle type {18,18,18} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-3 * y^-1 * x^2, x^7 * y^-1 * x * y^-1 ] T46.168 : Triangle type {18,18,18} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, (x * y^-1)^2, y^2 * x^-1 * z * y, x^-4 * y * x * z^-1, z^3 * x^-1 * z * x^-1 * z^4 ] T46.169 : Triangle type {18,18,18} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^2 * y^-4 * x^4 * y^-2, y^-1 * z * y^-1 * z * y^-4 * z^4 ] T46.170 : Triangle type {20,25,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, z^-2 * x^11 * z^-3 ] T46.171 : Triangle type {20,25,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-5 * z^3, x^2 * y^-4 * x^6 * y^-1 ] T46.172 : Triangle type {20,25,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^3 * z^-3, y^-2 * x * y^-4 * x^3 * y^-4 ] T46.173 : Triangle type {20,25,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^-5 * y^3 * x^-4 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y ] T46.174 : Triangle type {24,96,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-1 * x * y^-5 * x * y^-4 * x * y^-5 * x * y^-1 ] T46.175 : Triangle type {24,96,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, x^7 * y^-4 ] T46.176 : Triangle type {32,48,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^21 * y^-1 * x^8 * z^-1 * x^2 ] T46.177 : Triangle type {32,48,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, y^-1 * x * y^-1 * x * y^-1 * x^10 * z^-1 * x * y^-1 ] T46.178 : Triangle type {32,48,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, z^-3 * x * z^-2 * x^4 * z^-4 ] T46.179 : Triangle type {32,48,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x^7, y^3 * z^-8 * y ] T46.180 : Triangle type {32,48,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x * z^-1 * x * z^-2 * x^4 * z^-3, y^2 * z^-4 * x^-2 * y^3 ] T46.181 : Triangle type {32,48,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^-9 * x^2 * y^-6 ] T46.182 : Triangle type {32,48,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, z^-5 * x * z^-4 ] T46.183 : Triangle type {32,48,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^9 * x^-4 * z^2 * x^-1 * z * x^-1 * z * x^-1 * z^2 ] T46.184 : Triangle type {33,33,33} Group order 99 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^7 * x^-2 * y^4 * x^-1 * y^4 ] T46.185 : Triangle type {33,33,33} Group order 99 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^-5 * x^3 * y^-4 ] T46.186 : Triangle type {47,94,94} Group order 94 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^14 * x^-3 * y^8 ] T46.187 : Triangle type {47,94,94} Group order 94 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^20 * x^-2 * y^10 ] T46.188 : Triangle type {47,94,94} Group order 94 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^-1 * x * y^-3 * x^4 * y^-4 ] T46.189 : Triangle type {47,94,94} Group order 94 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y * x^-1 * y^3 * x^-7 * y^3 * x^-1 * y * x^-1 * y * x^-1 * y ] T46.190 : Triangle type {47,94,94} Group order 94 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, y^-1 * z * y^-1 * z * y^-5 * z^3 ] T46.191 : Triangle type {47,94,94} Group order 94 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-6 * x^4 * y^-4 ] T46.192 : Triangle type {47,94,94} Group order 94 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x * y^-2 * x^4 * y^-4 ] T46.193 : Triangle type {47,94,94} Group order 94 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^-10 * y^2 * z^-5 * y * z^-2 ] T46.194 : Triangle type {47,94,94} Group order 94 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^4 * y^-3 * x^-4 * z^3 ] T46.195 : Triangle type {47,94,94} Group order 94 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8 * z^-2, y^-1 * z * y^-6 * z^2 ] T46.196 : Triangle type {47,94,94} Group order 94 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y^3 * z^-3, x * y^-1 * x * y^-3 * x^6 * y^-2 ] T46.197 : Triangle type {47,94,94} Group order 94 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^7 * z^-4, y^-1 * z * y^-5 * z^3 ] T46.198 : Triangle type {47,94,94} Group order 94 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6 * z^-2, y^-1 * z * y^-1 * z * y^-4 * x * y^-4 ] T46.199 : Triangle type {47,94,94} Group order 94 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y^-2 * x * y^-1 * x * y^-3 * x^4 * y^-4 ] T46.200 : Triangle type {47,94,94} Group order 94 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * y^7, x^10 * z^-2 ] T46.201 : Triangle type {47,94,94} Group order 94 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^5 * y^-1 * x^8 * y^-1 * x^2 ] T46.202 : Triangle type {47,94,94} Group order 94 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4 * z^-2, y^6 * x^-1 * y^4 * z^-1 * y * z^-1 * y^3 ] T46.203 : Triangle type {47,94,94} Group order 94 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^4 * z^-4, y^-1 * z * y^-8 ] T46.204 : Triangle type {47,94,94} Group order 94 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x * z^-1 * x * z^-1 * x^7 * z^-6 ] T46.205 : Triangle type {47,94,94} Group order 94 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-1 * z^6 * x^-3 * z * x^-10 * z * x^-1 * z * x^-1 * z ] T46.206 : Triangle type {47,94,94} Group order 94 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x * y^-2 * x^8, y^-1 * z * y^-7 * z ] T46.207 : Triangle type {47,94,94} Group order 94 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-1 * z * y^-1 * z * y^-1 * z * y^-4 * x * y^-4 ] T46.208 : Triangle type {47,94,94} Group order 94 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^47, y * z^-1 ] T46.209 : Triangle type {93,93,93} Group order 93 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^41 * x^-1 * y^5, x * z^-1 ] T46.210 : Triangle type {93,93,93} Group order 93 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^-1 * y * x^-9 * y^3 * x^-1 * y * x^-1 * y * x^-1 * y ] T46.211 : Triangle type {93,93,93} Group order 93 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * y^-3 * x^-1 * z^3, x^2 * y^-1 * x * y^-3 * x^6 * y^-2 ] T46.212 : Triangle type {93,93,93} Group order 93 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * y^-3 * z^4, x^10 * z^-1 ] T46.213 : Triangle type {93,93,93} Group order 93 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-4 * x^4 * y^-3, x^7 * z^-4 ] T46.214 : Triangle type {93,93,93} Group order 93 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, y^-5 * x^3 * y^-4 ] Genus 47 T47.1 : Triangle type {2,4,96} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-88 * x * y * z^-7 ] T47.2 : Triangle type {2,4,96} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-30 * x * z^5 * y * z^-2 * x * z^2 * y^-1 * z^-7 ] T47.3 : Triangle type {2,4,188} Group order 376 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-86 * x * y^-1 * z^-7 ] T47.4 : Triangle type {2,6,141} Group order 282 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-19 * x * z^9 * y * z^-1 * x * z^5 * y * z^-1 * x * z^7 * y^-1 * z^-2 ] T47.5 : Triangle type {2,8,18} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, z^-1 * x * y^-2 * z^-2 * y, z^-4 * x * z^7 * y * x * y^-1 * z^-1 * x * y^-1 * z^-3 ] T47.6 : Triangle type {2,8,18} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, z^-3 * x * z^3 * y * x * z^2 * y^-1 * z^-8 ] T47.7 : Triangle type {2,8,64} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^10 * y * x * z^2 * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-8 * x * z^5 ] T47.8 : Triangle type {2,8,64} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^20 * y * z^-9 * x * z^2 ] T47.9 : Triangle type {2,12,30} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-2)^2, z * y * z^-1 * y^2 * z^-1 * x * z ] T47.10 : Triangle type {2,95,190} Group order 190 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^93 * z^-2 ] T47.11 : Triangle type {2,96,96} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-20 * y^11 * z^-2 * y^14 ] T47.12 : Triangle type {2,96,96} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^2 * y^-93 ] T47.13 : Triangle type {2,188,188} Group order 188 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^20 * z^-73 * y ] T47.14 : Triangle type {3,4,7} Group order 336 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^3 * y^-1 * x^-1 * z^3, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x * z * y^-1 ] T47.15 : Triangle type {3,141,141} Group order 141 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-36 * z * y^-1 * z * y^-6 * z^2 ] T47.16 : Triangle type {4,4,48} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^48 ] T47.17 : Triangle type {4,4,48} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^12 * y * z^-4 * x * y^-1 * x * z * y^-1 * z^-4 * x ] T47.18 : Triangle type {4,4,48} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^12 * y * z^-4 * x * y^-1 * x * z * y^-1 * z^-4 * x^-1 ] T47.19 : Triangle type {4,4,48} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, z^-1 * y * x^-1 * y^2, z^-17 * x * z^2 * y * z^-4 ] T47.20 : Triangle type {4,4,94} Group order 188 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^34 * y^-1 * z^-4 * x * z^8 ] T47.21 : Triangle type {4,5,6} Group order 240 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^-5, z^6, z^-2 * y * x^-1 * y * z^-1 * y ] T47.22 : Triangle type {4,6,28} Group order 168 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^-4 * x^-1 * z^3 * y * x^-1 * y * x * y^-1 * z^-4 ] T47.23 : Triangle type {4,8,20} Group order 160 Action chiral Defining relators: [ x * y * z, x^4, z * y * x^-1 * y^-2, (x * z * y^-1)^2, z^-2 * y * x^2 * z * y * z^-1 ] T47.24 : Triangle type {4,8,20} Group order 160 Action chiral Defining relators: [ x * y * z, x^4, (x * y^-1)^2, (y * z^-1 * y)^2, y^8, x^-1 * z * y^2 * x^-1 * z^3 ] T47.25 : Triangle type {4,8,20} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^3 * y * x^-1 * z * y * x^-1 * z^4 ] T47.26 : Triangle type {4,8,20} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, z^-4 * x^-1 * z * y * x^-1 * z * y * z^-2 ] T47.27 : Triangle type {4,8,20} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^13 * y * x * z * y * z^-2 * x * z^2 ] T47.28 : Triangle type {4,8,20} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * z^6 * y^-1 * z^-3 * x * y^-1 * z^-8 ] T47.29 : Triangle type {4,8,20} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^-1 * x^-1 * z * y * x^-1 * z * y^-1 * z^-1 * x * z * y * z^-2 ] T47.30 : Triangle type {4,8,20} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^8, z^3 * y * x^-1 * z * y * x * z^4 ] T47.31 : Triangle type {4,18,18} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * z * y, z^-1 * y^2 * x^-1 * y^-3, y * z^-1 * y^4 * z^-1 * y * z^-1 ] T47.32 : Triangle type {4,18,18} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * z * y^-1, y^-5 * z^3 * y^-7 * z^3 ] T47.33 : Triangle type {4,18,18} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, z^4 * y^-1 * z^3 * y^-1 * z^2 * y^-5 * z * y^-1 ] T47.34 : Triangle type {4,33,44} Group order 132 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z^2 * y^-1 * z * y^-5 * z ] T47.35 : Triangle type {4,64,64} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-7 * z^2 * y^-1 * z^4 * y^-1 * z * y^-15 * z ] T47.36 : Triangle type {4,64,64} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y^8 * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-2 * y^2 * z^-1 ] T47.37 : Triangle type {6,20,60} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-2 * x * y^-6 ] T47.38 : Triangle type {6,30,30} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, z * y^-2 * x * y^-1 * z ] T47.39 : Triangle type {6,57,114} Group order 114 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^3 * y^-7 * z ] T47.40 : Triangle type {8,8,9} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, (x * y^-1 * x)^2, z^4 * y^-1 * x^-1 * z^4 ] T47.41 : Triangle type {8,8,9} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, y^2 * x^-1 * y^-1 * z, z^9 ] T47.42 : Triangle type {8,8,32} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^3 * y^-1 * z^-1 * x * z * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z ] T47.43 : Triangle type {8,8,32} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^-9 * x^-1 * y * x^-1 * y * z^-5 ] T47.44 : Triangle type {8,15,24} Group order 120 Action chiral Defining relators: [ x * y * z, z * y^-1 * x * y^-1, y * x * z^-1 * x^-1 * z * y^2, x^8 ] T47.45 : Triangle type {8,15,24} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^3 * x * z * y, x^8 ] T47.46 : Triangle type {8,28,56} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, y^6 * z^-3 * y^4 * z^-1 ] T47.47 : Triangle type {8,28,56} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z * y^-1 * z * y^-1 * z * y^-7 * z ] T47.48 : Triangle type {10,12,20} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, y^3 * x^-1 * y^-1 * z^-1 * y, x^10 ] T47.49 : Triangle type {10,22,55} Group order 110 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^10, y^-2 * z * y^-4 * z^4 ] T47.50 : Triangle type {15,21,105} Group order 105 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * y^-3 * x^-1 * z^3, x^2 * y^-1 * x * y^-1 * x * y^-4 * x^6 * y^-1 ] T47.51 : Triangle type {20,50,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-7 * y^2 * x^-6 * z^2 * x^-5 ] T47.52 : Triangle type {20,50,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, z^-3 * x^6 * z^-7 ] T47.53 : Triangle type {20,50,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x * y^-3 * x^5 * y^-2, z^3 * y^-4 * x^-2 * z^3 ] T47.54 : Triangle type {20,50,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^2 * x^-7 * y^4 * x^-1 * y^4 ] T47.55 : Triangle type {48,96,96} Group order 96 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^48, y * z^-1 ] T47.56 : Triangle type {48,96,96} Group order 96 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-10 * z * x^-8 * z * x^-5 ] T47.57 : Triangle type {48,96,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^3 * z^-2 * x^8 ] T47.58 : Triangle type {48,96,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-2 * z^2 * y^-3 * x^4 * y^-4 * z^3 ] T47.59 : Triangle type {48,96,96} Group order 96 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-3 * y^4, z^-6 * x * z^-4 ] T47.60 : Triangle type {95,95,95} Group order 95 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^42 * x^-1 * y^5, x * z^-1 ] T47.61 : Triangle type {95,95,95} Group order 95 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x * z^-2 * x^4 * z^-3, y^-4 * x^3 * y^-4 ] T47.62 : Triangle type {95,95,95} Group order 95 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-8 * y, y^2 * z^-5 * y^2 * z^-2 ] T47.63 : Triangle type {95,95,95} Group order 95 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^22 * x^-4 * y^7 ] T47.64 : Triangle type {95,95,95} Group order 95 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-6 * z, x^2 * z^-1 * x * z^-2 * x^8 ] T47.65 : Triangle type {95,95,95} Group order 95 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^3 * z^-4 * x^-2 * y^4 ] T47.66 : Triangle type {95,95,95} Group order 95 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^4 * z^-1 * x^9 ] T47.67 : Triangle type {95,95,95} Group order 95 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^2 * x^-5 * y^9 * x^-2 * y^4 * x^-1 * y * x^-1 * y ] T47.68 : Triangle type {95,95,95} Group order 95 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^7 * z^-1, x^2 * z^-1 * x^9 ] Genus 48 T48.1 : Triangle type {2,4,51} Group order 408 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-35 * x * z^8 * y^-1 * z^-7 ] T48.2 : Triangle type {2,4,98} Group order 392 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-98 ] T48.3 : Triangle type {2,4,192} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-88 * x * y^-1 * z^-7 ] T48.4 : Triangle type {2,6,50} Group order 300 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^38 * y * x * y^-1 * z^-1 * x * y^-1 * z^-3 * x * z^5 ] T48.5 : Triangle type {2,8,34} Group order 272 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-12 * x * z^3 * y * x * z * y^-1 * z^-1 * x * y^-1 * z^-14 ] T48.6 : Triangle type {2,10,26} Group order 260 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^4 * y * x * z^2 * y * x * z * y * x * y * x * z^15 ] T48.7 : Triangle type {2,10,120} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, x * z^7 * y * z^-16 ] T48.8 : Triangle type {2,12,40} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^-5 * x * z^7 * y * x * y^-1 * z^-1 * x * y^-1 * z^-4 ] T48.9 : Triangle type {2,14,18} Group order 252 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^-1 * z^-1 * x * y^-1 * z * y * x * z * y * x * y^-6 * z^-1 * x, z^-2 * x * z^9 * y^-1 * z^-6 ] T48.10 : Triangle type {2,14,112} Group order 224 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, (y^-3 * z^4)^2, z^9 * y * x * z^6 ] T48.11 : Triangle type {2,26,104} Group order 208 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^-14 * z^2 * y^-7 * z^2 * y^-1 ] T48.12 : Triangle type {2,34,102} Group order 204 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-5 * y^11 * z^-2 * y^12 * z^-3 ] T48.13 : Triangle type {2,50,100} Group order 200 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-22 * y^11 * z^-1 * y^14 * z^-1 ] T48.14 : Triangle type {2,51,51} Group order 204 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^2 * z^-37 * y^11 * z^-1 ] T48.15 : Triangle type {2,97,194} Group order 194 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^94 * z^-2 * y ] T48.16 : Triangle type {2,98,98} Group order 196 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^3 * y^-93 * z ] T48.17 : Triangle type {2,192,192} Group order 192 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^2 * y^-92 * z ] T48.18 : Triangle type {3,3,97} Group order 291 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-1 * x^-1 * z^7 * y^-1 * z^-2 ] T48.19 : Triangle type {3,14,28} Group order 168 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, z^-3 * y * z^-1 * y^3 * z^-1 * y * z^-1 * y^2 * z^-1 ] T48.20 : Triangle type {3,26,39} Group order 156 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^-5 * z * y^-1 * z^4 * y^-1 * z ] T48.21 : Triangle type {3,49,147} Group order 147 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-38 * z * y^-1 * z * y^-7 * z ] T48.22 : Triangle type {3,50,50} Group order 150 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^37 * y^-3 * z * y^-7 * z ] T48.23 : Triangle type {3,144,144} Group order 144 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-37 * z * y^-1 * z * y^-6 * z^2 ] T48.24 : Triangle type {4,4,49} Group order 196 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-49 ] T48.25 : Triangle type {4,4,96} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^35 * y^-1 * z^-4 * x * z^8 ] T48.26 : Triangle type {4,6,42} Group order 168 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^-4 * x * z^4 * y * z^-5 ] T48.27 : Triangle type {4,10,16} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^4 * y^-1 * x * z^3, y^10 ] T48.28 : Triangle type {4,20,35} Group order 140 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^3 * y * x * z^3 ] T48.29 : Triangle type {4,33,132} Group order 132 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^12 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-2 * y^2 * z^-1 ] T48.30 : Triangle type {4,34,34} Group order 136 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, y^-9 * z^3 * y^-1 * z * y^-1 * z * y^-1 * z * y^-16 ] T48.31 : Triangle type {4,44,66} Group order 132 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^-1 * z^2 * y^-1 * z * y^-3 * z^2 * y^-1 ] T48.32 : Triangle type {4,128,128} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, z^-1 * y^7 * z^-2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-2 * y^2 * z^-1 ] T48.33 : Triangle type {5,26,26} Group order 130 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^-5, y^-1 * z * y^-3 * z^2 * y^-1 * z * y^-1 * z * y^-14 * z ] T48.34 : Triangle type {5,120,120} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-5, y^-5 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-2 * z^4 * y^-1 * z * y^-1 ] T48.35 : Triangle type {5,120,120} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^-1 * z * y^-3 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-2 * z^4 * y^-1 * z * y^-1 ] T48.36 : Triangle type {6,6,25} Group order 150 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^25 ] T48.37 : Triangle type {6,30,60} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^-1 * z^2 * y^-3 * x * y^-2 * z * y^-1 ] T48.38 : Triangle type {6,40,40} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^6, y^4 * z^-1 * y * z^-1 * x^-1 * y^3 * z^-1 * y^8 * z^-1 ] T48.39 : Triangle type {7,17,119} Group order 119 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, z^-1 * y^4 * x^-1 * y^2 * z^-4 * y * z^-1 * y * z^-1 * y * z^-1 ] T48.40 : Triangle type {7,18,18} Group order 126 Action reflexible [n] Defining relators: [ x * y * z, x^-1 * y^-1 * x * z^-1, x^-3 * z * y, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 * z * y^-5 * z^2 ] T48.41 : Triangle type {7,18,18} Group order 126 Action reflexible [n] Defining relators: [ x * y * z, z^-1 * x^2 * y^-1, z * x^-2 * y * x, y^-1 * z * y^-1 * z^3 * y^-3 * z * y^-5 * z * y^-2 ] T48.42 : Triangle type {7,18,18} Group order 126 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^-7, y^-2 * z * y^-1 * z * y^-10 * z * y^-1 * z ] T48.43 : Triangle type {7,112,112} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, z^3 * y^-1 * z * y^-1 * z * y^-4 * x^-1 * z^5 ] T48.44 : Triangle type {7,112,112} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, z * y^-1 * z * y^-1 * z * y^-1 * z * y^-4 * x^-1 * z^5 ] T48.45 : Triangle type {7,112,112} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-7, y^-2 * z * y^-1 * z * y^-1 * z * y^-4 * x^-1 * z^4 * y^-1 ] T48.46 : Triangle type {8,8,17} Group order 136 Action reflexible [n] Defining relators: [ x * y * z, x * z^-1 * y * z^-1, x^8, (x * y^-1 * x^2)^2 ] T48.47 : Triangle type {8,8,17} Group order 136 Action reflexible [n] Defining relators: [ x * y * z, z * y * x * z, x^8, (x * y^-1 * x^2)^2 ] T48.48 : Triangle type {8,8,17} Group order 136 Action reflexible [n] Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, z^2 * y * x * z^2, x^8 ] T48.49 : Triangle type {8,8,17} Group order 136 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^11 * y * x * z^5 ] T48.50 : Triangle type {8,15,40} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, y^-3 * x * z * y^-1, x^8 ] T48.51 : Triangle type {9,13,117} Group order 117 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-9, y^-1 * z * y^-1 * z^4 * y^-2 * z^4 ] T48.52 : Triangle type {9,14,14} Group order 126 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^-9, y^12 * z^-2 ] T48.53 : Triangle type {9,108,108} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-9, y^-1 * z * y^-1 * z * y^-4 * x * y^-4 ] T48.54 : Triangle type {9,108,108} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-9, y^-1 * z * y^-1 * z * y^-6 * z^2 ] T48.55 : Triangle type {9,108,108} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-9, y^-1 * z * y^-1 * z * y^-4 * x^-1 * z^4 ] T48.56 : Triangle type {10,10,13} Group order 130 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^10, z^8 * y * x * z^4 ] T48.57 : Triangle type {10,10,60} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-2 * x^2 * y^-2, z^3 * y * x^-1 * z^3 * y^-1 * x * z^4 ] T48.58 : Triangle type {10,10,60} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-2)^2, z * y^-1 * z^-1 * x^-1 * z^2 * y^-1 * z^-2 * x * z^4 ] T48.59 : Triangle type {10,12,30} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^3 * x^-1 * y * z^-1 * y, x^10 ] T48.60 : Triangle type {10,15,20} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z * y^2 * x * z^2, (y * z^-1 * y)^2, (z^-1 * x)^3 ] T48.61 : Triangle type {10,15,20} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, y^2 * x * z^-1, z^-2 * x^2 * z^-2, (x * y^-1)^4 ] T48.62 : Triangle type {10,15,20} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, x^-1 * z * x^-1 * y^-1 * z, y^-3 * x^2 * y^-3 ] T48.63 : Triangle type {12,12,20} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x * z * y^-1 * z^-3 * x * y^-1 * x * y^-1 * z^-3 ] T48.64 : Triangle type {12,27,108} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, x * y^-1 * x * y^-4 * x^2 * y^-4 ] T48.65 : Triangle type {12,27,108} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-5 * z^4, x^4 * y^-4 * x^2 * z^-4 * x^2 ] T48.66 : Triangle type {13,104,104} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^4 * y^-3 * x^4 * z^-3 * x^2 ] T48.67 : Triangle type {13,104,104} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, z^-2 * x^4 * z^-6 ] T48.68 : Triangle type {13,104,104} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, z * x^-1 * z^5 * x^-6 * z^2 ] T48.69 : Triangle type {13,104,104} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, x * y^-4 * x^2 * y^-4 ] T48.70 : Triangle type {13,104,104} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-4 * y * z^-3, x^2 * y^-1 * x * y^-4 * x^3 * y^-3 ] T48.71 : Triangle type {13,104,104} Group order 104 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^4 * y^-3 * x^4 * z^-3 * x^2 ] T48.72 : Triangle type {14,14,56} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, y^-3 * x^2 * y^-3, z * y * z^-2 * x^-1 * z^4 ] T48.73 : Triangle type {14,14,56} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^4 * y^-2, z^-1 * y^3 * z^-1 * y, z^2 * y * z^-1 * x^-1 * z^4 ] T48.74 : Triangle type {14,14,56} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-3)^2, z^3 * y * x^-1 * z^4 ] T48.75 : Triangle type {15,35,105} Group order 105 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-2 * z^4, x * y^-1 * x * y^-4 * x^4 * y^-2 ] T48.76 : Triangle type {15,35,105} Group order 105 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^5 * y^-3 * x^4 * z^-3 * x^3 ] T48.77 : Triangle type {15,35,105} Group order 105 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * y^-2 * x^-1 * z^3, x^-7 * y^4 * x^-1 * y * x^-1 * y^2 ] T48.78 : Triangle type {16,16,28} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^2 * x^-1 * z * y^-1, x^6 * y^-2, z * y * x^-1 * y * x^-1 * z^4 ] T48.79 : Triangle type {17,102,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x * y^-4 * x^4 * y^-2, y^-1 * z * y^-1 * z * y^-4 * x^-1 * z^4 ] T48.80 : Triangle type {17,102,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, y^-1 * z * y^-1 * z * y^-4 * x * y^-4 ] T48.81 : Triangle type {17,102,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^-8 * x * y^-4 ] T48.82 : Triangle type {17,102,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, x * z^-1 * x^7 * z^-5 * x^2 ] T48.83 : Triangle type {17,102,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^13 * y^-1 * x * z^-1 * x^2 ] T48.84 : Triangle type {17,102,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^2 * z^-1 * x^7 * z^-5 * x^3 ] T48.85 : Triangle type {17,102,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^4 * z^-4, x * y^-1 * x * y^-4 * x^5 * y^-1 ] T48.86 : Triangle type {17,102,102} Group order 102 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^6 * y^-3 * x^4 * y^-3 * x^4 ] T48.87 : Triangle type {18,27,27} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * x^-1 * y^-1 * z, x^-1 * z * y * x * y^-1 * z^-1, x * y^-1 * x^3 * y^-1 * x * y^-1 ] T48.88 : Triangle type {18,27,27} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, z * y^-1 * x * z, y * z^-1 * y * x * z * y, z^-1 * x^5 * z^-1 * x * z^-1 * x ] T48.89 : Triangle type {18,27,27} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, y * x^-2 * y^2, x^-1 * z * y * x * y^-1 * z^-1, x^-4 * z^3 ] T48.90 : Triangle type {25,100,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-6 * x^3 * y^-2, x^7 * z^-4 ] T48.91 : Triangle type {25,100,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * x^4 * y^-3, z^5 * x^-4 * y^-3 * z^4 ] T48.92 : Triangle type {25,100,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-4 * y * z^-3, x^2 * y^-4 * x^7 ] T48.93 : Triangle type {25,100,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, (x^-9 * z * x^-1 * z * x^-1)^2 ] T48.94 : Triangle type {25,100,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^5 * x^-4 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y ] T48.95 : Triangle type {25,100,100} Group order 100 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-12 * y^2 * x^-6 * y^2 * x^-5 ] T48.96 : Triangle type {25,100,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-5 * x * y^-3, x^-1 * z^4 * x^-7 ] T48.97 : Triangle type {25,100,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-3 * z^3, y^-4 * x * y^-4 * x^3 * y^-4 ] T48.98 : Triangle type {26,26,52} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * x^-1 * z^2, y^-4 * x^2 * y^-2 * z * y^-4 * x * y^-1 ] T48.99 : Triangle type {26,26,52} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * x^2 * z^-2, y^-2 * x^4 * y^-4 ] T48.100 : Triangle type {26,26,52} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6 * y^-2, y^5 * z^-1 * y * z^-1 ] T48.101 : Triangle type {26,26,52} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^4 * y^-2, z^-4 * x^2 * z^-4 ] T48.102 : Triangle type {26,26,52} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y^3 * z^-1 * y, x^8 * y^-2 ] T48.103 : Triangle type {26,26,52} Group order 104 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^-2 * x^-1 * z * y^-1, z^4 * x^-1 * z * x^-1 * z^4 * y^-1 * z * x^-1 * z ] T48.104 : Triangle type {33,99,99} Group order 99 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^5 * y^-3, z^5 * y^-7 * z^3 ] T48.105 : Triangle type {33,99,99} Group order 99 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x * z^-1 * x * z^-1 * x^7 * z^-7 ] T48.106 : Triangle type {33,99,99} Group order 99 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^7 * z^-3, y^-5 * x^3 * y^-4 ] T48.107 : Triangle type {33,99,99} Group order 99 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x * y^-1, x^-12 * z * x^-1 * z^5 * x^-3 * z^4 * x^-1 * z^2 ] T48.108 : Triangle type {33,99,99} Group order 99 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-19 * z * x^-8 * y * x^-5 ] T48.109 : Triangle type {33,99,99} Group order 99 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-6 * z^3, x^3 * y^-3 * x^7 ] T48.110 : Triangle type {33,99,99} Group order 99 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^12 * x^-2 * z^4 * x^-1 * z^2 ] T48.111 : Triangle type {33,99,99} Group order 99 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^2 * y^-1 * x * y^-4 * x^3 * y^-4 ] T48.112 : Triangle type {33,99,99} Group order 99 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^-2 * z * y^-1 * z * y^-1 * z * y^-4 * x * y^-4 ] T48.113 : Triangle type {34,34,51} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, z * y * z^-1 * x^-1 * z^3, y^-1 * x * y^-1 * x * y^-1 * x * y^-4 ] T48.114 : Triangle type {34,34,51} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, y * x^-1 * y * x^-1 * y * z^-1 * y ] T48.115 : Triangle type {34,34,51} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-3 * x * z^2, x^5 * y^-1 * z^-2 ] T48.116 : Triangle type {34,34,51} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * y * x^-1 * z * y, (z * x^-1 * z^3)^2 ] T48.117 : Triangle type {34,34,51} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, x^-4 * z^3 ] T48.118 : Triangle type {34,34,51} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, x^5 * z^-1 * x * z^-1 ] T48.119 : Triangle type {34,34,51} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, z * y^-1 * x * z, z^-1 * y * x^-1 * y^-2, x^-1 * z * x^-6 * y * x^-1 * z^3 * y ] T48.120 : Triangle type {34,34,51} Group order 102 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-1 * x * z, z^-4 * x * z^-5 * x * z^-4 * y * z^-1 * y * z^-1 ] T48.121 : Triangle type {49,98,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^15 * x^-1 * z^9 ] T48.122 : Triangle type {49,98,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^4 * x^-1 * y^4, x^2 * z^-2 * x^8 ] T48.123 : Triangle type {49,98,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, x^-1 * y * x^-7 * z^2 * x^-1 * z * x^-1 * z * x^-1 * z * x^-1 ] T48.124 : Triangle type {49,98,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^9 * y^-2, z^-2 * x * z^-2 * x^4 * z^-4 ] T48.125 : Triangle type {49,98,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^-5 * x^3 * y^-5 ] T48.126 : Triangle type {49,98,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, x * y^-10 * x * y^-1 * x * y^-1 * x^10 * y^-1 * x * y^-1 ] T48.127 : Triangle type {49,98,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^-16 * z * y^-3 ] T48.128 : Triangle type {49,98,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^-1 * x^2 * y^-1 * x * y^-1 * x * y^-1 * x * y^-4 * x * y^-5 * x * y^-1 ] T48.129 : Triangle type {49,98,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^2 * z^-2 * x^3 * z^-4, y^2 * z^-5 * x^-3 * y^3 ] T48.130 : Triangle type {49,98,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8 * y^-2, y * z^-9 ] T48.131 : Triangle type {49,98,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y^2 * z^-2, x^2 * y^-1 * x * y^-1 * x^10 * z^-1 * x * y^-1 ] T48.132 : Triangle type {49,98,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^3 * z^-2 * x^8 ] T48.133 : Triangle type {49,98,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, y * x^-1 * y, z^-28 * x * z^-4 ] T48.134 : Triangle type {49,98,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4 * z^-2, y^-4 * z * y^-3 * x^3 * y^-4 * z * y^-3 ] T48.135 : Triangle type {49,98,98} Group order 98 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^49, y * z^-1 ] T48.136 : Triangle type {49,98,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, y^3 * z^-3 * y * z^-4 * y^3 ] T48.137 : Triangle type {49,98,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6 * y^-2, z^-8 * x * z^-4 ] T48.138 : Triangle type {49,98,98} Group order 98 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x * z^-2 * x^3 * z^-4, y^-4 * x^3 * y^-4 ] T48.139 : Triangle type {50,50,50} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^3 * z^-1 * y^3 * x^-2 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y ] T48.140 : Triangle type {50,50,50} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6 * z^-2, y^-8 * x^2 * y^-4 ] T48.141 : Triangle type {50,50,50} Group order 100 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y^-1 * x^2 * y^-1, z^-16 * x^2 * z^-8 ] T48.142 : Triangle type {97,97,97} Group order 97 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^43 * x^-1 * y^5, x * z^-1 ] T48.143 : Triangle type {97,97,97} Group order 97 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-25 * x^2 * y^-6 ] T48.144 : Triangle type {97,97,97} Group order 97 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^-7 * x * y^-1 * x * y^-1 * x * y^-4 * x^3 * y^-5 * x * y^-1 ] T48.145 : Triangle type {97,97,97} Group order 97 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^3 * y^-1 * x * y^-1 * x * y^-1 * x * y^-4 * x * y^-5 * x * y^-1 ] T48.146 : Triangle type {97,97,97} Group order 97 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-2 * y^5 * x^-7 * y * x^-1 * y * x^-1 ] T48.147 : Triangle type {97,97,97} Group order 97 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-1 * x * y^-1 * x^7 * y^-5 ] T48.148 : Triangle type {97,97,97} Group order 97 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, y^-2 * x^7 * y^-4 ] T48.149 : Triangle type {97,97,97} Group order 97 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-4, x^11 * y^-1 ] T48.150 : Triangle type {97,97,97} Group order 97 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * x^3 * y^-4, z^-5 * x * z^-4 ] T48.151 : Triangle type {97,97,97} Group order 97 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * x^-2 * y^4, x * z^-1 * x * z^-2 * x^8 ] T48.152 : Triangle type {97,97,97} Group order 97 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^2 * z^-2 * x^4 * z^-3, y^-3 * x^4 * y^-4 ] T48.153 : Triangle type {97,97,97} Group order 97 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-5 * z^2, x * z^-1 * x * z^-1 * x * z^-2 * x^8 ] T48.154 : Triangle type {97,97,97} Group order 97 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * y^2, z^9 * y^-4 * z^8 ] T48.155 : Triangle type {97,97,97} Group order 97 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^2 * z^-1 * y^3 * x^-5 * y^3 * z^-1 * y ] T48.156 : Triangle type {97,97,97} Group order 97 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-4 * y^4, z^-2 * x * z^-2 * x^4 * z^-4 ] T48.157 : Triangle type {97,97,97} Group order 97 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-4 * z^3, y^-7 * x^2 * y^-6 ] T48.158 : Triangle type {97,97,97} Group order 97 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8 * y^-3, z^-4 * x^3 * z^-4 ] Genus 49 T49.1 : Triangle type {2,3,10} Group order 1440 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^10, z * y * x * z * y * x * z^3 * y * x * z * y * x * y^-1 * z^-3 * x, z^-1 * x * z^4 * y * x * z^2 * y * x * z * y^2 * z^-2 * x * y^-1 * z^-2 ] T49.2 : Triangle type {2,3,12} Group order 1152 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^12, x * z^3 * y * x * z^2 * y^-1 * z^-1 * x * z^2 * y^-1 * z^-1, z * y * z^-1 * x * z * y * x * z^2 * y * z^-1 * x * z^2 * y^-1 * z * y^-1 * z^-2 * x * z ] T49.3 : Triangle type {2,3,14} Group order 1008 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^2 * y * x * z^2 * y * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x, x * z^2 * y * z^-1 * x * z^2 * y * x * z * x * z^2 * y^-1 * z^-2 ] T49.4 : Triangle type {2,3,14} Group order 1008 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^5 * y * x * z * y^-1 * x * z^2 * y^-1 * z^-1 * x, x * z^2 * y * z^-1 * x * z^2 * y * x * z * y^-1 * z^-2 * x * z * y^-1 * z^-1 ] T49.5 : Triangle type {2,4,5} Group order 1920 Action chiral Defining relators: [ x^2, x * y * z, y^4, z^-2 * x * y * z^-2, y * x * z * y^-1 * z * y * z^-1 * y * x * y^-1 * z * y^-1 * z^-1 * y * z^-2 * y * z^-1, y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * z ] T49.6 : Triangle type {2,4,5} Group order 1920 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^-2 * x * y * z^-2, (y * z^-1)^6, z * y * x * z * y * x * z * y * z^-1 * y^2 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T49.7 : Triangle type {2,4,6} Group order 1152 Action chiral Defining relators: [ x^2, x * y * z, y^4, z^6, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^2 * y * z^-2 * y * z^-1 * y^2 * x * y^-1 * z^2 * y^-1 * z^-1 * x ] T49.8 : Triangle type {2,4,6} Group order 1152 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^6, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, (y * z^-1)^6 ] T49.9 : Triangle type {2,4,7} Group order 896 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^-3 * x * y * z^-3, (y * z^-1)^4, (y * z^-2)^4 ] T49.10 : Triangle type {2,4,10} Group order 640 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-4)^2, z^10, z * y * z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1 * x ] T49.11 : Triangle type {2,4,10} Group order 640 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z^10, z^-1 * x * z * y^-1 * z * y^-1 * z^-3 * y * z^-1 ] T49.12 : Triangle type {2,4,10} Group order 640 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^10, z * y * z^-3 * x * y^-1 * z^-4 * x ] T49.13 : Triangle type {2,4,12} Group order 576 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z * y * z^-2 * x * y^-1 * z^-3 * x, z^12 ] T49.14 : Triangle type {2,4,16} Group order 512 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, y^-1 * z * y * x * z * y * x * y^-1 * z * y^-1 * z^-1 * x * z, z^-1 * x * z^4 * y * z^-2 * x * y * z^-7 ] T49.15 : Triangle type {2,4,16} Group order 512 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-2 * z^-4 * y, x * z^3 * y * z^-4 * x * z^2 * y^-1 * z^-5 ] T49.16 : Triangle type {2,4,16} Group order 512 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, x * z^3 * y^-2 * z^-4 * y, z^6 * y * x * z^2 * y^-1 * x * z^3 * y^-1 * z^-1 * x * z ] T49.17 : Triangle type {2,4,16} Group order 512 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z^3 * y^-1 * z^-4, y^-1 * z * y * x * z * y * x * y^-1 * z * y^-1 * z^-1 * x * z ] T49.18 : Triangle type {2,4,16} Group order 512 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z^3 * y^-2 * z^-4 * y, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T49.19 : Triangle type {2,4,16} Group order 512 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z * y * z^-2 * x * y^-1 * z^-3 * x ] T49.20 : Triangle type {2,4,16} Group order 512 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z * y * z^-2 * x * y^-1 * z^-3 * x, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T49.21 : Triangle type {2,4,16} Group order 512 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, x * z^3 * y^-2 * z^-4 * y ] T49.22 : Triangle type {2,4,16} Group order 512 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z * y * z^-2 * x * y^-1 * z^-3 * x, y * z^-1 * y * z^-1 * y * z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T49.23 : Triangle type {2,4,16} Group order 512 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z * y * z^-2 * x * y^-1 * z^-3 * x, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^2 * y^-1 * z * y * z^-1 * x * y^-1 * z^2 * y^-1 * z * y^-1 ] T49.24 : Triangle type {2,4,16} Group order 512 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T49.25 : Triangle type {2,4,16} Group order 512 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z^3 * y^-1 * z^-4, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T49.26 : Triangle type {2,4,16} Group order 512 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, z * y * x * y^-1 * z^-1 * x, z^-9 * y * z^-1 * y^2 * z^-1 * y * z^-5 ] T49.27 : Triangle type {2,4,16} Group order 512 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1, z * y * z^-2 * x * y^-1 * z^-3 * x, z^-1 * y * z^-1 * y * z^-1 * y * x * y^-1 * z^2 * y^-1 * z^-1 * y * z^-1 * y * z^-2 ] T49.28 : Triangle type {2,4,20} Group order 480 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, (y * z^-4)^2, z^-2 * y * x * z * y^2 * z^-2 * x * y^-1 * z^-1 ] T49.29 : Triangle type {2,4,20} Group order 480 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T49.30 : Triangle type {2,4,28} Group order 448 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, (y * z^-3)^2, z^-14 * x * z^4 * y * z^-1 * x * z^3 * y^-1 * z^-4 ] T49.31 : Triangle type {2,4,52} Group order 416 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-37 * x * z^5 * y * z^-1 * x * z^2 * y^-1 * z^-5 ] T49.32 : Triangle type {2,4,100} Group order 400 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-100 ] T49.33 : Triangle type {2,4,196} Group order 392 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-8 * x * y^-1 * z^-89 ] T49.34 : Triangle type {2,5,5} Group order 960 Action chiral Defining relators: [ x^2, x * y * z, y^-5, z^-2 * x * y * z^-2, (y * z^-1)^6, y * z^-2 * y * x * y^-2 * z^-1 * y * x * y^-1 * z^-2 ] T49.35 : Triangle type {2,5,5} Group order 960 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^-5, z^-2 * x * y * z^-2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (y * z^-1)^6 ] T49.36 : Triangle type {2,5,6} Group order 720 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^-5, z^6, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T49.37 : Triangle type {2,6,6} Group order 576 Action chiral Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, (y * z^-1 * y)^4, (y * z^-2 * y * z^-1 * y)^2, y * x * y^-1 * z^2 * y^2 * z^-2 * x * z^2 ] T49.38 : Triangle type {2,6,6} Group order 576 Action chiral Defining relators: [ x^2, x * y * z, y^6, z^6, (y * z^-1)^4, z^-1 * y^2 * x * y^-2 * z^2 * y^-1 * z^-2 ] T49.39 : Triangle type {2,6,6} Group order 576 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z^6, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2 ] T49.40 : Triangle type {2,6,6} Group order 576 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, z^2 * y^-1 * z^2 * y^-1 * z^2 * y * z^-1 * x * z^2 * y * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T49.41 : Triangle type {2,6,6} Group order 576 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * z^2 * y^-1 * z * y^-1 * z^2 * y^-1 * z^-2, (y * z^-1 * y)^4 ] T49.42 : Triangle type {2,6,6} Group order 576 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z^6, y * x * z^2 * y^2 * x * z * y^-1 * z^-1, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, (y * z^-2 * y * z^-1 * y)^2 ] T49.43 : Triangle type {2,6,6} Group order 576 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, y^6, z^6, (y * z^-1)^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T49.44 : Triangle type {2,6,12} Group order 384 Action chiral Defining relators: [ x^2, x * y * z, y^6, y * z^-1 * y * x * y^-1 * z^-4, y * z^-1 * x * z * y^2 * x * z * y^-1 * z ] T49.45 : Triangle type {2,6,12} Group order 384 Action chiral Defining relators: [ x^2, x * y * z, y^6, y * z^-1 * y * x * y^-1 * z^-4, y * x * z^2 * y^2 * x * z * y^-1 * z^-1 ] T49.46 : Triangle type {2,6,12} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, (y * z^-1 * y)^4 ] T49.47 : Triangle type {2,6,12} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z^3 * y^-2 * z^-1 * x * y^-1 * z, z^-1 * x * y^-1 * z * y^2 * x * z * y^-1 * z^-1 ] T49.48 : Triangle type {2,6,12} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, x * y^-1 * z * y^-3 * z^-3 * y * z^-1 ] T49.49 : Triangle type {2,6,12} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z^3 * y^-2 * z^-1 * x * y^-1 * z, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1 ] T49.50 : Triangle type {2,6,12} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (z^-1 * y)^3, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, x * z^2 * y^-3 * z^-3 * y^2 ] T49.51 : Triangle type {2,6,12} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, x * z * y^-1 * z * y^-1 * z^-4, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, x * z^2 * y^-3 * z^-3 * y^2 ] T49.52 : Triangle type {2,6,12} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z * y * z^-3 * x * y^-1 * z^-4 * x ] T49.53 : Triangle type {2,6,12} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, x * z * y^-3 * z^-2 * y^2, x * y^-1 * z * y^-2 * z^-4, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T49.54 : Triangle type {2,6,12} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, (y * z^-1 * y)^4 ] T49.55 : Triangle type {2,6,12} Group order 384 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, x * z^2 * y^-1 * z^-3, z^-1 * y * z^-1 * x * y^-2 * z^-2 * y * z^-1 * y, (y * z^-1 * y)^4 ] T49.56 : Triangle type {2,6,15} Group order 360 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z^3 * y^2 * z^-1 * y * x ] T49.57 : Triangle type {2,6,15} Group order 360 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, x * z^4 * y^-1 * z^-5, x * z * y * z^-1 * x * z * y * z^-1 * x * y^-1 * z^-2 ] T49.58 : Triangle type {2,6,15} Group order 360 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, z^-8 * x * y * z^-6 ] T49.59 : Triangle type {2,6,15} Group order 360 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1)^4, (y^-2 * z)^3 ] T49.60 : Triangle type {2,6,15} Group order 360 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z * y * x * y^-1 * z^-1 * x, (y^-2 * z)^3 ] T49.61 : Triangle type {2,6,39} Group order 312 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1, z^-2 * x * z^4 * y * x * y^-1 * z^-5 ] T49.62 : Triangle type {2,6,51} Group order 306 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^40 * y * x * y * z^-7 * x * z^2 ] T49.63 : Triangle type {2,6,147} Group order 294 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-21 * x * z^16 * y * z^-1 * x * y^-1 * z^-9 ] T49.64 : Triangle type {2,7,7} Group order 448 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^-7, z^-3 * x * y * z^-3, y * x * y^-1 * z * y^2 * x * y^-2 * z^-1 ] T49.65 : Triangle type {2,7,14} Group order 336 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^-7, (y * z^-1)^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, (z * y^-1 * z)^3 ] T49.66 : Triangle type {2,8,24} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, (y * z^-1 * y^2)^2, (y^-1 * z)^6 ] T49.67 : Triangle type {2,8,24} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, (y * z^-1 * y^2)^2, y^-1 * z * y^-1 * z * y^-1 * z * y^2 * x * y^-1 * z * y^-1 * z ] T49.68 : Triangle type {2,9,18} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y^-9, z^2 * y^-3 * z^4, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T49.69 : Triangle type {2,10,10} Group order 320 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-4 * z^-4, x * y^-1 * z * y^-2 * z^-2 * y * z^-1, y^10 ] T49.70 : Triangle type {2,10,10} Group order 320 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y^-3 * z^-3 * y, z^-2 * x * y^-2 * z * y^-1 * z^-1 * y, y^10 ] T49.71 : Triangle type {2,10,10} Group order 320 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^10, (y * z^-1 * y^3)^2, (y * z^-1 * y * z^-1 * y)^2 ] T49.72 : Triangle type {2,10,10} Group order 320 Action reflexible [m] Defining relators: [ x^2, x * y * z, y * z^-1 * y^3 * z^-1 * x * z, y^10, z * y^2 * z^-1 * y^2 * z^-1 * y * x * y^-1 ] T49.73 : Triangle type {2,12,12} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^3 * y^-1 * z^-4, y^12 ] T49.74 : Triangle type {2,12,12} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, z^-1 * y * z^-1 * x * y^-1 * z^-2 * y * z^-1, x * z^3 * y^-1 * z^-4, y^12 ] T49.75 : Triangle type {2,12,12} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1 * y)^2, y^2 * x * z * y^2 * x * z^3, x * z^2 * y * x * y^-1 * z^-2 * x * y^-1 * z^-1 ] T49.76 : Triangle type {2,12,12} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * y^-1 * z * y^-2 * z^-4, x * z^2 * y * z^-1 * x * z * y^-1 * z^-2, y^12 ] T49.77 : Triangle type {2,12,12} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * z^3 * y^-1 * z^-4, y^12, y^2 * z^-1 * y^4 * z^-1 * y^2 * z^-2 ] T49.78 : Triangle type {2,12,12} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1 * y^2)^2, (y * z^-1)^4, z^3 * y^-2 * z^-2 * x * y^-1, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T49.79 : Triangle type {2,12,12} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1 * y^2)^2, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-1)^4, z^-4 * x * z^5 * y^-1 * z^-2 ] T49.80 : Triangle type {2,12,12} Group order 288 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^12, z^-12 ] T49.81 : Triangle type {2,12,60} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-12, z^-1 * x * z^8 * y * z^-4 * x * z * y^-1 * z^-4 ] T49.82 : Triangle type {2,16,16} Group order 256 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, x * z^9 * y^-1 * z^-6, y * x * y^-1 * z^-1 * x * y^-1 * z * y * x * z * y * x * y^-6 * z^-1 * y ] T49.83 : Triangle type {2,16,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, y^-6 * z^-1 * y * x, z^-1 * x * z^8 * y * z^-6 ] T49.84 : Triangle type {2,16,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^5 * y * z^-4 * x * z^2 * y^-1 * z^-3, (y^-4 * z^3 * y^-1)^2 ] T49.85 : Triangle type {2,16,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, y^5 * z^-1 * y * z^-1, z^-2 * x * z^7 * y^-1 * z^-6 ] T49.86 : Triangle type {2,16,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, z^3 * y^-3 * z^-1 * x * z^3 ] T49.87 : Triangle type {2,16,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, z^3 * y * x * y^-1 * z^-3 * x, y^-1 * z * y^-1 * z^3 * y^-7 * z^2 * y^-1 ] T49.88 : Triangle type {2,16,16} Group order 256 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (y * z^-1 * y^2)^2, (y * z^-1)^4, (y * z^-3)^2, x * y^-1 * z * y^3 * x * y^-2 * z^-1, z^2 * y * z^-1 * x * y^-1 * z^-2 * x * z ] T49.89 : Triangle type {2,16,16} Group order 256 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, x * z * y * x * z * y^3 * x * z^2 * y^-1 * z^-1 ] T49.90 : Triangle type {2,16,16} Group order 256 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, x * y^-4 * z^-1 * y^3, x * z^3 * y^-1 * z^-4 ] T49.91 : Triangle type {2,16,16} Group order 256 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, x * z^3 * y^-1 * z^-4, y^-1 * z * y^-1 * z^3 * y^-7 * z^2 * y^-1 ] T49.92 : Triangle type {2,16,16} Group order 256 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, (y * z^-1 * y^2)^2, z * y * x * z * y^3 * x * y^-1 * z^-3 * x ] T49.93 : Triangle type {2,16,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-2 * y)^2, (y * z^-1)^4, (y * z^-3)^2 ] T49.94 : Triangle type {2,16,16} Group order 256 Action reflexible [m] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, (y * z^-1)^4, (y * z^-3)^2 ] T49.95 : Triangle type {2,16,16} Group order 256 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, (y * z^-1 * y^2)^2, (y * z^-3)^2 ] T49.96 : Triangle type {2,16,16} Group order 256 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (y * z^-1 * y^2)^2, (y * z^-2 * y)^2, (y * z^-3)^2 ] T49.97 : Triangle type {2,16,16} Group order 256 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, y^-2 * z * y^-2 * z^2 * y^-6 * z * y^-2 ] T49.98 : Triangle type {2,16,16} Group order 256 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (y * z^-2 * y)^2, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y ] T49.99 : Triangle type {2,16,16} Group order 256 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z^-1 * y^4 * z^-3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, x * z * y^-1 * z * y^-1 * z^-2 * y * z^-1 ] T49.100 : Triangle type {2,16,16} Group order 256 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z^-1 * y^4 * z^-3, (y * z^-1)^4 ] T49.101 : Triangle type {2,16,16} Group order 256 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, (y * z^-1)^4 ] T49.102 : Triangle type {2,16,16} Group order 256 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, (y^3 * z^-1 * y * z^-1 * y^2)^2 ] T49.103 : Triangle type {2,16,112} Group order 224 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-2 * x * z^6 * y^-1 * z^-5, y^-4 * z^4 * y^-3 * z^4 * y^-1 ] T49.104 : Triangle type {2,16,112} Group order 224 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^-2 * x * z^10 * y^-1 * z^-1 ] T49.105 : Triangle type {2,20,20} Group order 240 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, (y * z^-2 * y)^2 ] T49.106 : Triangle type {2,20,20} Group order 240 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, (y * z^-2 * y)^2, x * y^-4 * z^-4, y^-1 * z * y^-3 * z^-1 * y * x * y^-1 ] T49.107 : Triangle type {2,27,54} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y^2, y^-27 ] T49.108 : Triangle type {2,28,28} Group order 224 Action reflexible [n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-1 * y * z^-1, y^-1 * z * y^-1 * z^10 * y^-15 ] T49.109 : Triangle type {2,28,28} Group order 224 Action reflexible [n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-4 * z^-3 * y, y^-10 * z^2 * y^-1 * z ] T49.110 : Triangle type {2,28,28} Group order 224 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, x * y^-3 * z^-3, y^-1 * z * y^-11 * z^3 * y^-10 * z^2 ] T49.111 : Triangle type {2,30,105} Group order 210 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-4 * z^2 * y^-4 * z^5 ] T49.112 : Triangle type {2,36,36} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-3 * z^-1 * y^2, z^-8 * y^11 * z^-4 * y * z^-12 ] T49.113 : Triangle type {2,52,52} Group order 208 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-24 * y^11 * z^-2 * y^12 * z^-2 ] T49.114 : Triangle type {2,99,198} Group order 198 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^95 * z^-4 ] T49.115 : Triangle type {2,100,100} Group order 200 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^4 * y^-95 ] T49.116 : Triangle type {2,196,196} Group order 196 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^3 * y^-94 ] T49.117 : Triangle type {3,3,5} Group order 720 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^2 * y^-1 * x^-1 * z^2, z * y * z^-1 * x^-1 * z * y * x * z * y^-1 * z^-1 * x, z^-1 * x^-1 * y * x * z * y * x^2 * y^-1 * x * z^2 * y ] T49.118 : Triangle type {3,3,6} Group order 576 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^6, (y * x^-1 * z)^3, z^2 * y^-1 * z^-1 * x^-1 * z^2 * y * x, (x * z * y)^4 ] T49.119 : Triangle type {3,3,6} Group order 576 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^3, z^6, (y * x^-1 * z)^3, x^-1 * z * y^-1 * z^-1 * x^-1 * y * z^-1 * x^-1 * z ] T49.120 : Triangle type {3,3,7} Group order 504 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^3 * y^-1 * x^-1 * z^3, (z^-1 * x^-1 * y^-1)^3, z^2 * y * z^-1 * x^-1 * z * y^-1 * z^-1 * x ] T49.121 : Triangle type {3,3,7} Group order 504 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, x^-1 * z^2 * y^-1 * x * z^3, z^3 * y^-1 * x^-1 * z^3, z * y * x * z * y * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x ] T49.122 : Triangle type {3,4,4} Group order 576 Action chiral Defining relators: [ x^3, x * y * z, y^4, z^4, (y * z^-1)^4, z^-1 * y * x^-1 * y * x^-1 * y * z^-1 * x^-1 * y^-1 ] T49.123 : Triangle type {3,4,4} Group order 576 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (y * z^-1)^4, (y * x^-1 * z)^3 ] T49.124 : Triangle type {3,4,6} Group order 384 Action chiral Defining relators: [ x^3, x * y * z, y^4, z^6, z * y * z^-1 * x^-1 * z * y^-1 * z, z^-1 * y * x * y^-1 * x * z * y * z^-1 ] T49.125 : Triangle type {3,4,6} Group order 384 Action chiral Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^6, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, y * z^-1 * x^-1 * y^-1 * z^-1 * x * z^-1 * x * z * y * x * z ] T49.126 : Triangle type {3,4,6} Group order 384 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^6, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x * z^-1 * x * z * y * x * z ] T49.127 : Triangle type {3,4,6} Group order 384 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z * x^-1 * y^-1 * x * y^-1 * x, z^6, (x^-1 * z^2 * y)^2 ] T49.128 : Triangle type {3,4,6} Group order 384 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^6, z * y * z^-1 * x^-1 * z * y^-1 * z, (x^-1 * z^2 * y)^2 ] T49.129 : Triangle type {3,4,6} Group order 384 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^6, z^-1 * y * x^-1 * y^-1 * x * y^-1 * z * y, y * z^-1 * x^-1 * y^-1 * z^-1 * x * z^-1 * x * z * y * z^-1 * x^-1 ] T49.130 : Triangle type {3,4,12} Group order 288 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^2, z^-2 * x * y^-1 * x * y^-1 * z^-2, z * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x * z * y^-1 * x * z ] T49.131 : Triangle type {3,4,12} Group order 288 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * z^-1 * x * z * y^-1 * z^-1 ] T49.132 : Triangle type {3,4,12} Group order 288 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, (z^-1 * y)^3, z^-2 * y * x^-1 * z * y^2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y, z^-4 * x^-1 * z^3 * y^-1 ] T49.133 : Triangle type {3,4,12} Group order 288 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1 ] T49.134 : Triangle type {3,5,5} Group order 360 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^-5, z^2 * y^-1 * x^-1 * z^2, (x * z * y)^2, (z^-1 * y)^3 ] T49.135 : Triangle type {3,5,15} Group order 240 Action chiral Defining relators: [ x^3, x * y * z, y^-5, (x * z * y)^2, y * x^-1 * y * x^-1 * y * z^-2 ] T49.136 : Triangle type {3,6,6} Group order 288 Action chiral Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, z^2 * x^-1 * y^-1 * x * y^-1 * z * y^-1 ] T49.137 : Triangle type {3,6,6} Group order 288 Action chiral Defining relators: [ x^3, x * y * z, y^6, (x^-1 * z * y)^2, z^6, y * z^-1 * x^-1 * y^-1 * x * z^2 * y ] T49.138 : Triangle type {3,6,6} Group order 288 Action chiral Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y^2 * x^-1 * y * x^-1 * z * y^-1 * x * z, y * z^-1 * y^2 * x^-1 * z * y^-1 * z * y ] T49.139 : Triangle type {3,6,6} Group order 288 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^6, (x * z * y)^2, (z^-1 * y)^3, z^6 ] T49.140 : Triangle type {3,6,6} Group order 288 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^6, (x * z * y)^2, z^6, y * z^-2 * x^-1 * y * z^-2 ] T49.141 : Triangle type {3,6,6} Group order 288 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * z^-1 * y, x * z * y * x^-1 * y * z^-1 * y ] T49.142 : Triangle type {3,6,6} Group order 288 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, y^6, z^6, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 * z^-1 ] T49.143 : Triangle type {3,6,6} Group order 288 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, (x^-1 * y^-1 * z^-1)^4 ] T49.144 : Triangle type {3,6,6} Group order 288 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^6, z^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y * z^-2 * x^-1 * y^-2 * z, y^2 * z^-1 * y * x^-1 * z * y^-1 * z^2 ] T49.145 : Triangle type {3,6,6} Group order 288 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^6, (x * z * y)^2, z^6, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1, x^-1 * y * x^-1 * y * x^-1 * z * y^-2 * z^-1 ] T49.146 : Triangle type {3,6,6} Group order 288 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^6, (x^-1 * z * y)^2, (y * z^-2)^2, z^6, y * x^-1 * y^2 * x^-1 * y^2 * x * z^-1 ] T49.147 : Triangle type {3,6,6} Group order 288 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^6, (x^-1 * z * y)^2, (z^-1 * y)^3, z^6 ] T49.148 : Triangle type {3,6,6} Group order 288 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^6, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * y)^3, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T49.149 : Triangle type {3,6,6} Group order 288 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y * z^-2 * y * z^-1 * y^2 * x^-1 * y^-2 * z^-1 * y * z^-2 * y^2 * z^-1 ] T49.150 : Triangle type {3,6,6} Group order 288 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y^2 * x^-1 * y * x^-1 * z * y^-1 * x * z, y * z^-1 * y^2 * x^-1 * y^-1 * z^3 ] T49.151 : Triangle type {3,6,6} Group order 288 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-2 * x^-1 * y^-2 * z, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1, y^2 * x^-1 * y * x^-1 * z * y^-1 * x * z ] T49.152 : Triangle type {3,6,10} Group order 240 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^6, z^-1 * y^2 * x^-1 * y^3, z^-2 * y * x^-1 * z * y^-1 * z^-1, z * y * x^-1 * y * x^-1 * y^-1 * z^-1 * y * x ] T49.153 : Triangle type {3,8,24} Group order 192 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, y^8 ] T49.154 : Triangle type {3,12,12} Group order 192 Action chiral Defining relators: [ x^3, x * y * z, y^3 * x^-1 * z * y * z^-1, z^2 * y * x^-1 * y^-1 * z^2, y^2 * z^-1 * x^-1 * y^-2 * z^-1 ] T49.155 : Triangle type {3,12,12} Group order 192 Action chiral Defining relators: [ x^3, x * y * z, y^3 * x^-1 * z * y * z^-1, z^2 * y * x^-1 * y^-1 * z^2, y * z^-2 * x^-1 * y^-2 * z ] T49.156 : Triangle type {3,12,12} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T49.157 : Triangle type {3,12,12} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, z^-1 * y^3 * z^-2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, x^-1 * z * y^2 * x * z^2 * y ] T49.158 : Triangle type {3,12,12} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, (x * z * y)^2, y^3 * x^-1 * y^-1 * z * y ] T49.159 : Triangle type {3,12,12} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, (y * z^-1)^2, (x * z * y)^2, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T49.160 : Triangle type {3,12,12} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, (y * z^-1)^2, z^-2 * x^-1 * y^-1 * x * y^-3 ] T49.161 : Triangle type {3,12,12} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3 * x^-1 * y^-1 * z * y, z * y^-1 * z^-1 * x^-1 * y^-2 * z ] T49.162 : Triangle type {3,12,12} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-2 * x * z^2, y^-1 * z * y * x^-1 * y^-3, (y * z^-1)^4 ] T49.163 : Triangle type {3,12,12} Group order 192 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, (y * z^-1)^4, z^-1 * y^4 * x^-1 * y^-1 * z^-1 * y^3 ] T49.164 : Triangle type {3,14,42} Group order 168 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, y^14 ] T49.165 : Triangle type {3,15,15} Group order 180 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, y * z^-3 * y * z^-2 * y^3 * z^-1 * y^4 ] T49.166 : Triangle type {3,15,15} Group order 180 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3 * x * y^-1 * z^-1, z * y^-1 * z^-1 * x * z^2 ] T49.167 : Triangle type {3,15,15} Group order 180 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^5 * x^-1 * y^-2 * z * y * z^-1, y^-1 * z^2 * y^-2 * x^-1 * z * y^-1 * z^2 ] T49.168 : Triangle type {3,15,15} Group order 180 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, z * x^-1 * y^-1 * x * y^-1 * x, (x^-1 * z * y)^2 ] T49.169 : Triangle type {3,15,15} Group order 180 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, (y * z^-1)^2, z * x^-1 * y^-1 * x * y^-1 * x ] T49.170 : Triangle type {3,39,39} Group order 156 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, (x * z * y)^2, y^-1 * z^2 * y^-1 * z * y^-4 * z^2 * y^-2 ] T49.171 : Triangle type {3,50,150} Group order 150 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-39 * z * y^-1 * z * y^-7 * z ] T49.172 : Triangle type {3,51,51} Group order 153 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-40 * z * y^-1 * z * y^-7 * z ] T49.173 : Triangle type {3,147,147} Group order 147 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-38 * z * y^-1 * z * y^-8 ] T49.174 : Triangle type {4,4,5} Group order 320 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, z^2 * y * x^-1 * y^-1 * z^-1 * x, (x * y^-1)^4 ] T49.175 : Triangle type {4,4,5} Group order 320 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * x^2 * z * y^-1, z^2 * y^-1 * x^-1 * z^2, (x * y^-1)^4 ] T49.176 : Triangle type {4,4,5} Group order 320 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^2 * y^-1 * x^-1 * z^2, y^-2 * z^-1 * y * x^-1 * y^-1 * z * y^-1 * z ] T49.177 : Triangle type {4,4,5} Group order 320 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^2 * y^-1 * x^-1 * z^2, (y * z^-1)^4 ] T49.178 : Triangle type {4,4,5} Group order 320 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, (x * z^-1 * y)^2, x^-1 * z * y * x^-1 * z * y * z^-1 ] T49.179 : Triangle type {4,4,5} Group order 320 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, (x * z^-2)^2, y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x ] T49.180 : Triangle type {4,4,5} Group order 320 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, z^2 * y * x^-1 * z * y^-1 * x, y * x * z^-1 * x^-1 * z * x^-1 * z ] T49.181 : Triangle type {4,4,5} Group order 320 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^2 * y^-1 * x^-1 * z^2, (x * z^-1 * y)^2, z^2 * y * x^-1 * z * y^-1 * x ] T49.182 : Triangle type {4,4,6} Group order 288 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (x^-1 * z * y)^2, (x * z * y)^2, z^6 ] T49.183 : Triangle type {4,4,6} Group order 288 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^6 ] T49.184 : Triangle type {4,4,8} Group order 256 Action chiral Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, x^-1 * z * y * x * z * y, z^8, z^-2 * y * z^-1 * x^-1 * y * z^-1 * y * z^-1 ] T49.185 : Triangle type {4,4,8} Group order 256 Action chiral Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, y^-2 * z^-1 * x^-1 * y^-1 * z^2, z^8 ] T49.186 : Triangle type {4,4,8} Group order 256 Action chiral Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, x^-1 * z * y * x^-1 * y^-1 * z^-1, (y * z^-1)^4 ] T49.187 : Triangle type {4,4,8} Group order 256 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^-1 * x * y^-1 * x * z * y, (x * z^-1 * y)^2 ] T49.188 : Triangle type {4,4,8} Group order 256 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * z * y^-1, (x * y^-1)^4 ] T49.189 : Triangle type {4,4,8} Group order 256 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * y^-1)^4 ] T49.190 : Triangle type {4,4,8} Group order 256 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^-2 * x^-1 * z * y^-1, (x * z^-1)^4, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1 ] T49.191 : Triangle type {4,4,8} Group order 256 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^8, y * x^-1 * y * x^-2 * y^-1 * x * z * x^-1 ] T49.192 : Triangle type {4,4,8} Group order 256 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^-1 * z * y^2, z^8 ] T49.193 : Triangle type {4,4,8} Group order 256 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, y * z^-1 * x^-2 * z^2 * x^-1, z^8 ] T49.194 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, z^-2 * y * x^-1 * z * y^2, x^-1 * z * y * x^2 * y^-1 * z^-1 * x^-1, x^-1 * y * x^-1 * y^-1 * x * z^-1 * x * z ] T49.195 : Triangle type {4,4,8} Group order 256 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, (x * z * y)^2 ] T49.196 : Triangle type {4,4,8} Group order 256 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (x * z * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-2 * y * x^-1 * z * y^2 ] T49.197 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (x^-1 * z * y)^2, (x * z * y)^2, (y * z^-1)^4 ] T49.198 : Triangle type {4,4,8} Group order 256 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x * z^-1 * y)^2, (x^-1 * z * y)^2 ] T49.199 : Triangle type {4,4,8} Group order 256 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, (x * y^-1)^4, z^-1 * x * z^-1 * y * x * z * y * z^-1 ] T49.200 : Triangle type {4,4,8} Group order 256 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^8, z^-4 * x^-1 * z^3 * y^-1 ] T49.201 : Triangle type {4,4,8} Group order 256 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * z * y^2 ] T49.202 : Triangle type {4,4,8} Group order 256 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^8, z^-3 * y * x^2 * z^3 * y ] T49.203 : Triangle type {4,4,8} Group order 256 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^8 ] T49.204 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, (x^-1 * z * y)^2, x^-1 * y * x^-2 * z^3 ] T49.205 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, y^-1 * z * y * x^-1 * y^-1 * z^2, z^8 ] T49.206 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, (y * z^-1)^4, z^8, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z ] T49.207 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y^-1 * x * y^-1 * x * z^2, (x * z^-1 * y)^2, (y * z^-1)^4 ] T49.208 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-1)^4 ] T49.209 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (x^-1 * z * y)^2, (x * z * y)^2, z^8, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z ] T49.210 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, z^8 ] T49.211 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^8, z^-1 * y * z^-1 * y * x^-1 * z^2 * y * z^-1 ] T49.212 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1, z^8, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z ] T49.213 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y^-1 * x * y^-1 * x * z^2, (x * z^-1 * y)^2, y * z^-1 * y * z^-1 * x^-1 * z^2 * y * z^-1 ] T49.214 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^8, z * y^-1 * z^-1 * y * x^-1 * z^2 * y^-1 * z, y * z^-1 * y * z^-1 * x^-1 * z^2 * y * z^-1 ] T49.215 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, x^-1 * z * y * x * y^-1 * z^-1 ] T49.216 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z * y * x^-1 * y^-1 * z^2 ] T49.217 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y^-1 * x * y^-1 * x * z^2, (x * z * y)^2 ] T49.218 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x^-1 * z * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, z^-1 * y * z^-1 * x^-1 * y^-1 * z * y^-1 ] T49.219 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z * y)^2, y * z^-1 * x^-2 * z^2 * x^-1, y^-1 * z * y * x^-1 * y^-1 * z^2 ] T49.220 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y^-1 * x * y^-1 * x * z^2, (x^-1 * z * y)^2 ] T49.221 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^4, z^8, y^-1 * z * y * z^-1 * x^-1 * y^-1 * z^3 ] T49.222 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1 * y)^2, (y * z^-2)^2, z^-1 * x * z^-1 * x^-1 * y * x * z^-1, z^8 ] T49.223 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-1 * z^2, x^-1 * y * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y * z^-1 ] T49.224 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^8, z^2 * y * x^-2 * z^3 * x^-1, z^-1 * x * z^-2 * x^-1 * z * y^-1 * z^-1 * x ] T49.225 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^8, z^-1 * x * z^-1 * x^-2 * z^2 * y * z^-1 ] T49.226 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * y^-1 * x * z * y^-1, z^8 ] T49.227 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, (x * z^-3)^2, z^8, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1 ] T49.228 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^8, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1, z^2 * y * x^-2 * z^3 * x^-1 ] T49.229 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, (x * z^-1)^4, (x * z^-3)^2, z^8 ] T49.230 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * x * y^-1 * x * y^-1 * z^-1, (x * z^-1 * y)^2, z * x^-1 * y * x^-2 * z * x^-1 * z * x^-1 ] T49.231 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * x * y^-1 * x * y^-1 * z^-1, (x * z^-1 * y)^2, z^-1 * x * z^-2 * x^-1 * z * x^-1 * z * y ] T49.232 : Triangle type {4,4,8} Group order 256 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z * y * x^-1 * z^2, x^-1 * y * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 * z^-1 ] T49.233 : Triangle type {4,4,10} Group order 240 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (y^-1 * x)^3, (x * z * y)^2 ] T49.234 : Triangle type {4,4,10} Group order 240 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (x * z * y)^2, (x * z^-2)^2, (y * z^-2)^2, z * x^-1 * y * x^2 * z * y * x^-1 ] T49.235 : Triangle type {4,4,10} Group order 240 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^2, z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y * x * z * y^-1 ] T49.236 : Triangle type {4,4,14} Group order 224 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, (x * z^-1 * y)^2, z^-4 * x * z * y * x * y^-1 * x * y^-1 * z^-3 * x^-1 * z^2 * y^-1 ] T49.237 : Triangle type {4,4,26} Group order 208 Action reflexible [n] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^2 * x^-1 * z^3 * y^-1 * z^4 ] T49.238 : Triangle type {4,4,26} Group order 208 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^16 * y^-1 * x * z * y * z^-7 * x^-1 ] T49.239 : Triangle type {4,4,50} Group order 200 Action reflexible [n] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^2 * y^-1 * z^-1 * x^-1 * z^4 ] T49.240 : Triangle type {4,4,50} Group order 200 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^36 * y^-1 * x^-1 * z^13 ] T49.241 : Triangle type {4,4,98} Group order 196 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^-42 * x * y^-1 * z^-6 ] T49.242 : Triangle type {4,6,12} Group order 192 Action chiral Defining relators: [ x * y * z, x^4, y^6, z^2 * y * x * z * y^-1, (z^-1 * x)^3 ] T49.243 : Triangle type {4,6,12} Group order 192 Action chiral Defining relators: [ x * y * z, x^4, y^6, z^2 * y * x * z * y^-1, y * x^-1 * y * x^-1 * z * y * z^-1, z * y^-1 * z^-1 * x^-1 * z^2 * x^-1 ] T49.244 : Triangle type {4,6,12} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^6, z * y^-1 * z^-1 * x * z * y^-1, y * x^-1 * y * x^-1 * y^-1 * z^-2, z^2 * y * x^-1 * z^2 * x^-1 ] T49.245 : Triangle type {4,6,12} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^6, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * x)^3 ] T49.246 : Triangle type {4,6,12} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^-1 * z^2 * y^-1 ] T49.247 : Triangle type {4,6,12} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * z * y, z^-2 * y * x^-1 * y * z^-1 * y ] T49.248 : Triangle type {4,6,12} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, (y * z^-1 * y)^2, y * z^-2 * x^-1 * z^3 ] T49.249 : Triangle type {4,6,12} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, x^-1 * z * y * x * y^-1 * z^-1, (y * z^-2)^2 ] T49.250 : Triangle type {4,6,12} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^-2 * y * x^-1 * y^-1 * z * y^-1, z^-1 * y * z^-1 * x^-1 * z * y^-2 ] T49.251 : Triangle type {4,6,12} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (z^-1 * x)^3, (y * z^-2)^2, y * z^-1 * y * x^-1 * y * x * z ] T49.252 : Triangle type {4,6,12} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^6, z^2 * y * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^3, y * z^-1 * y * x^-1 * y * x * z, x * z^-2 * x^-1 * z * y * z^-1 ] T49.253 : Triangle type {4,6,12} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^6, (x * z * y)^2, z^2 * y * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^3, x * z^-2 * x^-1 * z * y * z^-1 ] T49.254 : Triangle type {4,6,12} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^6, (x^-1 * z * y)^2, (x * z * y)^2, (z^-1 * x)^3 ] T49.255 : Triangle type {4,6,12} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^2 * x * z^-1, z^-3 * x^-1 * y * z^-2, z * y * x^-1 * z * y^-1 * z^-3 * x * z * y^-1 * z^-1 * x^-1 ] T49.256 : Triangle type {4,6,12} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, y * x * z^-1 * x^-2 * z * x^-1 * z * x^-1 ] T49.257 : Triangle type {4,6,84} Group order 168 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^6, z^-4 * x * z^7 * y * z^-2 ] T49.258 : Triangle type {4,8,40} Group order 160 Action chiral Defining relators: [ x * y * z, x^4, z^2 * x^-1 * y^-1 * z, (x^-1 * z * y)^2 ] T49.259 : Triangle type {4,8,40} Group order 160 Action chiral Defining relators: [ x * y * z, x^4, x * y^-2 * x * z^-2, y^-1 * z^-1 * y * x * z * x^-1, y^8 ] T49.260 : Triangle type {4,8,40} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, y * x^-1 * z^2 * y^-1 * z^-4 * x * z^2 ] T49.261 : Triangle type {4,8,40} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, y * x^-1 * z^2 * y^-1 * z^-2 * x * z^4 ] T49.262 : Triangle type {4,8,40} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, y * x^-1 * z^2 * y^-1 * z^-4 * x^-1 * z^2 ] T49.263 : Triangle type {4,8,40} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y^8, y * x^-1 * z^2 * y^-1 * z^-2 * x^-1 * z^4 ] T49.264 : Triangle type {4,8,40} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^-1 * x^-1 * z^6 * y^-1 * z^-3 * x * z * y * z^-7 ] T49.265 : Triangle type {4,8,40} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^13 * y * z^-1 * x * z^5 ] T49.266 : Triangle type {4,10,20} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^10 ] T49.267 : Triangle type {4,18,36} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1, z^-1 * y^2 * x^-1 * y^-3, z^-1 * y^5 * z^-1 * y^2 ] T49.268 : Triangle type {4,18,36} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-7 * y^6 * z^-1 * y^4 ] T49.269 : Triangle type {4,20,70} Group order 140 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^3 * y * x^-1 * z^3 ] T49.270 : Triangle type {4,24,24} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, y^3 * x^-1 * y^-2 * z, y * z^-1 * y^2 * z^-1 * y^2 * x^-1 * y^3 * z^-1 * y ] T49.271 : Triangle type {4,24,24} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y * z^-1 * y^8 * z^-1 * y ] T49.272 : Triangle type {4,24,24} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x * z ] T49.273 : Triangle type {4,24,24} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, (y * z^-1)^2, y * x^-2 * z * x^-1, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T49.274 : Triangle type {4,28,35} Group order 140 Action chiral Defining relators: [ x * y * z, x^4, x * y^-2 * x * z^-2, y^-1 * z^-1 * y * x * z * x^-1, y^-4 * x^-1 * z * y^-1 * z ] T49.275 : Triangle type {4,28,35} Group order 140 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z * y^-3 * x * z^3 ] T49.276 : Triangle type {4,34,68} Group order 136 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^-15 * z^2 * y^-7 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T49.277 : Triangle type {4,66,132} Group order 132 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^14 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-2 * y^3 ] T49.278 : Triangle type {5,10,10} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, x^-5, (x * y^-2)^2, (y * z^-1 * y)^2 ] T49.279 : Triangle type {5,10,10} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^-5, (x * y^-2)^2, (y * z^-1 * y)^2, z * y^-1 * z^-1 * x * z^2 ] T49.280 : Triangle type {5,10,10} Group order 160 Action reflexible [m,n] Defining relators: [ x * y * z, (y * z^-1)^2, x^-5, x^-1 * y^-1 * x^2 * z * x^-1, (x * z * y)^2 ] T49.281 : Triangle type {5,10,10} Group order 160 Action reflexible [m,n] Defining relators: [ x * y * z, x^-5, x^-1 * y^-1 * x^2 * z * x^-1, y^3 * x^-1 * y^-1 * z ] T49.282 : Triangle type {6,6,6} Group order 192 Action chiral Defining relators: [ x * y * z, x^6, z^-1 * x * y^-1 * x * z^-1 * y, x^-1 * y^-2 * x * z^2, z * y * x^-2 * y * x^2 ] T49.283 : Triangle type {6,6,6} Group order 192 Action chiral Defining relators: [ x * y * z, x^6, z^-1 * x * y^-1 * x * z^-1 * y, x^-1 * y^-2 * x * z^2, y^-1 * z^-1 * x^-2 * y * x * y^-1 ] T49.284 : Triangle type {6,6,6} Group order 192 Action reflexible [n] Defining relators: [ x * y * z, (y * z^-1)^2, x^6, y^2 * x^2 * z^2, y^6 ] T49.285 : Triangle type {6,6,6} Group order 192 Action reflexible [n] Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, z^-1 * x * y^-1 * x * z^-1 * y, x^-1 * z * y^-1 * x * y^-1 * z ] T49.286 : Triangle type {6,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, y^6, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z ] T49.287 : Triangle type {6,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y * z^-1, x^6, y^6, z^-1 * y^2 * x^-1 * y^3, y * z^-1 * x^-1 * y^-1 * x * z * x^-1 * z ] T49.288 : Triangle type {6,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, (y * z^-1)^2, x^6, y^6, (x * z * y)^2, z^6, y * x^-3 * z * x^-2 ] T49.289 : Triangle type {6,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^6, y^-2 * x^2 * y^-1 * z, y * z^-1 * x^2 * z^-2, y^6, (x * z * y)^2 ] T49.290 : Triangle type {6,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, (y * z^-1)^2, x^6, y^6, z^6, y * x^-3 * z * x^-2, z * y * x^-2 * z * y * x ] T49.291 : Triangle type {6,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^6, y^-2 * x^2 * y^-1 * z, y * z^-1 * x^2 * z^-2, y^6, z^6, z * y * x^-2 * z * y * x ] T49.292 : Triangle type {6,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, y^6, (y * z^-1)^4 ] T49.293 : Triangle type {6,6,6} Group order 192 Action reflexible [m,n] Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, x^6, y^6, (y * z^-1)^4 ] T49.294 : Triangle type {6,8,24} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^-1 * y, z^-2 * x^2 * z * y ] T49.295 : Triangle type {6,8,24} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, z^-2 * x^-1 * z * y, x^6, y^2 * x^2 * z^-1 * y ] T49.296 : Triangle type {6,8,24} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * x * z^-1 * x * z^-2 ] T49.297 : Triangle type {6,8,24} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y * x^-3 * z * x^-2, y^8 ] T49.298 : Triangle type {6,8,24} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^2 * y * x^-1 * z^3 ] T49.299 : Triangle type {6,8,24} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-3 * x^-1 * z^2 * y^-1, y^8 ] T49.300 : Triangle type {6,8,24} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^6, y * z^-2 * x^-1 * z^3, y^8 ] T49.301 : Triangle type {6,8,24} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, x^6, z^2 * y * x^-1 * z^3 ] T49.302 : Triangle type {6,12,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * x^-1 * y^-1 * x * z * y, (z^-1 * y)^3 ] T49.303 : Triangle type {6,12,12} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^2 * x^-1 * z^2, x^6, y^-1 * z^3 * y^-8 ] T49.304 : Triangle type {6,12,12} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^6, z^-1 * y^3 * z^-2, x^-1 * z * y * x * y^-1 * z^-1 ] T49.305 : Triangle type {6,12,12} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, y^2 * x^-1 * z^2, x^6, y * x^-3 * z * x^-2, z * y * x^-2 * z * y * x, y * z^-2 * x^-1 * y * z^-2 ] T49.306 : Triangle type {6,12,12} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^6, y^2 * x^2 * z^2, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * y^3 * z^-2, (x * z * y)^2 ] T49.307 : Triangle type {6,12,12} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^-2 * z^2 * y^-1 * z * y^-3 * z^3 ] T49.308 : Triangle type {6,12,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, z * y^2 * x^-1 * z * x^-1, (z^-1 * y)^3 ] T49.309 : Triangle type {6,12,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, x^6, y^2 * x^2 * z * y, (z^-1 * y)^3 ] T49.310 : Triangle type {6,12,12} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * y^-1 * z, x^-1 * y^-2 * x * z^-2, (y * z^-1 * y)^2, (x^-1 * z * y)^2 ] T49.311 : Triangle type {6,12,12} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^6, y * z^-1 * x^2 * y^-1 * z, x^-1 * y^-2 * x * z^-2, (x^-1 * z * y)^2, (z^-1 * y)^3 ] T49.312 : Triangle type {6,12,12} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, x^6, z * y^2 * x^-1 * z * y^-1 * z, z^-1 * y^4 * z^-3 ] T49.313 : Triangle type {6,12,12} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, (z^-1 * y)^3, z^-1 * y^4 * z^-3 ] T49.314 : Triangle type {6,12,12} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, y * z^-1 * x^-1 * y^-1 * z, x^6, y^-1 * z * y^-1 * z^2 * y^-2 * z * y^-3 * z ] T49.315 : Triangle type {6,12,12} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, x^6, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * y)^3, y^3 * x^-1 * y^-2 * z ] T49.316 : Triangle type {6,12,12} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, x^6, y^-1 * z * y * x^-1 * y^-3, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T49.317 : Triangle type {6,12,12} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, y^-1 * z * y^-6 * z * y^-1 * z^2 ] T49.318 : Triangle type {6,12,12} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1)^2, x^6, z * y * z^-1 * x^-1 * y^-3, z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 ] T49.319 : Triangle type {6,12,12} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6, x^-2 * y^-1 * x^2 * z * y^-1 * z ] T49.320 : Triangle type {6,12,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^2, z^-2 * x^-1 * z * y^-1, x^6, y^12 ] T49.321 : Triangle type {6,12,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, x^6, y^3 * x * z * y^3 * x * y^-3 * z^-1 * y ] T49.322 : Triangle type {6,18,63} Group order 126 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^-1 * y^3 * z^-1 * y, z * y^-1 * z^-2 * x * z^3 ] T49.323 : Triangle type {6,18,63} Group order 126 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, (y * z^-2)^2, z^2 * y * z^-1 * x^-1 * z^3 ] T49.324 : Triangle type {6,21,42} Group order 126 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, y^-12 * z * y^-1 * z * y^-1 * z * y^-1 * z^3 ] T49.325 : Triangle type {6,21,42} Group order 126 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y^2 * x^-1 * y^-3, y^-4 * x * y^-1 * z * y^-1 ] T49.326 : Triangle type {6,21,42} Group order 126 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, x^6, z^-1 * y^2 * x^-1 * y^-3, y^-4 * z * y^-1 * z ] T49.327 : Triangle type {6,40,120} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6, z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-2 * x * y^-4 * z^2 ] T49.328 : Triangle type {6,60,60} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^6, z^-2 * y^6 * z^-4 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 ] T49.329 : Triangle type {7,7,7} Group order 168 Action reflexible [m,n] Defining relators: [ x * y * z, (y^-1 * x)^3, (x * z * y^-1)^2, (x * z^-1 * y)^2, (x^-1 * z * y)^2, (z^-1 * x)^3 ] T49.330 : Triangle type {8,8,12} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1 * x)^2, y^-1 * z^-1 * y * x * z * x^-1, z^-3 * x^-1 * z^2 * y^-1 ] T49.331 : Triangle type {8,8,12} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, (x * y^-1)^2, (x * z^-1 * x)^2, y^-1 * z^-1 * y * x * z * x^-1, z^3 * x^-1 * z^2 * y^-1 ] T49.332 : Triangle type {8,15,120} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-4 * z^2 ] T49.333 : Triangle type {8,16,16} Group order 128 Action chiral Defining relators: [ x * y * z, z^2 * x^-1 * y^-1 * z, y * z^-1 * x^2 * z^-1 * y, x^8 ] T49.334 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, z^-1 * y^4 * z^-3 ] T49.335 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * x^-1 * y^-1 * x * z * y, y^-1 * z^-1 * y * x * z * x^-1, z^-2 * y^3 * z^-2 * y ] T49.336 : Triangle type {8,16,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z * y^2 * x^-1 * z * x^-1, y^2 * z^-1 * y^2 * z^-3 ] T49.337 : Triangle type {8,16,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y^-1 * x * z * y, z^-1 * y^4 * z^-3 ] T49.338 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, (y * z^-1)^4 ] T49.339 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * x * y^-1 * x * y^-1 * z^-1, z * y^2 * x^-1 * z * x^-1, z^-1 * y^4 * z^-3 ] T49.340 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * x^-3 * y * z^-1 * y, z * x^-3 * y^-1 * z^2 ] T49.341 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z * x^-1 * y^-1 * x * z * y^-1, x^8 ] T49.342 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, y * x^-2 * z * x^-1, y^-1 * z^7 * y^-1 * z * y^-1 * z * y^-1 * z * y^-2 ] T49.343 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y * z^-1 * y^2 * x^-1 * y * z^-1 * y * z^-1 ] T49.344 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^8, y^14 * z^-2 ] T49.345 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^6 * z^-2 ] T49.346 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y^-1 * x * y^-1 * x * y^-2, z^-1 * x * z^-1 * x * z^-2, x^8 ] T49.347 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, x^8, y * x^-4 * z * x^-3 ] T49.348 : Triangle type {8,16,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, z^-2 * x^2 * z^-2, (x^-1 * z * y)^2 ] T49.349 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, (x^-1 * z * y)^2 ] T49.350 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, z^-2 * x^2 * z^-2, (x^-1 * z * y)^2 ] T49.351 : Triangle type {8,16,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, z^-2 * x^2 * z^-2, x^-1 * z * y * x * y^-1 * z^-1 ] T49.352 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, z^-2 * x^2 * z^-2, x^-1 * z * y * x * y^-1 * z^-1, y * x^-1 * y * x^-1 * y * z^-1 * x^-1 ] T49.353 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, x^-1 * z * y * x * y^-1 * z^-1, x^8 ] T49.354 : Triangle type {8,16,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, y^-2 * x^2 * y^-2, z^-4 * x^-1 * z^2 * y * z^-1 ] T49.355 : Triangle type {8,16,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, (x * z^-2)^2, z^2 * y * z^-1 * x^-1 * z^4 ] T49.356 : Triangle type {8,16,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z * x^-1 * y^-2, (x * y^-2)^2, z^-3 * x^-1 * y^-1 * x * y^-1 * z^-3 ] T49.357 : Triangle type {8,16,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^8, z^-4 * x^-1 * z^2 * y * z^-1 ] T49.358 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, (y * z^-1)^2, y * x^-2 * z * x^-1, (x * z * y)^2 ] T49.359 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z * x^-1 * y^-1 * x * y^-1 * z, (x * z * y)^2 ] T49.360 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-2 * z * x^-1, z * x^-1 * y^-1 * x * y^-1 * z, x^-1 * z * y * x * y^-1 * z^-1 ] T49.361 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, (y * z^-1)^2, y * x^-2 * z * x^-1, x^-1 * z * y * x * y^-1 * z^-1 ] T49.362 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, (x^-1 * z * y)^2 ] T49.363 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (x * y^-2)^2, (x^-1 * z * y)^2 ] T49.364 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (x * y^-2)^2, x^-1 * z * y * x * y^-1 * z^-1, (x * z^-2)^2 ] T49.365 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, x^-1 * z * y * x * y^-1 * z^-1, x^8 ] T49.366 : Triangle type {8,16,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^2 * z^-2, y * x^-1 * y * x^-1 * y * z^-1 * x^-1 ] T49.367 : Triangle type {8,16,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, z * y^2 * x^-1 * z * x^-1 ] T49.368 : Triangle type {8,16,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^2 * z^-2, z * y^2 * x^-1 * z * x^-1 ] T49.369 : Triangle type {8,16,16} Group order 128 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^8 ] T49.370 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^8, z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^5 * z^-4 ] T49.371 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, x^-3 * z * y, z^-1 * x^-2 * y^-1 * x, z^-1 * y^3 * z^-1 * y * z^-1 * y * z^-3 * y^3 * z^-2 ] T49.372 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y * z^-1 * y^3 * z^-3 ] T49.373 : Triangle type {8,16,16} Group order 128 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^8, y^4 * x^-1 * y^3 * z^-1 ] T49.374 : Triangle type {8,24,30} Group order 120 Action chiral Defining relators: [ x * y * z, y * x^-2 * y * z^-1, y^2 * x^2 * z^2, z * x^-3 * z^2 * x^-1 ] T49.375 : Triangle type {8,24,30} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * y * x^-1 * z * y * z^-1, z^3 * x^-1 * z^2 * y^-1 ] T49.376 : Triangle type {8,112,112} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z * y^-1 * z * y^-1 * z * y^-6 * z^2 ] T49.377 : Triangle type {8,112,112} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z * y^-1 * z * y^-1 * z * y^-8 ] T49.378 : Triangle type {8,112,112} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^8, y^-1 * z * y^-1 * z * y^-1 * z * y^-4 * z^4 ] T49.379 : Triangle type {9,9,9} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^3 * y^-2, z^-1 * x^3 * z^-2, y^2 * x^2 * z^2, y * z^-1 * x^-1 * y^-1 * x * z * x^-1 * z ] T49.380 : Triangle type {9,14,18} Group order 126 Action chiral Defining relators: [ x * y * z, y^2 * x^-1 * y * z^-1, z * y * x^2 * z * y^-1, x^9 ] T49.381 : Triangle type {10,12,60} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^10, z * y^-1 * z^4 * y^-2 * x^-1 * z^4 ] T49.382 : Triangle type {10,15,30} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, x^-1 * z * x^-1 * y^-1 * z, x^-1 * z * y * x * y^-1 * z^-1, y^-3 * x^2 * y^-3 ] T49.383 : Triangle type {10,15,30} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, y^2 * x * z^-1, x^-1 * z * y * x * y^-1 * z^-1, x^10 ] T49.384 : Triangle type {10,15,30} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (y * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1, (z^-1 * x)^3 ] T49.385 : Triangle type {10,55,110} Group order 110 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^10, z^3 * y^-4 * x^-1 * z^4 ] T49.386 : Triangle type {10,55,110} Group order 110 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^10, y^-2 * z * y^-5 * z^3 ] T49.387 : Triangle type {10,55,110} Group order 110 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^10, y^-2 * z * y^-7 * z ] T49.388 : Triangle type {12,12,30} Group order 120 Action reflexible [n] Defining relators: [ x * y * z, (x * y^-1)^2, x^-1 * z * y^-1 * x * z^-1 * y, y^-1 * z^-1 * y * x * z * x^-1, y^-1 * z^2 * x^-1 * z^3 ] T49.389 : Triangle type {12,12,30} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, z^3 * y^-1 * z^-2 * x^-1 * z^4 ] T49.390 : Triangle type {12,54,108} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-5 * x^2 * y^-4, z^5 * x^-1 * z^4 ] T49.391 : Triangle type {12,54,108} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-7 * z^2, x^4 * y^-4 * x^2 * z^-4 * x^2 ] T49.392 : Triangle type {14,16,112} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-4 * y * z^-3, x * y^-1 * x * y^-1 * x * y^-4 * x^4 * y^-2 ] T49.393 : Triangle type {14,28,28} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^4 * z^-3, y^5 * z^-1 * y * z^-1 ] T49.394 : Triangle type {14,28,28} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-2 * x^2 * z^-2, y^-4 * x^2 * y^-4 ] T49.395 : Triangle type {14,28,28} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * y * z^-1, x^-3 * y * x^-7 * z * y * x^-1 * z * x^-1 ] T49.396 : Triangle type {15,105,105} Group order 105 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-4 * x * y^-3, z^-1 * x^7 * z^-6 ] T49.397 : Triangle type {15,105,105} Group order 105 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x * y^-4 * x^3 * y^-3, x^-1 * z^4 * x^-3 * z^3 ] T49.398 : Triangle type {16,16,56} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x^3 * z^-1 * x, z^-1 * y^3 * z^-1 * y, z^3 * y * x^-1 * z^3 ] T49.399 : Triangle type {16,16,56} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * y^-1 * z^-1 * x * z^3 ] T49.400 : Triangle type {16,16,56} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-3 * x * z^3, z^3 * x^-2 * z^4 ] T49.401 : Triangle type {18,36,36} Group order 108 Action reflexible [n] Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, x^-1 * z * y^-1 * x * z^-1 * y, z^-1 * y^3 * z^-2, x^-4 * y * x^-1 * z ] T49.402 : Triangle type {18,36,36} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z^-1 * y^2 * z^-1, x^-5 * z * y * x^-8 * y * x^-2 * z * x^-1 ] T49.403 : Triangle type {18,36,36} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^6 * z^-2 * x^6 * y^-2 * x^4 ] T49.404 : Triangle type {18,36,36} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, (z^-1 * y)^3, x^-4 * z * x^-1 * z ] T49.405 : Triangle type {21,35,105} Group order 105 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * x^-1 * z^2, x^-2 * y * x^-3 * y * x^-8 * z^2 * x^-6 ] T49.406 : Triangle type {21,35,105} Group order 105 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, z^7 * y^-1 * x^-6 * z^2 ] T49.407 : Triangle type {21,35,105} Group order 105 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-4 * z^4, y^-2 * x * y^-4 * x^2 * y^-4 ] T49.408 : Triangle type {21,35,105} Group order 105 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x * y^-4 * x^5 * y^-1, z^4 * y^-2 * x^-1 * z^4 ] T49.409 : Triangle type {21,35,105} Group order 105 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^2 * x^-6 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y^2 ] T49.410 : Triangle type {26,52,52} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-8 * x^2 * y^-4 ] T49.411 : Triangle type {26,52,52} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-6 * x * y^-4 * x * y^-3 * z * y^-1 * x * y^-1 ] T49.412 : Triangle type {26,52,52} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, x^8 * z^-4 * x^2 ] T49.413 : Triangle type {26,52,52} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-4 * x^2 * z^-4, x^2 * y^-4 * x^6 ] T49.414 : Triangle type {26,52,52} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6 * z^-4, y^-1 * z * y^-1 * z * y^-6 * z^2 ] T49.415 : Triangle type {26,52,52} Group order 104 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-12 * y * x^-8 * z * x^-5 ] T49.416 : Triangle type {27,27,27} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * y^-1 * x^2 * y^-1 * z^-1, y^2 * x^2 * z^2, z^-1 * y^3 * z^-2 ] T49.417 : Triangle type {27,27,27} Group order 108 Action reflexible [m,n] Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, (y * z^-1)^2, x^-1 * z * y * x^-8 * y * x^-3 ] T49.418 : Triangle type {34,51,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^3 * z^-2 * y^13 ] T49.419 : Triangle type {34,51,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^7 * y^-3 * x^-2 * z^5 ] T49.420 : Triangle type {34,51,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y^2 * x^-4 * y^3 * x^-1 * y^4 * x^-2 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y^3 ] T49.421 : Triangle type {34,51,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^5 * z^-3, y^-8 * x^2 * y^-4 ] T49.422 : Triangle type {34,51,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-5 * z^4, x^3 * y^-3 * x^7 ] T49.423 : Triangle type {34,51,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-7 * z^2, x^-1 * z^3 * x^-8 ] T49.424 : Triangle type {34,51,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x * z^-1 * x * z^-1 * x^10 * y^-1 * x * z^-1 * x * z^-1 ] T49.425 : Triangle type {34,51,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, x^2 * y^-4 * x^4 * y^-2 ] T49.426 : Triangle type {34,51,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x * y^-3 * x^7, z^5 * x^-1 * z^4 ] T49.427 : Triangle type {34,51,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^4 * z^-4, y^-5 * x^2 * y^-4 ] T49.428 : Triangle type {34,51,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, z^5 * y^-3 * x^-1 * z^4 ] T49.429 : Triangle type {34,51,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * x^2 * y^-3, z^7 * x^-5 * z^2 ] T49.430 : Triangle type {34,51,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^12 * x^-2 * z^4 * x^-1 * z * x^-1 * z ] T49.431 : Triangle type {34,51,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^-1 * z, x^-14 * y * x^-3 * y * x^-9 * y * x^-6 ] T49.432 : Triangle type {34,51,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^7 * z^-3, x * y^-1 * x * y^-4 * x^2 * y^-4 ] T49.433 : Triangle type {50,100,100} Group order 100 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^50, y * z^-1 ] T49.434 : Triangle type {50,100,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^4, x * y^-4 * x^7 ] T49.435 : Triangle type {50,100,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^4, x^9 * z^-2 ] T49.436 : Triangle type {50,100,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, z^7 * x^-5 * z^3 ] T49.437 : Triangle type {50,100,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * y^6 * z^-1, x^3 * y^-1 * x^6 * z^-3 * x ] T49.438 : Triangle type {50,100,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, z^4 * y^-4 * z^4 ] T49.439 : Triangle type {50,100,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^18 * x^-1 * y^3 * x^-4 * y^9 ] T49.440 : Triangle type {50,100,100} Group order 100 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * x^4 * y^-3, z^2 * y^-1 * z^3 * x^-6 * z^4 ] T49.441 : Triangle type {99,99,99} Group order 99 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^44 * x^-1 * y^5, x * z^-1 ] T49.442 : Triangle type {99,99,99} Group order 99 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^11 * z^-1 * y^5 ] T49.443 : Triangle type {99,99,99} Group order 99 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * y^-3 * x^-1 * z^3, x^-1 * z * x^-6 * y^4 * x^-4 ] T49.444 : Triangle type {99,99,99} Group order 99 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * y^7, x^8 * z^-5 ] T49.445 : Triangle type {99,99,99} Group order 99 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-4 * y, z^5 * y^-1 * z * y^-1 * z * y^-1 * z^4 * x^-1 * y^-3 * z^2 * y^-1 * z ] Genus 50 T50.1 : Triangle type {2,3,13} Group order 1092 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z * y * x * z^3 * y * x * z * y^-1 * z^3 * y^-1 * z^-1 * x, z^2 * y * z^-1 * x * z^4 * y * x * z * y^-1 * x * z * y^-1 * z^-2 * x ] T50.2 : Triangle type {2,4,6} Group order 1176 Action chiral Defining relators: [ x^2, x * y * z, y^4, z^6, (y * z^-2)^4, x * z * y * z^-1 * y * x * z * y^-2 * z^-1 * y * z^-2 * y ] T50.3 : Triangle type {2,4,102} Group order 408 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-102 ] T50.4 : Triangle type {2,4,200} Group order 400 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-9 * x * y^-1 * z^-90 ] T50.5 : Triangle type {2,6,6} Group order 588 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, z^2 * y^-1 * z * y^-1 * z^3 * y * z^-1 * x * z^2 * y * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T50.6 : Triangle type {2,6,6} Group order 588 Action chiral Defining relators: [ x^2, x * y * z, y^6, z^6, y * z^-1 * x * z * y^2 * x * y^-1 * z^2 ] T50.7 : Triangle type {2,6,6} Group order 588 Action reflexible [n] Defining relators: [ x^2, x * y * z, y^6, z^6, x * y^-1 * z^2 * y^2 * z^-1 * x * y^-1 * z^-1 ] T50.8 : Triangle type {2,6,6} Group order 588 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-1 * y)^2, z^6, x * z * y^-1 * z^2 * y^-1 * z^2 * y * z^-1 * x * z^2 * y * x * y^-1 * z^-1 * x * z * y^-1 * z^-2 ] T50.9 : Triangle type {2,6,24} Group order 336 Action chiral Defining relators: [ x^2, x * y * z, y^6, z^3 * y^-2 * z^-1 * x * z * y^-1, z^3 * y * x * y^-1 * z^-3 * x ] T50.10 : Triangle type {2,6,24} Group order 336 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, z^-1 * x * z * y * x * y^-1 * z^-1 * x * z * y^-1 * z^-1 ] T50.11 : Triangle type {2,6,52} Group order 312 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-30 * x * z^3 * y * x * z * y * x * y^-1 * z^-15 ] T50.12 : Triangle type {2,6,150} Group order 300 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-20 * x * z * y * x * z^16 * y * z^-1 * x * z * y^-1 * z^-4 * x * z^2 * y^-1 * z^-1 ] T50.13 : Triangle type {2,8,8} Group order 392 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, (y * z^-1)^4, z^-1 * y * x * y^-2 * z^-1 * y * z^-2 ] T50.14 : Triangle type {2,8,68} Group order 272 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^-12 * x * z^3 * y * x * z * y * z^-16 ] T50.15 : Triangle type {2,12,22} Group order 264 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^12, z^-3 * x * z * y * x * z * y * x * y * x * y^-1 * z^-1 * x * y^-1 * z^-11 ] T50.16 : Triangle type {2,12,120} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-12, x * z^9 * y * z^-4 * x * z^3 * y^-1 * z^-2 ] T50.17 : Triangle type {2,15,40} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, y * z^-2 * x * y^-1 * z^-3 ] T50.18 : Triangle type {2,18,18} Group order 252 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, z^2 * y * x * y^-1 * z^-2 * x, y^2 * z^-1 * y^2 * z^-1 * y^8 * z^-1 * y^2 * z^-1 ] T50.19 : Triangle type {2,20,24} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, z * y * x * z^5 * y * x * y^-3 * z^-1 * x * y^-1 * z^-1 * x ] T50.20 : Triangle type {2,22,110} Group order 220 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^3 * y * z^-4 * x * z^2, y^-10 * z^2 * y^-7 * z^2 * y^-1 ] T50.21 : Triangle type {2,42,105} Group order 210 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, z^3 * y * z^-4 * x * z^2, y^-9 * z^2 * y^-6 * z^3 * y^-1 ] T50.22 : Triangle type {2,52,104} Group order 208 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^-14 * z^2 * y^-8 * z^2 ] T50.23 : Triangle type {2,101,202} Group order 202 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^96 * z^-4 * y ] T50.24 : Triangle type {2,102,102} Group order 204 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^5 * y^-95 * z ] T50.25 : Triangle type {2,200,200} Group order 200 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^4 * y^-94 * z ] T50.26 : Triangle type {3,3,4} Group order 1176 Action chiral Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x * z, z * y * x * z * y * z^-1 * y * x * z^-1 * x * z * y * x, x * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x^-1 * z * y * x^-1 * z * y * z^-1 ] T50.27 : Triangle type {3,3,4} Group order 1176 Action chiral Defining relators: [ x^3, x * y * z, y^3, z^4, x^-1 * z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x * z, z * y * x * z * y * z^-1 * y * x * z^-1 * x * z * y * x, x^-1 * z * y * x * y^-1 * z^-1 * x^-1 * y * x^-1 * y^-1 * x * z * y^-1 * z^-2 ] T50.28 : Triangle type {3,3,52} Group order 312 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, y^-1 * z^-1 * x * y^-1 * x * z * y^-1 * x, z * y^-1 * z^-2 * x^-1 * z^4 ] T50.29 : Triangle type {3,4,4} Group order 588 Action chiral Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (z^-1 * x^-1 * y^-1)^3, y * z^-1 * x^-1 * y^-2 * x * z * y^-1 * z^2 ] T50.30 : Triangle type {3,4,4} Group order 588 Action chiral Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, (z^-1 * x^-1 * y^-1)^3, z^-1 * y * z^-1 * x * y^-1 * x * y^-1 * z * y^-1 * z^-1 ] T50.31 : Triangle type {3,4,4} Group order 588 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^4, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, z^-1 * x^-1 * z * y * x^-1 * z * y * x * y^-1 ] T50.32 : Triangle type {3,6,6} Group order 294 Action chiral Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, y * z^-1 * y * z^-1 * y^2 * z^-1 * y * z^-1 * y * x * y * z^-1 * y * z^-1 * y * z^-1 ] T50.33 : Triangle type {3,6,6} Group order 294 Action chiral Defining relators: [ x^3, x * y * z, y^6, z^6, y^-2 * z^-1 * x^-1 * y^-1 * z^2 ] T50.34 : Triangle type {3,6,6} Group order 294 Action chiral Defining relators: [ x^3, x * y * z, y^6, z^6, y * z^-1 * y * x^-1 * y^-2 * z^-1, z^-1 * y * z^-1 * x^-1 * z * y^-1 * z^-1 ] T50.35 : Triangle type {3,6,6} Group order 294 Action chiral Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, z * x^-1 * z * y * x * z * y * x * y^-1 * x * z * y * x ] T50.36 : Triangle type {3,6,6} Group order 294 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x^-1 * y^-1 * x * z, y^6, z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * x * y^2 * z^-1 * y * z^-1 * y ] T50.37 : Triangle type {3,6,6} Group order 294 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, y^6, z^-1 * x^-1 * y * x^-1 * y^-1 * z * y * x * z * y^-1 * z * y^-1 * z^-1 * x ] T50.38 : Triangle type {3,21,28} Group order 168 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-4 * x * z * y^-1 * z ] T50.39 : Triangle type {3,24,24} Group order 168 Action chiral Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * y * z^-1 * y^2 * z^-2 * y ] T50.40 : Triangle type {3,24,24} Group order 168 Action chiral Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, y^3 * x^-1 * z * y^-1 * z, y * z^-1 * y^3 * z^-3 ] T50.41 : Triangle type {3,52,52} Group order 156 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^39 * y^-3 * z * y^-7 * z ] T50.42 : Triangle type {3,150,150} Group order 150 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-39 * z * y^-1 * z * y^-6 * z^2 ] T50.43 : Triangle type {4,4,4} Group order 392 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, (x * y^-1)^4, y * x^-1 * z * y * x^-1 * y * z^-1 * x^-1 * z, x^-1 * y^-1 * z * y * x^-1 * z * x^-1 * y^-1 * z ] T50.44 : Triangle type {4,4,4} Group order 392 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, (x * y^-1)^4, y^-1 * z^-1 * y * x^-2 * z * y^-1 * x * z, y^-1 * z * x^-1 * y * x^-1 * z * y^-1 * z * x^-1 ] T50.45 : Triangle type {4,4,51} Group order 204 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^4, y^-1 * z^-1 * y * x * z * x^-1, z^-1 * x * z^-1 * y * z^-2 ] T50.46 : Triangle type {4,4,51} Group order 204 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^37 * y^-1 * x^-1 * z^13 ] T50.47 : Triangle type {4,4,100} Group order 200 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^36 * y^-1 * x * z^13 ] T50.48 : Triangle type {4,12,12} Group order 168 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * y^-2 * z, z^-1 * y^2 * x^-1 * y^3, z^-3 * x^-1 * y * z^-2, z^-1 * x^-1 * z * y * x * z^2 * y ] T50.49 : Triangle type {4,18,72} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, z^-5 * y * z^-2 * y^2 * z^-1 * y * z^-2 * y^4 ] T50.50 : Triangle type {4,28,70} Group order 140 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z * y^-3 * x^-1 * z^3 ] T50.51 : Triangle type {4,68,68} Group order 136 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, z * y^-8 * z^3 * y^-1 * z * y^-1 * z * y^-1 * z * y^-14 * z * y^-1 ] T50.52 : Triangle type {5,26,130} Group order 130 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^2 * z^-1 * y^6 * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-1 * y^4 ] T50.53 : Triangle type {5,125,125} Group order 125 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, y^4 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-1 * y^4 ] T50.54 : Triangle type {5,125,125} Group order 125 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5, z^-1 * y^3 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^7 * z^-1 * y^3 * z^-1 ] T50.55 : Triangle type {6,6,12} Group order 168 Action chiral Defining relators: [ x * y * z, x^6, y * x * y^-1 * x * z^-2, z * y^-2 * x * z * x^-1, x * z * y^-1 * x * y^-1 * z^-1 ] T50.56 : Triangle type {6,6,12} Group order 168 Action chiral Defining relators: [ x * y * z, (x * z^-1)^2, x^6, y^6, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-2 * y * x^-1 * y^-1 * z^-1 * y ] T50.57 : Triangle type {6,6,12} Group order 168 Action chiral Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, x^6, y * x^-1 * y * x^-1 * y * x * z ] T50.58 : Triangle type {6,6,26} Group order 156 Action reflexible [n] Defining relators: [ x * y * z, z^2 * x^-1 * y^-1 * z, x^6, (x * y^-1 * x)^2 ] T50.59 : Triangle type {6,6,26} Group order 156 Action reflexible [n] Defining relators: [ x * y * z, z^-2 * x^-1 * y^-1 * z^-1, x^6, y^6, y * x^-3 * z * x^-2 ] T50.60 : Triangle type {6,6,26} Group order 156 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^6, z^26 ] T50.61 : Triangle type {6,6,75} Group order 150 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, (x * z^-1)^2, z^-12 * x * y^-1 * x * y^-1 * z^-3 * x * z * y * z^-6 ] T50.62 : Triangle type {6,22,22} Group order 132 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^6, y * z^-1 * y^14 * z^-1 * y * z^-1 * y^2 * z^-1 ] T50.63 : Triangle type {6,120,120} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^6, y^-2 * z * y^-1 * z * y^-1 * z * y^-1 * z^4 * y^-2 * x * y^-5 * z ] T50.64 : Triangle type {8,8,34} Group order 136 Action reflexible [n] Defining relators: [ x * y * z, z * x^-2 * y^-1 * x, z * y * x^-1 * y^-2, y^2 * x^-2 * z^3 ] T50.65 : Triangle type {8,8,34} Group order 136 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^11 * y * x^-1 * y * x^-1 * z^4 ] T50.66 : Triangle type {8,24,60} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z * y^-1 * z^-1 * x * z^2, x^8 ] T50.67 : Triangle type {8,24,60} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^2 * y * x^-1 * z^2 ] T50.68 : Triangle type {8,30,40} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * z * y^-1, z^-1 * y^2 * x * z^-2, x^8 ] T50.69 : Triangle type {9,18,18} Group order 126 Action chiral Defining relators: [ x * y * z, y * z^-1 * x^-1 * y^-1 * z^-1, y^2 * x^2 * z^2, x^-9 ] T50.70 : Triangle type {9,18,18} Group order 126 Action chiral Defining relators: [ x * y * z, y^2 * x^2 * z^2, z^-1 * x * y^-1 * x * z * y^-1, z^-1 * y^3 * z^-2 ] T50.71 : Triangle type {9,18,18} Group order 126 Action chiral Defining relators: [ x * y * z, (x * z^-1)^2, x * y^-2 * x * z * y^-1, z^-2 * y^2 * z^-1 * y ] T50.72 : Triangle type {9,18,18} Group order 126 Action chiral Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, z^-2 * y^2 * z^-1 * y, x^-9 ] T50.73 : Triangle type {10,20,30} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z * y * z^-1 * x^-1 * z^3 ] T50.74 : Triangle type {10,20,30} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, z^-3 * x^-1 * y * z^-2 ] T50.75 : Triangle type {10,20,30} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^2 * z^-3 ] T50.76 : Triangle type {10,24,24} Group order 120 Action reflexible [n] Defining relators: [ x * y * z, x^-3 * y^-1 * z^-1, z * x^-2 * y * x^-1, y * z^-3 * y^2 * z^-1 * y^2 * z^-1 * y^2 ] T50.77 : Triangle type {10,24,24} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^10, z * y^-3 * z * y^-3 * x * z * y^-1 * z * y^-1 ] T50.78 : Triangle type {11,12,12} Group order 132 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, y^10 * z^-2, x^2 * z^-1 * y * z^-1 * y * z^-1 * x^-2 * y^-1 * z * y^-1 * z * y^-1 * x^2 ] T50.79 : Triangle type {11,110,110} Group order 110 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-6 * x^2 * y^-4, z^4 * y^-2 * x^-1 * z^4 ] T50.80 : Triangle type {11,110,110} Group order 110 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-5 * z^3, x^11 ] T50.81 : Triangle type {11,110,110} Group order 110 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * y^-4 * x^-1 * z^4, x^11 ] T50.82 : Triangle type {11,110,110} Group order 110 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * y^-3 * x^-1 * z^4, y^-2 * x * y^-4 * x^2 * y^-4 ] T50.83 : Triangle type {11,110,110} Group order 110 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^4, x^11 ] T50.84 : Triangle type {12,12,60} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^3 * x^-1 * z^2 * y^-1, y * x * z^2 * y^-1 * z^-2 * x * z^4 ] T50.85 : Triangle type {12,20,20} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, z * y^-1 * z * y^-1 * z * y^-1 * x * z * y^-1 * z * y^-1 ] T50.86 : Triangle type {14,28,56} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z * y * x^-1 * z^2, y^5 * z^-1 * y * z^-1 ] T50.87 : Triangle type {14,28,56} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, y * x^-1 * y * x^-1 * y * x^-1 * z ] T50.88 : Triangle type {14,28,56} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * z * y^-1, z^-2 * x * z^-1 * x * z^-3 ] T50.89 : Triangle type {14,28,56} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^-2 * y^2 * z^-2 ] T50.90 : Triangle type {14,28,56} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^-5 * z^3 * y ] T50.91 : Triangle type {15,15,20} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, z * y * x^-1 * z * x^-1, y * z^-1 * x^-1 * y * z^-1 ] T50.92 : Triangle type {15,15,20} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-2 * x^-1 * z * y^-1, y * x * y^-1 * x * y^-1 * z, x^-1 * z * x^-2 * y^-1 * z * x^-1 ] T50.93 : Triangle type {18,54,54} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^4 * y^-4, z^5 * y^-3 * x^-1 * z^4 ] T50.94 : Triangle type {18,54,54} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^4 * z^-2, x^3 * z^-1 * x^10 * y^-1 * x^4 ] T50.95 : Triangle type {18,54,54} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x^2 * z^-3, y^-8 * x^2 * y^-4 ] T50.96 : Triangle type {21,105,105} Group order 105 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^5 * z^-4, y^-6 * x * y^-4 ] T50.97 : Triangle type {21,105,105} Group order 105 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * y^-2 * x^-1 * z^2, x^-4 * y * x^-9 * z * x^-1 * y * x^-1 * y * x^-1 * y^3 ] T50.98 : Triangle type {21,105,105} Group order 105 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-4 * z^4, x * y^-1 * x * y^-4 * x^6 ] T50.99 : Triangle type {22,22,55} Group order 110 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, x^-3 * y^-1 * z, x * y^-1 * x * y^-1 * x * z^2 * y^-1 ] T50.100 : Triangle type {22,22,55} Group order 110 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, z^-1 * x^-1 * y * x^-1 * z * y * z^-1 ] T50.101 : Triangle type {22,22,55} Group order 110 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^2 * y^-1 * x * z^2 ] T50.102 : Triangle type {22,22,55} Group order 110 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z * y^-1 * z^-1 * x * z^2, x^5 * z^-1 * x * z^-1 ] T50.103 : Triangle type {22,22,55} Group order 110 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, y^-1 * z^-2 * x * z^2, y * z^-1 * y * z^-3 * x^3 * z^-1 * y * z^-3 ] T50.104 : Triangle type {26,104,104} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^5 * y^-4 * x^-3 * z^3 ] T50.105 : Triangle type {26,104,104} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x * y^-4 * x^6, y^-1 * z * y^-1 * z * y^-5 * z^3 ] T50.106 : Triangle type {26,104,104} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * z^-1, x^-1 * z^6 * x^-2 * z * x^-1 * z * x^-1 * z * x^-10 * z * x^-1 * z * x^-1 * z ] T50.107 : Triangle type {26,104,104} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-1 * y^8 * x^-1 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T50.108 : Triangle type {26,104,104} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^8 * y^-2 * z^6 ] T50.109 : Triangle type {26,104,104} Group order 104 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^3 * y^-1 * x * y^-4 * x^5 * z^-1 * x ] T50.110 : Triangle type {51,102,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^2 * z^-1, y^14 * x^-2 * y^4 * x^-1 * y^6 ] T50.111 : Triangle type {51,102,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-3 * z^4, x * y^-1 * x * y^-4 * x^3 * y^-3 ] T50.112 : Triangle type {51,102,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-7 * z, x^-1 * z^4 * x^-6 ] T50.113 : Triangle type {51,102,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-1 * y^2 * x^-1 * y^5 * x^-1 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y * x^-2 ] T50.114 : Triangle type {51,102,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * y^2, z^3 * y^-1 * z * y^-1 * z * y^-4 * x^-1 * z^5 ] T50.115 : Triangle type {51,102,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-4 * y * z^-3, y^-1 * x * y^-1 * x * y^-4 * x^2 * y^-4 ] T50.116 : Triangle type {51,102,102} Group order 102 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8 * y^-2, y^-1 * z * y^-1 * z * y^-7 * z ] T50.117 : Triangle type {51,102,102} Group order 102 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-51, y * z^-1 ] T50.118 : Triangle type {52,52,52} Group order 104 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, z^-1 * y * x^-1 * y^-2, y * x^-1 * y * x^-1 * y * x^-1 * y^2 * x^-1 * y * x^-1 * y * x^-1 * y^3 ] T50.119 : Triangle type {52,52,52} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2, y^-1 * x * y^-1 * x^3 * y^-4 ] T50.120 : Triangle type {52,52,52} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x^6 * y^-2, z^-3 * x^2 * z^-3 ] T50.121 : Triangle type {101,101,101} Group order 101 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^-45 * x * y^-5, x * z^-1 ] T50.122 : Triangle type {101,101,101} Group order 101 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^17 * x^-1 * y^3 * x^-3 * y^11 ] T50.123 : Triangle type {101,101,101} Group order 101 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, y * x^-5 * y^3 * x^-1 * y^4 * x^-2 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y^3 ] T50.124 : Triangle type {101,101,101} Group order 101 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, y^8 * x^-1 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y^3 ] T50.125 : Triangle type {101,101,101} Group order 101 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, y^2 * x^-6 * y^4 * x^-1 * y^5 ] T50.126 : Triangle type {101,101,101} Group order 101 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, y^-2 * x * y^-1 * x * y^-4 * x^2 * y^-4 ] T50.127 : Triangle type {101,101,101} Group order 101 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, y^-2 * x * y^-4 * x^2 * y^-4 ] T50.128 : Triangle type {101,101,101} Group order 101 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x^2 * y^-4 * x^5 * y^-1 ] T50.129 : Triangle type {101,101,101} Group order 101 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x * y^-2 * x^8, y^-2 * z * y^-8 ] T50.130 : Triangle type {101,101,101} Group order 101 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7 * y^2, y^-2 * z * y^-1 * z * y^-5 * z^3 ] T50.131 : Triangle type {101,101,101} Group order 101 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x^3 * y^-3, x * z^-1 * x^7 * z^-5 * x * z^-1 ] T50.132 : Triangle type {101,101,101} Group order 101 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * z * y^-6 * z^2, x^-1 * z^4 * x^-5 * y * x^-1 ] T50.133 : Triangle type {101,101,101} Group order 101 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-4 * y^3, z^7 * y^-6 * z^4 ] T50.134 : Triangle type {101,101,101} Group order 101 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * z * y^-4 * z^4, x * y^-1 * x * y^-4 * x^4 * y^-2 ] T50.135 : Triangle type {101,101,101} Group order 101 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * z^4, x^2 * y^-1 * x * y^-4 * x^2 * y^-4 ] T50.136 : Triangle type {101,101,101} Group order 101 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-3 * z^2, x^-6 * y * x^-7 * y^2 * x^-6 ] T50.137 : Triangle type {101,101,101} Group order 101 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-5 * z^2, x^4 * y^-2 * x^4 * z^-4 * x^3 ] Genus 51 T51.1 : Triangle type {2,3,12} Group order 1200 Action chiral Defining relators: [ x^2, y^3, x * y * z, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^12, z^3 * y * x * z^4 * y * x * z * y^2 * z^-3 * x * z^2 ] T51.2 : Triangle type {2,3,12} Group order 1200 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z * y * z^-3 * x * y^-1 * z^-4 * x, z^-1 * x * z^3 * y * z^-1 * x * z * y * x * z * y * x * z * y * x * z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-1 ] T51.3 : Triangle type {2,3,30} Group order 750 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, x * z * y * x * z * y * x * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1, x * z^6 * y * x * z * x * y^-1 * z^-4 ] T51.4 : Triangle type {2,4,8} Group order 800 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^4, z^8, z * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x, z^2 * y * z^-3 * y * z^-1 * x * z * y^-1 * z^2 ] T51.5 : Triangle type {2,4,8} Group order 800 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y * x * z * y * x * z * y * x * z * y * z^-1 * y^2 * z^-1 * x * y^-1 * z^-1 * y * z^-1 * y * z^-1 * x ] T51.6 : Triangle type {2,4,8} Group order 800 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y * x * z * y * x * z * y * x * z * y * z^-1 * y^2 * z^-1 * x * y^-1 * z * y^-1 * z^-2 * y * x ] T51.7 : Triangle type {2,4,8} Group order 800 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z * y^-1 * z * y * x * z * y * x * z * y^-1 * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * y * z^-1 * x ] T51.8 : Triangle type {2,4,8} Group order 800 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^8, z^-1 * x * z * y * x * z * y * x * z * y^-1 * z * y^-1 * z * y^-1 * z^-1 * x * y^-1 * z^-1 * x * y^-1 * z^-2 * y * z^-1 * y ] T51.9 : Triangle type {2,4,12} Group order 600 Action chiral Defining relators: [ x^2, x * y * z, y^4, x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1, z^-3 * y * x * y^-1 * z^3 * y^-1 * z^-1 ] T51.10 : Triangle type {2,4,12} Group order 600 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^-2 * x * z^3 * y^-1 * z^-6, z^2 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * x * y^-1 * z^-1 * x ] T51.11 : Triangle type {2,4,12} Group order 600 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z^-2 * x * z^3 * y^-1 * z^-6, z * y^-1 * z * y * z^-1 * y * x * z * y * x * y^-1 * z^-1 * x * y^-1 * z^-1 * x ] T51.12 : Triangle type {2,4,20} Group order 500 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z^3 * y^-1 * z^-4, (z^-1 * y)^5 ] T51.13 : Triangle type {2,4,24} Group order 480 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * z^-1 * y * x * y^-1 * z^-1 * x * y^-1 * z, z^-6 * x * z^5 * y * z^-2 * x * y^-1 * z^-9 ] T51.14 : Triangle type {2,4,24} Group order 480 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y^-1 * z * y^-1 * z * y^-2 * z^-1 * x * y^-1 * z^-1 * y * z^-1 * x, z^5 * y * x * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x ] T51.15 : Triangle type {2,4,24} Group order 480 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (z^-1 * y)^3, z^-1 * x * z * y * x * z^2 * y^-1 * z^-1 * x * y^-1 * z^-2 ] T51.16 : Triangle type {2,4,24} Group order 480 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-1 * z * y^-2 * z^-2 * y * z^-1 * y, z^-3 * x * z * y^-1 * z^-4 * y ] T51.17 : Triangle type {2,4,44} Group order 440 Action chiral Defining relators: [ x^2, x * y * z, y^4, (y * z^-3)^2, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z^-1 * x * z^2 * y * x * z^8 * y * z^-3 * x * z^4 * y^-1 * z^-1 ] T51.18 : Triangle type {2,4,54} Group order 432 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-2)^2, z^-38 * x * z^8 * y^-1 * z^-7 ] T51.19 : Triangle type {2,4,104} Group order 416 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-104 ] T51.20 : Triangle type {2,4,104} Group order 416 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, x * z * y^-2 * z^-2 * y, z^-37 * x * z^5 * y * z^-1 * x * y^-1 * z^-7 ] T51.21 : Triangle type {2,4,204} Group order 408 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-10 * x * y^-1 * z^-91 ] T51.22 : Triangle type {2,6,8} Group order 480 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, x * z * y^-1 * z * y^-2 * z * y^-1 * z * y^-1 * z^-1 ] T51.23 : Triangle type {2,6,8} Group order 480 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, (y * z^-3)^2, z^8, x * z * y^-1 * z * y^-2 * z * y^-1 * z^-2 * y ] T51.24 : Triangle type {2,6,28} Group order 336 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, y * x * z * y^2 * x * y^-1 * z^-1, (y * z^-1)^4, z^-2 * x * z^3 * y * z^-1 * x * z^2 * y^-1 * z^-4 ] T51.25 : Triangle type {2,8,8} Group order 400 Action reflexible [n] Defining relators: [ x^2, x * y * z, y^8, (y * z^-2 * y)^2, (y * z^-1)^4, z^3 * y^3 * x * y^-1 * z^-1 * x ] T51.26 : Triangle type {2,8,8} Group order 400 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z^-1 * x * z * y^-1 * z * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y * z^-1 * y ] T51.27 : Triangle type {2,8,8} Group order 400 Action chiral Defining relators: [ x^2, x * y * z, z * y * x * y^-1 * z^-1 * x, y^8, (y * z^-1)^4, z^8, y * z^-1 * x * y^-3 * z^3 * y^-1 * z^-1 ] T51.28 : Triangle type {2,8,8} Group order 400 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z^-1 * y * z^-1 * y * z^-1 * y * x * y^-1 * z * y^-1 * z * y^-1 * z^-2 * y ] T51.29 : Triangle type {2,8,8} Group order 400 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z^-1 * x * z * y * z^-1 * y * z^-1 * y * x * y^-1 * z^2 * y^-2 * z^-1 * y * z^-1 * y ] T51.30 : Triangle type {2,8,8} Group order 400 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^8, z^-1 * x * z * y * z^-1 * y * z^-1 * y * x * y^-1 * z^-1 * y * z^-1 * x * y^-1 * z^-1 * y ] T51.31 : Triangle type {2,8,16} Group order 320 Action chiral Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, z * y * x * z * y^2 * z^-1 * x * z * y^-1, z * y * z^-2 * x * y^-1 * z^-3 * x ] T51.32 : Triangle type {2,8,16} Group order 320 Action chiral Defining relators: [ x^2, x * y * z, y^8, (y * z^-1 * y^2)^2, (y * z^-3)^2, y * z^-1 * x * z * y^2 * z^-1 * x * y^-1 * z^-1, z * y * z^-2 * x * y^-1 * z^-3 * x ] T51.33 : Triangle type {2,8,36} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-2)^2, y^8, (y * z^-1 * y^2)^2, z^7 * y * x * z^2 * y * z^-6 * x * z ] T51.34 : Triangle type {2,8,36} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, z^-1 * x * y^-2 * z^-2 * y, z^-4 * x * z^7 * y * z^-1 * x * y^-1 * z^-4 ] T51.35 : Triangle type {2,8,36} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^8, z^17 * y * x * z^3 * y * x * z * y^-1 * z^-5 * x * y^-1 * z^-1 * x * z^5 ] T51.36 : Triangle type {2,8,36} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^16 * y * z^-2 * x * z^6 * y * x * y^-1 * z^-8 * x * z ] T51.37 : Triangle type {2,8,136} Group order 272 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-8 * x * z^7 * y * z^-1 * x * z^4 * y * z^-2 * x * z^2 * y^-1 * z^-2 * x * z^2 * y^-1 * z^-2 ] T51.38 : Triangle type {2,8,136} Group order 272 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^8, z^-7 * x * z^8 * y * z^-1 * x * z^4 * y * z^-9 * x * z^2 * y^-1 ] T51.39 : Triangle type {2,12,12} Group order 300 Action chiral Defining relators: [ x^2, x * y * z, (z^-1 * y)^3, y * x * y^-3 * z^4 ] T51.40 : Triangle type {2,12,12} Group order 300 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y^12, x * z * y^2 * z^-1 * x * y^-1 * z^-2 * y * z^-1 * y ] T51.41 : Triangle type {2,12,12} Group order 300 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, y * z^-1 * y * x * y^-2 * z^-1 * y * z^-1 * y * z^-1 ] T51.42 : Triangle type {2,14,119} Group order 238 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-3 * z^3 * y^-5 * z^3, z^-1 * x * z^5 * y * z^-10 ] T51.43 : Triangle type {2,15,60} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-3 * z^-1 * y^2, x * z^2 * y^-1 * z^-3, y^11 * z^-1 * y^2 * z^-1 ] T51.44 : Triangle type {2,20,30} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z^2 * y^-1 * z^-3, x * y^-4 * z^-1 * y^3, x * y^-1 * z * y^-2 * z^-1 * y * z^-1 * y, z^-1 * y^5 * z^-2 * y * z^-1 ] T51.45 : Triangle type {2,24,24} Group order 240 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, x * z * y^-2 * z^-1 * y * z^-1, y^-6 * z * y^-3 * z^2 * y^-5 * z * y^-1 * z * y^-2 * z * y^-1 ] T51.46 : Triangle type {2,24,24} Group order 240 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z * y * z^-1 * y * x * y^-1 * z * y^-1 * z^-1 * x, z^-1 * y^6 * z^-1 * y * z^-1 * y * z^-1 ] T51.47 : Triangle type {2,28,56} Group order 224 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^3 * y^-1 * z^-4, y^-15 * z^4 * y^-5 * z^4 ] T51.48 : Triangle type {2,28,56} Group order 224 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-1 * z^-2, x * y^-4 * z^-1 * y^3, y^-1 * z^10 * y^-1 * z^4 * y^-10 * z^2 ] T51.49 : Triangle type {2,44,44} Group order 220 Action chiral Defining relators: [ x^2, x * y * z, x * y^-3 * z^-3, z^-1 * y * x * y^-1 * z * y^-1 * z^-1, z * y^-2 * z * y^-1 * z^3 * y^-8 * z * y^-1 * z * y^-1 * z^2 ] T51.50 : Triangle type {2,54,54} Group order 216 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-2, y^2 * z^-40 * y^11 * z^-1 ] T51.51 : Triangle type {2,70,105} Group order 210 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y^-1 * z^-3, y * z^-6 * y^11 * z^-2 * y^14 * z^-1 ] T51.52 : Triangle type {2,103,206} Group order 206 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^97 * z^-6 ] T51.53 : Triangle type {2,104,104} Group order 208 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, y * z^-24 * y^11 * z^-2 * y^14 ] T51.54 : Triangle type {2,104,104} Group order 208 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^6 * y^-97 ] T51.55 : Triangle type {2,204,204} Group order 204 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^5 * y^-96 ] T51.56 : Triangle type {3,3,6} Group order 600 Action chiral Defining relators: [ x^3, x * y * z, y^3, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y^-1 * z^-2 * x^-1 * y * x * z * y^-1 * z^-2 * x ] T51.57 : Triangle type {3,3,6} Group order 600 Action chiral Defining relators: [ x^3, x * y * z, y^3, z^6, x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * z, y^-1 * z^-1 * x * z^2 * x^-1 * z^2 * y * x^-1 * z ] T51.58 : Triangle type {3,3,6} Group order 600 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^6, z^2 * y * x^-1 * z * y^-1 * x, z^-1 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y * x * z * y^-1 * z^-1 * x^-1 * y * x^-1 * y * x ] T51.59 : Triangle type {3,3,15} Group order 375 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3, z^-3 * x^-1 * z^2 * y^-1, z * x^-1 * z * x^-1 * y^-1 * x * y^-1 * x * y^-1 * x ] T51.60 : Triangle type {3,3,28} Group order 336 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-6 * x^2 * z^3 * y^-1 * z^-2 ] T51.61 : Triangle type {3,3,103} Group order 309 Action reflexible [n] Defining relators: [ x^3, x * y * z, y^3, z * x^-1 * y^-1 * x * y^-1 * x, z^-2 * x * z^2 * y * z^-1 * x * y * z^-4 ] T51.62 : Triangle type {3,4,12} Group order 300 Action chiral Defining relators: [ x^3, x * y * z, y^4, x^-1 * z * y^-1 * x * z^2, y * x^-1 * y^-2 * x * z * y * z^-1 ] T51.63 : Triangle type {3,4,12} Group order 300 Action reflexible [m] Defining relators: [ x^3, x * y * z, y^4, z^-1 * y * x^-1 * y^2, z^2 * y * x^-1 * z^3, x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * z^-1 * x^-1 * y^-1 * x * z * y * x * z * y * z^-1 ] T51.64 : Triangle type {3,8,8} Group order 240 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3 * x^-1 * z^3, z^-1 * y * x^-1 * y^-1 * x * z * y^2 ] T51.65 : Triangle type {3,8,8} Group order 240 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^3 * x^-1 * z^3, z^-1 * y * x^-1 * y^-1 * x * z * y^-2 ] T51.66 : Triangle type {3,21,42} Group order 168 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * x^-1 * y * x^-1 * y^-1 * x * y^-1, z^-1 * y^2 * x^-1 * y^-3, y^-1 * z * y^-2 * x * z^2 * y^-1 ] T51.67 : Triangle type {3,28,28} Group order 168 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * z^-1 * x^-1 * y^-1 * z, (x^-1 * z * y)^2, y^-1 * z * y^-1 * z * y^-1 * z^3 * y^-4 * z^2 ] T51.68 : Triangle type {3,52,156} Group order 156 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-41 * z * y^-1 * z * y^-7 * z ] T51.69 : Triangle type {3,153,153} Group order 153 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-40 * z * y^-1 * z * y^-8 ] T51.70 : Triangle type {4,4,4} Group order 400 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, z^-1 * y * x^-1 * y^2, y^-1 * x * z^-1 * x^-2 * z * x^-1 * z * x^-1 * y * x^2 * z * x^-1 * z * y^-1 * x ] T51.71 : Triangle type {4,4,4} Group order 400 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, (x^-1 * z * y)^2, z * x^-1 * y * x^2 * y^-1 * z^-1 * x^-1, (y * z^-1)^4 ] T51.72 : Triangle type {4,4,4} Group order 400 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z^-1 * y)^2, (x * y^-1)^4, y * z^-1 * x * z^-1 * x * z * y * z^-1 ] T51.73 : Triangle type {4,4,4} Group order 400 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, (x * y^-1)^4, x * z^-2 * y * x^-1 * z * y * z^-1 ] T51.74 : Triangle type {4,4,4} Group order 400 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * x^-1 * y^-1 * z^-2 * y * z^-1 * y * x^-1 * y^-2 * x * y^-1 * z * y^2 * z^-1 ] T51.75 : Triangle type {4,4,4} Group order 400 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, y * x^-2 * z * x^-1, y * x^-1 * z * y^-1 * z * y * z^-1 * y * x^-1 * y^-2 * x * y^-1 * z^-1 * x * z * y^-1 * z ] T51.76 : Triangle type {4,4,4} Group order 400 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, z^4, (x * z * y)^2, z * x^-1 * y * x^2 * y^-1 * z^-1 * x ] T51.77 : Triangle type {4,4,4} Group order 400 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^4, z^-2 * x^-1 * z * y^-1, y * x * z * y * x^-1 * y * x^-1 * y * x^-1 * y * x^-2 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T51.78 : Triangle type {4,4,6} Group order 300 Action chiral Defining relators: [ x * y * z, x^4, y^4, (y^-1 * x)^3, z^6, z^-1 * y * z^-1 * x^-1 * y * z^-1 * x ] T51.79 : Triangle type {4,4,6} Group order 300 Action chiral Defining relators: [ x * y * z, x^4, y^4, (y^-1 * x)^3, z^6, z^-1 * y * x^-2 * z * y^-1 * z^-1 ] T51.80 : Triangle type {4,4,6} Group order 300 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, x * z * y * x * z^-1 * y * x^-2 * y^2 * x * y^-1 ] T51.81 : Triangle type {4,4,6} Group order 300 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z^6, x * z * x^-1 * y * x^-2 * y^-1 * x * y^-1 * x * y^-1 ] T51.82 : Triangle type {4,4,12} Group order 240 Action chiral Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * x^-1 * z * y * x * z * y^-1 * z^-1 ] T51.83 : Triangle type {4,4,12} Group order 240 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, x^-1 * y * x^-1 * y * x^-1 * y^-1 * z^-3 ] T51.84 : Triangle type {4,4,12} Group order 240 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, z * x^-1 * y * x^-1 * y^2 * x, z^5 * y * x * y^-1 * x * z^4 * y^-1 * x ] T51.85 : Triangle type {4,4,12} Group order 240 Action chiral Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * x^-1 * z * y * x * z^2 * y ] T51.86 : Triangle type {4,4,22} Group order 220 Action chiral Defining relators: [ x * y * z, x^4, y^4, z^2 * x^-1 * z * y^-1, x^-1 * y * x^-2 * y^-1 * z^-1 * y, x^-1 * z^4 * y^-1 * z^-1 * x * z * y^-1 * z^-3 ] T51.87 : Triangle type {4,4,27} Group order 216 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, (x * z^-1)^2, (y * z^-1)^2, z^19 * y^-1 * x * z * y * z^-4 * x * z ] T51.88 : Triangle type {4,4,52} Group order 208 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z^-3 * x^-1 * y^-1 * z^-2 ] T51.89 : Triangle type {4,4,52} Group order 208 Action reflexible [n] Defining relators: [ x * y * z, x^4, y^4, (x * z * y^-1)^2, y^-1 * z^-1 * y * x * z * x^-1, z * y^-1 * z * x^-1 * z^3 ] T51.90 : Triangle type {4,4,52} Group order 208 Action reflexible [m] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^16 * y * x * z * y * z^-7 * x^-1 ] T51.91 : Triangle type {4,4,52} Group order 208 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, z^16 * y * x * z * y * z^-7 * x ] T51.92 : Triangle type {4,4,52} Group order 208 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^38 * y^-1 * x^-1 * z^13 ] T51.93 : Triangle type {4,4,102} Group order 204 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^37 * y^-1 * x * z^13 ] T51.94 : Triangle type {4,6,6} Group order 240 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^6, x^-1 * z * y^2 * x * y^-1 * z^-2 ] T51.95 : Triangle type {4,6,6} Group order 240 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^6, z^6, x^-1 * z * y^2 * x * z * y * z^-1 ] T51.96 : Triangle type {4,6,6} Group order 240 Action reflexible [m] Defining relators: [ x * y * z, x^4, (x * y^-2)^2, y^6, (x * z * y)^2, z^6 ] T51.97 : Triangle type {4,6,6} Group order 240 Action reflexible [m] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^6, z^6, z^-3 * x^-1 * z^2 * y^-1 ] T51.98 : Triangle type {4,6,16} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^6, z^3 * y * x^-1 * z^6 * y * x^-1 * z^5 ] T51.99 : Triangle type {4,6,16} Group order 192 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^2, y^6, y * z^-1 * x^-2 * z^2 * x^-1, z * y^-1 * z^-2 * x^-1 * z^4 ] T51.100 : Triangle type {4,8,8} Group order 200 Action chiral Defining relators: [ x * y * z, x^4, (y * z^-1)^2, (x^-1 * z * y)^2, z * x^-1 * y * x^2 * z * y * x, y^3 * x^2 * y^-2 * z^-1 ] T51.101 : Triangle type {4,8,8} Group order 200 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y * x^-1 * y^-1 * z * y^-1 * z * y^-1 * z^-1 * x^-1 * z * y^-1 * z ] T51.102 : Triangle type {4,8,8} Group order 200 Action chiral Defining relators: [ x * y * z, x^4, (x * y^-2)^2, (x^-1 * z * y)^2, (x * z^-2)^2, y^-1 * z^-1 * y * x^-1 * y^-1 * z * y^-1 ] T51.103 : Triangle type {4,8,8} Group order 200 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y * x^-1 * y^-1 * z * y^-1 * z * y^-1 * z^-1 * x * z * y^-1 * z ] T51.104 : Triangle type {4,8,8} Group order 200 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z^-1 * y * z^-1 * y * z^-1 * x * z * y^-1 * z^2 * y ] T51.105 : Triangle type {4,8,8} Group order 200 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, z^-1 * y * z^-1 * y * z^-1 * x * z * y^-1 * z * y^-1 * z^-1 ] T51.106 : Triangle type {4,10,40} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * y * z^-1 * y^3 * z^-1 * y * z^-1 * y ] T51.107 : Triangle type {4,10,40} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * z^2 * y^-1 * x * z * y * z^-2, y^10 ] T51.108 : Triangle type {4,12,14} Group order 168 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^3 * x^-1 * y^-1 * z * y, z^-4 * x^-1 * z^2 * y^-1 * z^-1 * x^-1 * y * x * y^-1 * z^-4 ] T51.109 : Triangle type {4,12,39} Group order 156 Action chiral Defining relators: [ x * y * z, x^4, y^-1 * z^-1 * y * x * z * x^-1, (y * z^-1 * y)^2, z^-1 * y * x^-2 * z * y * z^-1 ] T51.110 : Triangle type {4,12,39} Group order 156 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^7 * y * z^-1 * x * z^4 ] T51.111 : Triangle type {4,16,16} Group order 160 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, y * z^-1 * y * x^-1 * y^-1 * z^2, (y * z^-1 * y^2)^2 ] T51.112 : Triangle type {4,16,16} Group order 160 Action chiral Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^3 * x^-1 * z^3, z^-2 * y * x^-1 * y^-1 * z * y^-1, (y * z^-1 * y^2)^2 ] T51.113 : Triangle type {4,35,140} Group order 140 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^-9 * z * y^-1 * z^4 * y^-8 * z^3 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T51.114 : Triangle type {4,36,36} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * z^2, z^4 * y^-1 * z^3 * y^-1 * z^2 * y^-3 * z^2 * y^-2 ] T51.115 : Triangle type {4,36,36} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * z * y^-1, y^-5 * z^3 * y^-10 ] T51.116 : Triangle type {4,36,36} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-6 * y^6 * z^-1 * y^3 * z^-1 ] T51.117 : Triangle type {4,36,36} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, z * y^-8 * z * y^-3 * z * y^-1 * z * y^-7 * z^4 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T51.118 : Triangle type {4,36,36} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, y * x^-1 * z, x^4, y * z^-1 * y^21 * z^-1 * y^5 * z^-1 * y * z^-5 ] T51.119 : Triangle type {4,136,136} Group order 136 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, z * y^-14 * z^2 * y^-7 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z^2 ] T51.120 : Triangle type {4,136,136} Group order 136 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^4, y^-15 * z^2 * y^-7 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T51.121 : Triangle type {6,6,14} Group order 168 Action reflexible [n] Defining relators: [ x * y * z, z * x^-2 * y^-2, x^6, z * x^-1 * y^-1 * x * z * x^-1, y^-1 * z^-2 * x^-1 * z^3 ] T51.122 : Triangle type {6,6,14} Group order 168 Action reflexible [n] Defining relators: [ x * y * z, z * y * x^-1 * y^-1 * x, x^6, (x * y^-1 * x)^2, z^3 * x^-1 * z * y^-1 * z ] T51.123 : Triangle type {6,6,14} Group order 168 Action reflexible [m,n] Defining relators: [ x * y * z, z^2 * x^-1 * z * y^-1, x^6, (x * y^-1 * x)^2, (x * y^-2)^2, y^-1 * x * z * y * x^-1 * z^4 ] T51.124 : Triangle type {6,9,36} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, y * x^-2 * y^2, x^-1 * z * x^-1 * y^-1 * z, z^-3 * x^-1 * z^2 * y^-1 ] T51.125 : Triangle type {6,9,36} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, y^2 * x * z^-1, x^6, z^-3 * x^-1 * z^2 * y^-1 ] T51.126 : Triangle type {6,10,15} Group order 150 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, x^6, z^2 * y^-1 * x * z^2 ] T51.127 : Triangle type {7,18,126} Group order 126 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, y^-1 * z^4 * y^-5 * z * y^-1 * z * y^-1 * z * y^-3 ] T51.128 : Triangle type {7,119,119} Group order 119 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, y^5 * x^-1 * y^2 * z^-4 * y * z^-1 * y * z^-1 * y * z^-1 ] T51.129 : Triangle type {7,119,119} Group order 119 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7, z^3 * y^-1 * z * y^-1 * z^4 * y^-2 * x * y^-4 * z ] T51.130 : Triangle type {7,119,119} Group order 119 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, x^-7, y^5 * x^-1 * y^2 * z^-4 * y * z^-1 * y * z^-1 * y^2 ] T51.131 : Triangle type {8,8,8} Group order 160 Action chiral Defining relators: [ x * y * z, y * x^-2 * z * x^-1, (x * z * y^-1)^2, (x * z^-1 * y)^2, y^-2 * z^-1 * x^-1 * z * y^-1 * z ] T51.132 : Triangle type {8,8,8} Group order 160 Action chiral Defining relators: [ x * y * z, y * x^-2 * z * x^-1, (x * z * y^-1)^2, (x * z^-1 * y)^2, y^2 * z^-1 * x^-1 * z * y^-1 * z ] T51.133 : Triangle type {8,8,18} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y * x, y^2 * x^-1 * y^-1 * z, x * z * y^-1 * z^-2 * x * y * z^-4 ] T51.134 : Triangle type {8,8,18} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, (x * z^-1)^2, (y * z^-1)^2, (x * y^-1 * x)^2, z^-4 * x^-1 * y * x * y^-1 * z^-3 ] T51.135 : Triangle type {8,8,18} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, x^-1 * z^4 * y * z^-1 * x * z * y^-1 * z^-2 * x * z * y * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 ] T51.136 : Triangle type {8,8,18} Group order 144 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^8, z^-11 * x^-1 * y * x * y^-1 * z^-5 ] T51.137 : Triangle type {8,8,68} Group order 136 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^5 * y * x * z * y^-1 * z^-2 * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x * z ] T51.138 : Triangle type {8,8,68} Group order 136 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * x^2 * y^-1, z^2 * x^-1 * z * y^-1, z^4 * y^-1 * z^-1 * x * z^4 * y * x * z * y^-1 * z^-1 * x * z * y^-1 * z^-1 * x ] T51.139 : Triangle type {8,30,120} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^8, z^2 * y^-1 * z * y^-1 * z^4 * y^-2 * x^-1 * z^4 ] T51.140 : Triangle type {8,40,60} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y * x^-1 * y * x^-1 * y * z^-1 * y, z * x^-1 * z * x^-1 * z^3 ] T51.141 : Triangle type {8,40,60} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-3 * x^-1 * z^2, x^8 ] T51.142 : Triangle type {9,9,12} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, z * x^-2 * y^-2, z * x^-1 * y^-1 * x * z * x^-1, z * y^2 * x^-1 * z^2 ] T51.143 : Triangle type {9,39,117} Group order 117 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-9, y^-1 * z * y^-1 * z^4 * y^-5 * z ] T51.144 : Triangle type {9,39,117} Group order 117 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-9, y^-3 * z^4 * y^-2 * x * y^-4 ] T51.145 : Triangle type {10,20,60} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, (x * z^-2)^2, z^2 * y * x^-1 * z^3, y^-1 * x^4 * y^-3 ] T51.146 : Triangle type {10,20,60} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, (y * z^-1)^2, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z * y * z^-1, x^10 ] T51.147 : Triangle type {10,20,60} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, y^-2 * x^2 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z^-2 * x^3 * z^-2 * x ] T51.148 : Triangle type {10,30,30} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, (y * z^-1 * y)^2, x^-1 * z * y * x * y^-1 * z^-1, y * x^-3 * z^2 * y ] T51.149 : Triangle type {10,30,30} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y^3 * z^-2, x^-1 * z * y * x * y^-1 * z^-1, y * x^-3 * z^2 * y ] T51.150 : Triangle type {12,20,30} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-1 * z^3 * y^-3 * z^3, x^3 * y^-5 * x * z^-5 * x^3 ] T51.151 : Triangle type {12,24,24} Group order 120 Action chiral Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-2 * x^-1 * y * z^-1, y^-1 * z * x^-1 * y^-2, y * z^-1 * y * x^-1 * y^-1 * z^-2, x * y^-1 * x^3 * y^-2 * z^-1 ] T51.152 : Triangle type {12,24,24} Group order 120 Action chiral Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, y^-1 * z^-1 * x^-1 * z * y^-1, x^-2 * y^2 * x^-2 * y^2 * x^-6 ] T51.153 : Triangle type {14,56,56} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^6 * z^-2, z^-2 * x^7 * z^-5 * x * z^-1 ] T51.154 : Triangle type {14,56,56} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, x * z^-1 * x^3 * z^-3, y^5 * z^-1 * y * z^-1 ] T51.155 : Triangle type {14,56,56} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-4 * x^2 * y^-4, z^-2 * x^4 * z^-6 ] T51.156 : Triangle type {14,56,56} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2, y^-4 * x^2 * y^-4 ] T51.157 : Triangle type {14,56,56} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^4 * z^-3, x^5 * y^-4 * x^2 * y^-4 * x^3 ] T51.158 : Triangle type {14,56,56} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * y^2 * z^-1, z^-1 * x^-2 * y^-1 * x, x^-2 * z * x^-1 * z * x^-7 * z^2 * x^-2 ] T51.159 : Triangle type {15,15,30} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * z * y^-1, z^-2 * x^-1 * y^-1 * x, y^2 * z^-1 * y * x^-1 * y^2 * z^-1 * y ] T51.160 : Triangle type {15,15,30} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, y^-1 * z^-1 * x * z, y^-1 * x^3 * y^-2, z^2 * x^-3 * z^4 ] T51.161 : Triangle type {15,20,20} Group order 120 Action reflexible [m] Defining relators: [ x * y * z, (x * z^-1)^2, y^2 * x^2 * z^-1 * y, z * y^2 * x^-1 * z * y^-1 * z ] T51.162 : Triangle type {15,20,20} Group order 120 Action reflexible [m,n] Defining relators: [ x * y * z, x^-1 * y^-1 * x * z, (z^-1 * y)^3, y * x^-3 * y^3 ] T51.163 : Triangle type {16,28,112} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-4 * x^-1 * z^3, x^-9 * z^3 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 ] T51.164 : Triangle type {16,28,112} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x * y^-4 * x^3 * y^-3, z^6 * x^-5 * z ] T51.165 : Triangle type {18,108,108} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, x^-1 * z * x^-1 * z^5 * x^-9 ] T51.166 : Triangle type {18,108,108} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x * y^-1 * x * y^-4 * x^5 * y^-1, y^-1 * z * y^-1 * z * y^-6 * z^2 ] T51.167 : Triangle type {18,108,108} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * y * z^-2, x^3 * y^-1 * x * y^-1 * x * y^-4 * x^8 ] T51.168 : Triangle type {27,36,108} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x * y^-4 * x^2 * y^-4, x^7 * z^-4 * x ] T51.169 : Triangle type {27,36,108} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * y * z^-1, y^-7 * x^4 * y^-1 * x * y^-1 * x * y^-1 * x^10 * y^-1 * x * y^-1 * x ] T51.170 : Triangle type {27,36,108} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6 * y^-4, z^4 * y^-4 * x^-1 * z^4 ] T51.171 : Triangle type {27,36,108} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^3 * z^-1 * y^3 * x^-1 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y^3 ] T51.172 : Triangle type {27,36,108} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-3 * y^3, z^-2 * x * z^-4 * y^2 * z^-8 ] T51.173 : Triangle type {27,36,108} Group order 108 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^3 * y^-1 * x^5 * z^-5 * x^2 ] T51.174 : Triangle type {28,28,28} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * x^4 * z^-3, y^-3 * x * y^-1 * x * y^-4 * x^2 * y^-4 ] T51.175 : Triangle type {28,28,28} Group order 112 Action reflexible [m,n] Defining relators: [ x * y * z, z^-1 * x^2 * z^-1, z^-1 * y * x^-1 * y^-2, (y^2 * x^-1 * y * x^-1 * y^3)^2 ] T51.176 : Triangle type {28,28,28} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x^4 * z^-3, y^-3 * x^2 * y^-3 ] T51.177 : Triangle type {28,28,28} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^2 * y^-4 * x^6, y^-1 * z * y^-1 * z * y^-6 * z^2 ] T51.178 : Triangle type {28,28,28} Group order 112 Action reflexible [m] Defining relators: [ x * y * z, z^-1 * x^-2 * y^-1 * x, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, z^-1 * x * z^-1 * x * z^-2, y^-3 * x * y^-1 * x * y^-4 ] T51.179 : Triangle type {35,105,105} Group order 105 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * x * y^-1, z^-8 * x * z^-1 * x * z^-4 * x^3 * z^-5 * x * z^-1 * x * z^-2 ] T51.180 : Triangle type {35,105,105} Group order 105 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-6 * y^3, z^5 * y^-4 * x^-3 * z^3 ] T51.181 : Triangle type {35,105,105} Group order 105 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^3 * z^-2, x^-10 * y^3 * x^-6 ] T51.182 : Triangle type {35,105,105} Group order 105 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-1 * x^3 * z^-2, y^3 * z^-1 * y^14 ] T51.183 : Triangle type {35,105,105} Group order 105 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-2 * z, x^-35 ] T51.184 : Triangle type {35,105,105} Group order 105 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-5 * x^2 * y^-4, x^-1 * z^4 * x^-5 * y * x^-1 ] T51.185 : Triangle type {35,105,105} Group order 105 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-3 * y^4, z^-2 * x^5 * y * z^-6 ] T51.186 : Triangle type {35,105,105} Group order 105 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * y^-2 * x^-1 * z^4, x^2 * y^-3 * x^7 ] T51.187 : Triangle type {52,104,104} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^3 * x^-1 * y^3, z^-2 * x^7 * z^-5 * x * z^-1 ] T51.188 : Triangle type {52,104,104} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * y^-4 * x^-1 * z^4, x * y^-2 * x^8 ] T51.189 : Triangle type {52,104,104} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x^2 * z^-2, y^-1 * x * y^-1 * x * y^-1 * x * y^-1 * x * y^-4 * x * y^-3 * z * y^-1 * x * y^-1 ] T51.190 : Triangle type {52,104,104} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^-23 * x * y^-4 * x^3 * y^-5 ] T51.191 : Triangle type {52,104,104} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x * y^-4 * x^4 * y^-2, z^4 * y^-2 * x^-1 * z^4 ] T51.192 : Triangle type {52,104,104} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * z^2, y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-8 ] T51.193 : Triangle type {52,104,104} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^-1 * z * y^-1 * z * y^-8 ] T51.194 : Triangle type {52,104,104} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-1, z * x^-1 * z * x^-1 * z^5 * x^-7 * z^3 ] T51.195 : Triangle type {52,104,104} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-3 * z^2, y^2 * z^-1 * y^6 * x^-2 * y^4 * z^-1 * y * z^-1 * y * z^-1 * y * z^-1 * y^2 ] T51.196 : Triangle type {52,104,104} Group order 104 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^6 * z^-4, y^-6 * x * y^-4 ] T51.197 : Triangle type {52,104,104} Group order 104 Action reflexible [m,n] Defining relators: [ y^-1 * x^-1 * y^-1, x^-52, y * z^-1 ] T51.198 : Triangle type {52,104,104} Group order 104 Action reflexible [m,n] Defining relators: [ x * y * z, x * z * y, z^-1 * y^2 * z^-1, x^-12 * y * x^-8 * y * x^-5 ] T51.199 : Triangle type {103,103,103} Group order 103 Action reflexible [m,n] Defining relators: [ x^-2 * y^-1, y^-46 * x * y^-5, x * z^-1 ] T51.200 : Triangle type {103,103,103} Group order 103 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z * x^-1 * z, y^22 * x^-2 * y^11 ] T51.201 : Triangle type {103,103,103} Group order 103 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-2 * x * z^-1, x^-7 * y^3 * x^-1 * y^4 * x^-2 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y^3 ] T51.202 : Triangle type {103,103,103} Group order 103 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^2 * x^-1 * z^2, x^-1 * y^2 * x^-1 * y^5 * x^-1 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 * y ] T51.203 : Triangle type {103,103,103} Group order 103 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-3 * x * z^-2, x^-1 * y * x^-6 * y^4 * x^-1 * y * x^-1 * y * x^-1 * y * x^-1 ] T51.204 : Triangle type {103,103,103} Group order 103 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^3 * x^-1 * z^3, x^-7 * y^4 * x^-1 * y * x^-1 * y^2 ] T51.205 : Triangle type {103,103,103} Group order 103 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^-4 * x * z^-3, x^2 * y^-1 * x * y^-4 * x^6 ] T51.206 : Triangle type {103,103,103} Group order 103 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, z^4 * x^-1 * z^4, x^2 * y^-4 * x^3 * y^-3 ] T51.207 : Triangle type {103,103,103} Group order 103 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x * y^-4 * x^6, z^5 * x^-1 * z^4 ] T51.208 : Triangle type {103,103,103} Group order 103 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^7 * y^-3, z^6 * x^-1 * z^4 ] T51.209 : Triangle type {103,103,103} Group order 103 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-5 * y^4, z^5 * y^-8 * z^2 ] T51.210 : Triangle type {103,103,103} Group order 103 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^2 * x^-2 * y^3, x^-1 * z * x^-1 * z^5 * x^-6 * z^3 ] T51.211 : Triangle type {103,103,103} Group order 103 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^-7 * z^2, y^-7 * x^2 * y^-4 ] T51.212 : Triangle type {103,103,103} Group order 103 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x * y^-4 * x^2 * y^-4, x^-1 * z^4 * x^-5 * z ] T51.213 : Triangle type {103,103,103} Group order 103 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^5 * z^-3, x^-2 * z^3 * x^-9 ] T51.214 : Triangle type {103,103,103} Group order 103 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y * x^-2 * y^2, z^11 * x^-4 * z^4 * x^-1 * z * x^-1 * z ] T51.215 : Triangle type {103,103,103} Group order 103 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-4 * z^3, x^-3 * z^3 * x^-10 ] T51.216 : Triangle type {103,103,103} Group order 103 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, y^-5 * x^2 * y^-4, z^4 * y^-3 * x^-1 * z^4 ] Genus 52 T52.1 : Triangle type {2,3,8} Group order 2448 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^8, z^-1 * x * z^3 * y * z^-1 * x * z^3 * y * z^-1 * x * z^2 * y^-1 * z^-1 ] T52.2 : Triangle type {2,3,8} Group order 2448 Action reflexible [m] Defining relators: [ x^2, y^3, x * y * z, z^8, y * x * z * y * x * z^2 * y * x * z^2 * y * z^-3 * x * z * y^-1 * z^-1 * x * z^2 ] T52.3 : Triangle type {2,4,106} Group order 424 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-106 ] T52.4 : Triangle type {2,4,208} Group order 416 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^4, (y * z^-1)^2, z^-11 * x * y^-1 * z^-92 ] T52.5 : Triangle type {2,6,20} Group order 360 Action reflexible [m] Defining relators: [ x^2, x * y * z, y^6, z^2 * y^-2 * z^-1 * x * y^-1, z^-5 * x * z * y * z^-2 * x * z * y * z^-1 * x * z^2 * y^-1 * z^-5 ] T52.6 : Triangle type {2,6,54} Group order 324 Action chiral Defining relators: [ x^2, x * y * z, y^6, (y * z^-2)^2, y^-2 * z * y^-2 * z^-1 * x * y^-1 * z, x * z * y * z^-1 * x * z^4 * y * x * y^-1 * z^-6 * x * z^2 * y^-1 ] T52.7 : Triangle type {2,6,54} Group order 324 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^6, z^-36 * x * y^-1 * z^-6 * x * y^-1 * z^-10 ] T52.8 : Triangle type {2,6,54} Group order 324 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^-25 * x * z^16 * y * z^-1 * x * z * y^-1 * z^-4 * x * z^2 * y^-1 * z^-2 ] T52.9 : Triangle type {2,6,156} Group order 312 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^6, z^23 * y * x * z^16 * y * z^-1 * x * y * z^-7 * x * z^2 ] T52.10 : Triangle type {2,10,28} Group order 280 Action reflexible [m] Defining relators: [ x^2, x * y * z, (y * z^-1)^2, y^10, z^-3 * x * z * y * x * z * y * x * z * y * x * z * y * x * y * z^-9 * x * y^-1 * z^-6 ] T52.11 : Triangle type {2,10,130} Group order 260 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^10, z^8 * y * x * y * z^-16 * x ] T52.12 : Triangle type {2,12,16} Group order 288 Action reflexible [m] Defining relators: [ x^2, x * y * z, z^2 * y^-2 * z^-1 * x * y^-1, x * z * y * z^-1 * x * z * y^-2 * z * y^-1 * z^-2 ] T52.13 : Triangle type {2,16,16} Group order 272 Action chiral Defining relators: [ x^2, x * y * z, y * z^-1 * y^3 * z^-2 * y ] T52.14 : Triangle type {2,16,16} Group order 272 Action chiral Defining relators: [ x^2, x * y * z, z^-1 * y^4 * z^-2 * y ] T52.15 : Triangle type {2,18,117} Group order 234 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z^2 * y * z^-10 ] T52.16 : Triangle type {2,24,30} Group order 240 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y^-2 * z^-2 * y, x * y^-4 * z^-1 * y^3, z^-3 * x * z * y^-1 * z^-5 ] T52.17 : Triangle type {2,28,112} Group order 224 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, y^-3 * z^4 * y^-2 * z^4 * y^-1 ] T52.18 : Triangle type {2,54,108} Group order 216 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * y^-2 * z^-1 * y, x * z * y^-1 * z^-2, z^-26 * y^11 * z^-2 * y^15 ] T52.19 : Triangle type {2,105,210} Group order 210 Action reflexible [m] Defining relators: [ x^2, x * y * z, x * z * y, y^98 * z^-6 * y ] T52.20 : Triangle type {2,106,106} Group order 212 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^7 * y^-97 * z ] T52.21 : Triangle type {2,208,208} Group order 208 Action reflexible [m,n] Defining relators: [ x^2, x * y * z, x * z * y, y^-1 * z^6 * y^-96 * z ] T52.22 : Triangle type {3,9,63} Group order 189 Action chiral Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y * z^-1 * y * x^-1 * z^3, y^-9 ] T52.23 : Triangle type {3,9,63} Group order 189 Action chiral Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, z^2 * y * x * z^2 ] T52.24 : Triangle type {3,9,63} Group order 189 Action chiral Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, z^-2 * y * x^-1 * y * z^-2, z^2 * y * z^-1 * y * z^-2 * x^-1 ] T52.25 : Triangle type {3,15,30} Group order 180 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-2 * x^-1 * z * y^-1, y * x * y^-1 * x * y^-1 * z^-1, z^-1 * y * z^-1 * y^2 * z^-1 * y^4 * z^-3 * y^2 ] T52.26 : Triangle type {3,20,20} Group order 180 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y^2 * x^-1 * y^-1 * z, y * z^-1 * x^-1 * z^2, y * z^-1 * y^10 * z^-1 * y^2 * z^-1 * y^2 * z^-1 * y ] T52.27 : Triangle type {3,24,56} Group order 168 Action chiral Defining relators: [ x^3, x * y * z, y * x * y^-1 * x * y^-1 * z^-1, y^2 * z^-1 * x^-1 * z^3, y * z^-2 * y^2 * z^-3 ] T52.28 : Triangle type {3,28,42} Group order 168 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-3 * x^-1 * z^2 * y^-1, z * y^-1 * z * y^-1 * x * z * y^-1 * z ] T52.29 : Triangle type {3,53,159} Group order 159 Action reflexible [m] Defining relators: [ x^3, x * y * z, x * z * y, y^-42 * z * y^-1 * z * y^-7 * z ] T52.30 : Triangle type {3,54,54} Group order 162 Action chiral Defining relators: [ x^3, x * y * z, y^2 * x^-1 * z^2, z^-1 * x^-1 * y^-1 * x * z * y, z^-4 * y^11 * z^-1 * y * z^-1 ] T52.31 : Triangle type {3,54,54} Group order 162 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-43 * z * y^-1 * z * y^-7 * z ] T52.32 : Triangle type {3,54,54} Group order 162 Action reflexible [m] Defining relators: [ x^3, x * y * z, z^-1 * y * x^-1 * y^-2, z^-2 * x^-1 * z * y^-1, y * z^-2 * y * z^-2 * y^6 * z^-1 * y * z^-2 * y * z^-1 ] T52.33 : Triangle type {3,54,54} Group order 162 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, y * x^-1 * z, y^-1 * z^41 * y^-3 * z * y^-7 * z ] T52.34 : Triangle type {3,156,156} Group order 156 Action reflexible [m,n] Defining relators: [ x^3, x * y * z, x * z * y, y^-41 * z * y^-1 * z * y^-8 ] T52.35 : Triangle type {4,4,53} Group order 212 Action reflexible [n] Defining relators: [ x * y * z, x^4, (x * y^-1)^2, y^4, z^3 * x^-1 * z * y^-1 * z^4 ] T52.36 : Triangle type {4,4,53} Group order 212 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^39 * y^-1 * x^-1 * z^13 ] T52.37 : Triangle type {4,4,104} Group order 208 Action reflexible [m,n] Defining relators: [ x * y * z, z * x^-1 * y^-1, x^4, z^38 * y^-1 * x * z^13 ] T52.38 : Triangle type {4,5,8} Group order 240 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-2 * x^-1 * y * z^-1, y^-5, y * x^-1 * z * y * x^-1 * y^-1 * z^-1 * x^-1 * z ] T52.39 : Triangle type {4,6,9} Group order 216 Action chiral Defining relators: [ x * y * z, x^4, y^6, z^-1 * y^2 * x * y^-1 * z^-1, y^2 * x^-2 * y^-1 * z * x^-1 ] T52.40 : Triangle type {4,6,9} Group order 216 Action reflexible [m] Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, y^6, y * x * z^-1 * x^-1 * z * x^-1 * z, z^9 ] T52.41 : Triangle type {4,6,12} Group order 204 Action chiral Defining relators: [ x * y * z, x^4, z^-1 * y * x^-1 * y^-2, z^-1 * x * y^-1 * x * y^-1 * z^-1, y^6, z^-1 * x * z^-1 * x^-2 * z * y * z^-1 * x ] T52.42 : Triangle type {4,8,22} Group order 176 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, y^2 * x^-1 * y^-1 * z, z^-1 * y * x^-1 * y^2, z^4 * y * x^-1 * z^4 * y^-1 * x^-1 * z^4 * y^-1 * z^-1 * x * z^6 ] T52.43 : Triangle type {4,10,80} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * x^-1 * z^2 * y^-1 * x * y^-1 * z^-3, y^10 ] T52.44 : Triangle type {4,12,78} Group order 156 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, z^-1 * y^3 * z^-1 * y, z^7 * y * z^-1 * x^-1 * z^4 ] T52.45 : Triangle type {4,16,20} Group order 160 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^2, y^4 * x^-1 * y^-3 * z, z^-1 * x^-1 * z * y * x^-1 * z * y^-1 * z^-1 * x * z * y * z^-2 ] T52.46 : Triangle type {4,36,72} Group order 144 Action reflexible [m] Defining relators: [ x * y * z, x^4, y * x^-2 * z * x^-1, z^-1 * y * x^-1 * y^-2, y * z^-1 * x^-1 * z^2, z^-5 * y * z^-2 * y^5 * z^-1 * y^4 ] T52.47 : Triangle type {4,70,140} Group order 140 Action reflexible [m] Defining relators: [ x * y * z, x * z * y, x^4, y^-12 * z^3 * y^-8 * z^3 * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 * z * y^-1 ] T52.48 : Triangle type {5,6,15} Group order 180 Action reflexible [m] Defining relators: [ x * y * z, x^-5, z^-1 * y * x^-1 * y^-2, y^6, z^2 * y * x^-1 * z^2, (z^-1 * x)^3 ] T52.49 : Triangle type {5,27,135} Group order 135 Action reflexible [m] Definin