Chiral orientably-regular maps of genus 2 to 101 ------------------------------------------------ Below is a list of all chiral (irreflexible) orientably-regular maps on surfaces of genus 2 to 101, up to isomorphism and duality and reflection - hence with one of each chiral pair listed. The notation "Cg.n" is used for the nth chiral map of genus g. These were found by Marston Conder (University of Auckland) with the help of the "LowIndexNormalSubgroups" routine in Magma, in August 2006. For background information (and chiral maps of genus up to 15), see: Marston Conder and P. Dobcs\'anyi, Determination of all regular maps of small genus, J. Combinatorial Theory, Series B 81 (2001), 224-242. Total number of maps in list below: 594 C7.1 : Type {6,9}_18 Order 54 mV = 3 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^-1 * R^-3 * S * R^-1 * S^-1 ] C7.2 : Type {7,7}_4 Order 56 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-7, S * R^-3 * S^2 * R^-1 ] C8.1 : Type {6,6}_14 Order 84 mV = 2 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^6, S^-1 * R * S^-1 * R^3 * S * R^-1 * S^-1 * R ] C10.1 : Type {3,8}_12 Order 432 mV = 1 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, S^8, S^-2 * R^-1 * S^2 * R^-1 * S^2 * R^2 * S^-2 * R * S^-3 * R * S^-1 ] C10.2 : Type {4,8}_8 Order 144 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^8, R * S^-3 * R^2 * S^-2 * R * S^-1 ] C10.3 : Type {8,8}_6 Order 72 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, R * S^-1 * R^3 * S^-3, R^-1 * S * R^3 * S^-1 * R * S^-1 ] C11.1 : Type {4,8}_40 Order 160 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, S^-1 * R^-1 * S * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S^-1 ] C11.2 : Type {4,8}_40 Order 160 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, R * S^-2 * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S^-1 ] C11.3 : Type {4,12}_30 Order 120 mV = 3 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S * R * S^-2 * R^2 * S^-1 * R * S^2 ] C11.4 : Type {8,8}_20 Order 80 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, S^-1 * R^-1 * S * R^2 * S^-1 * R * S^-1 ] C11.5 : Type {8,8}_10 Order 80 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, R * S^-2 * R^2 * S^-1 * R * S^-1 ] C11.6 : Type {12,12}_10 Order 60 mV = 3 mF = 3 Self-dual Defining relations for automorphism group: [ (R * S)^2, S^-2 * R^2 * S^-1 * R ] C12.1 : Type {5,10}_22 Order 110 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-5, S * R^-1 * S * R^2 * S^-1 * R * S ] C12.2 : Type {5,10}_22 Order 110 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-5, S^-1 * R * S^-1 * R^-2 * S^-4 ] C14.1 : Type {6,6}_26 Order 156 mV = 2 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^6, R * S^-1 * R * S^-1 * R^3 * S^-1 * R^2 * S^-1 * R ] C15.1 : Type {3,12}_56 Order 336 mV = 2 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, (R * S^-5)^2, S * R^-1 * S^2 * R * S^-2 * R * S^-1 * R * S^-2 * R * S^3 * R^-1 * S ] C16.1 : Type {6,18}_18 Order 108 mV = 6 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^-1 * R^-1 * S * R^3 * S^-4 ] C17.1 : Type {3,7}_16 Order 1344 mV = 1 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, S^-7, S^-1 * R * S^-2 * R * S^-2 * R * S^-2 * R^-1 * S * R^-1 * S * R^-1 * S^-2 * R * S^-2 * R * S^-2 * R * S^-1, S * R * S^-2 * R * S^-3 * R * S^-2 * R * S^-1 * R * S^3 * R^-1 * S^2 * R^-1 * S^-2 * R * S^2 ] C17.2 : Type {4,6}_12 Order 384 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^6, S * R^-1 * S * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S, (R * S^-2)^4 ] C17.3 : Type {6,6}_8 Order 192 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, S * R * S^-1 * R^2 * S * R^-1 * S, R^2 * S^-2 * R^3 * S^-1 * R * S^3 ] C17.4 : Type {7,14}_4 Order 112 mV = 2 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-7, S^2 * R^-2 * S * R^-1 * S ] C18.1 : Type {8,8}_34 Order 136 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-2 * R)^2, S^-3 * R^2 * S * R^-1 * S^-1 ] C19.1 : Type {4,8}_8 Order 288 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^8, S^-3 * R * S^-1 * R^2 * S^-3 * R * S^-1 ] C19.2 : Type {8,8}_6 Order 144 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-2 * R^3 * S^-1 * R * S^-1 ] C20.1 : Type {6,6}_38 Order 228 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-1 * R)^2, S^6, R^-1 * S * R * S^-2 * R * S^-2 * R * S^-1 * R * S^-2 * R * S^-2 ] C21.1 : Type {4,8}_10 Order 320 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^8, (S^-1 * R)^5, R * S^-2 * R * S^-1 * R^2 * S^3 * R^-1 * S ] C21.2 : Type {4,8}_40 Order 320 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S * R^-1 * S^-1 * R * S^-1 ] C21.3 : Type {4,8}_20 Order 320 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S^-1 * R * S * R^-1 * S^-1 ] C21.4 : Type {4,12}_60 Order 240 mV = 3 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, R * S^-2 * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S^-1, S^12 ] C21.5 : Type {4,20}_10 Order 200 mV = 5 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S^-1 * R * S^-1, S^-1 * R^-1 * S * R * S^-1 * R^-1 * S * R^-1 * S^-6 ] C21.6 : Type {8,8}_20 Order 160 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S^-1 * R * S^-1 ] C21.7 : Type {8,8}_20 Order 160 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, S^-1 * R * S^-1 * R * S^-1 * R^2 * S^2 * R^-2 * S^-1 ] C21.8 : Type {12,12}_10 Order 120 mV = 3 mF = 3 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S * R * S^-1 * R^2 * S * R^-1 * S, R^12 ] C21.9 : Type {14,14}_4 Order 112 mV = 2 mF = 2 Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S * R^-1 * S, R * S^-2 * R^8 * S^-1 * R^2 ] C21.10 : Type {20,20}_10 Order 100 mV = 5 mF = 5 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S * R * S^-1 * R^2 * S * R^-1 * S, R^6 * S^-1 * R * S^-2 ] C22.1 : Type {3,12}_42 Order 504 mV = 1 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, S^12, (S^2 * R^-1 * S^2)^3, S * R * S^-2 * R * S^-2 * R * S^-1 * R * S^-3 * R * S^3 ] C22.2 : Type {6,6}_42 Order 252 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, S^-2 * R^-1 * S * R^2 * S^2 * R^-1 * S^-1 ] C22.3 : Type {6,6}_42 Order 252 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-1 * R)^2, S^6, R^-1 * S * R^-1 * S^2 * R * S^-2 * R * S^-1 * R * S^-2 * R * S^-2 ] C22.4 : Type {6,12}_28 Order 168 mV = 2 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S * R * S^-1 * R^3 * S^2 * R^-2, S * R^2 * S^-1 * R^2 * S^4, R * S^-3 * R^2 * S * R^-1 * S^-2 ] C22.5 : Type {6,12}_28 Order 168 mV = 4 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, R^-2 * S * R^3 * S^-1 * R * S^2 ] C22.6 : Type {9,18}_14 Order 126 mV = 3 mF = 3 Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S * R^-2, R^-9, S^2 * R^-3 * S^4, S^2 * R^-1 * S * R^-1 * S^2 * R^-1 * S ] C25.1 : Type {4,16}_8 Order 256 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^-2 * R * S^-1 * R^2 * S^2 * R^-1 * S^-1 ] C25.2 : Type {6,9}_36 Order 216 mV = 3 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^-9, S^-1 * R^2 * S^-1 * R^-3 * S * R^-1 * S * R^-2 * S^-1 ] C25.3 : Type {6,27}_54 Order 162 mV = 9 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^-1 * R^2 * S^-1 * R^2 * S * R^-1 * S^-1 * R, R * S^-4 * R^-3 * S^5 ] C25.4 : Type {16,16}_8 Order 128 mV = 4 mF = 4 Self-dual Defining relations for automorphism group: [ (R * S)^2, (R * S^-1 * R^2)^2, S^-2 * R^3 * S * R^-1 * S^-1 ] C26.1 : Type {8,8}_10 Order 200 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-2 * R)^2, (R * S^-1)^4, R^-1 * S * R^4 * S^-1 * R^2 * S ] C27.1 : Type {3,12}_104 Order 624 mV = 2 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, (R * S^-5)^2, S * R^-1 * S^2 * R * S^-2 * R * S^-2 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S ] C27.2 : Type {4,8}_104 Order 416 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, R^-1 * S * R * S^-1 * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S * R^-1 * S^-1 * R * S^-1 * R * S^2 ] C27.3 : Type {4,8}_104 Order 416 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, R^-1 * S * R * S^-1 * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S * R^-1 * S^-1 * R * S^-1 * R * S^-2 ] C27.4 : Type {4,12}_78 Order 312 mV = 3 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^12, S^-1 * R^-1 * S * R * S^-1 * R^-1 * S * R^-1 * S * R^-1 * S * R^-1 * S^-2 ] C27.5 : Type {8,8}_26 Order 208 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, R * S^-2 * R^-1 * S * R^2 * S^-1 * R * S^-1 * R * S^-1 ] C27.6 : Type {8,8}_52 Order 208 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, R * S^-1 * R * S^-2 * R^2 * S^-1 * R * S^-1 * R * S^-1 ] C27.7 : Type {12,12}_26 Order 156 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, (S^-1 * R)^3, R^-1 * S * R^4 * S^-1 * R^2 * S^-1 ] C27.8 : Type {12,12}_26 Order 156 mV = 3 mF = 3 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, R * S^-1 * R * S^-1 * R^2 * S^-1 * R * S^2 ] C28.1 : Type {3,8}_36 Order 1296 mV = 1 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, S^8, S * R * S^-3 * R * S^-2 * R * S^-1 * R * S^3 * R^-1 * S^-2 * R * S^2 ] C28.2 : Type {3,18}_18 Order 486 mV = 1 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, (S^2 * R^-1 * S^2)^3, S * R * S^-2 * R^-1 * S^3 * R^-1 * S^-4 * R * S^2 ] C28.3 : Type {4,8}_24 Order 432 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^8, S * R * S^-1 * R * S^-1 * R^2 * S^-1 * R * S * R^-1 * S, S^-2 * R^-1 * S^2 * R^2 * S^-2 * R * S^-2 ] C28.4 : Type {8,8}_6 Order 216 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S * R^-1 * S * R^2 * S^-1 * R * S, S^-2 * R^4 * S^2 * R^-1 * S^-1 ] C28.5 : Type {9,18}_18 Order 162 mV = 3 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-9, S * R^-4 * S * R^-1 * S^2 ] C29.1 : Type {6,6}_28 Order 336 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-1 * R)^2, S^6, S^-1 * R^-1 * S * R * S^-1 * R * S^-2 * R^-1 * S * R^2 * S^2 * R^-1 * S^-2 * R * S^-2 ] C29.2 : Type {6,15}_70 Order 210 mV = 5 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^-1 * R^-1 * S * R^-3 * S^-1 * R * S * R^-1 * S^-1 ] C29.3 : Type {12,12}_14 Order 168 mV = 2 mF = 4 Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S * R^-2, S * R^2 * S^-1 * R^2 * S^4, S * R * S^-2 * R^2 * S * R^-1 * S^2, R^12 ] C31.1 : Type {4,16}_80 Order 320 mV = 4 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, R * S^-1 * R^-1 * S * R * S^-1 * R^2 * S^-2 * R * S^3 ] C31.2 : Type {4,16}_80 Order 320 mV = 4 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S^-1 * R * S^-1, S^16 ] C31.3 : Type {4,28}_70 Order 280 mV = 7 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S^-1 * R * S^-1, S * R * S^-5 * R^-1 * S * R^-1 * S^-2 * R * S^5 ] C31.4 : Type {16,16}_10 Order 160 mV = 4 mF = 4 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S * R * S^-1 * R^2 * S * R^-1 * S, R * S^-3 * R^8 * S^-1 * R^3 ] C31.5 : Type {16,16}_20 Order 160 mV = 4 mF = 4 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S^-1 * R * S^-1 * R^2 * S^-2 * R ] C31.6 : Type {28,28}_10 Order 140 mV = 7 mF = 7 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S * R^-1 * S * R^2 * S^-1 * R * S, R^2 * S^-2 * R^9 * S^-1 ] C32.1 : Type {5,10}_62 Order 310 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-5, (R * S^-3 * R)^2, (R * S^-2 * R * S^-1)^2, S^2 * R * S^-2 * R^-1 * S^4 * R^-1 ] C32.2 : Type {5,10}_62 Order 310 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-5, (R * S^-3 * R)^2, S^-1 * R^-1 * S^2 * R^2 * S * R^-1 * S^-2 ] C32.3 : Type {6,6}_62 Order 372 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-1 * R)^2, S^6, S * R * S^-1 * R * S^-2 * R * S^-2 * R * S^3 * R^-1 * S^2 * R^-1 * S ] C33.1 : Type {3,12}_16 Order 768 mV = 1 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, S^12, S^2 * R^-1 * S^2 * R * S^-3 * R * S^-1 * R * S^-2 * R * S^2 ] C33.2 : Type {4,6}_12 Order 768 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^6, S * R * S^-2 * R * S^-1 * R^2 * S^2 * R^-1 * S^-1 * R * S ] C33.3 : Type {4,6}_24 Order 768 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^6, S * R^-1 * S * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S, S^2 * R * S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S^2 * R^-1 * S^-1 * R * S ] C33.4 : Type {6,6}_8 Order 384 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, S * R * S^-1 * R^2 * S * R^-1 * S, (R * S^-1 * R)^4 ] C33.5 : Type {6,6}_8 Order 384 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, S^-1 * R * S^-1 * R^3 * S * R^-1 * S^-2 ] C34.1 : Type {6,36}_36 Order 216 mV = 12 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^-1 * R^2 * S^-1 * R^2 * S * R^-1 * S^-1 * R, S^-4 * R^-1 * S * R * S^-1 * R^-1 * S * R^-1 * S^-5 ] C34.2 : Type {9,12}_18 Order 216 mV = 1 mF = 3 Defining relations for automorphism group: [ (R * S)^2, (R * S^-1 * R)^2, R^-9, S * R^-1 * S^2 * R^2 * S^2 * R^-1 * S, S^4 * R^-2 * S^-3 * R * S ] C34.3 : Type {10,10}_22 Order 220 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^10, (R * S^-1 * R^3)^2, S^-1 * R * S^-1 * R^3 * S^-4 ] C34.4 : Type {10,10}_22 Order 220 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, S * R^-1 * S * R^2 * S^-1 * R * S, R^10, (R * S^-1 * R^3)^2 ] C35.1 : Type {4,8}_136 Order 544 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, S^-1 * R * S^-2 * R^-1 * S * R^-1 * S * R * S^-1 * R^-2 * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R ] C35.2 : Type {4,8}_136 Order 544 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, S^-2 * R^-1 * S * R^-1 * S * R^-1 * S * R * S^-1 * R^-2 * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R ] C35.3 : Type {4,12}_102 Order 408 mV = 3 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^12, R * S^-1 * R^-1 * S * R * S^-1 * R^-2 * S^-1 * R * S^2 * R^-1 * S * R^-1 * S ] C35.4 : Type {8,8}_34 Order 272 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, S^-2 * R^-1 * S * R * S^-1 * R * S^-1 * R^-2 * S^-1 * R * S^-1 * R * S^-1 * R ] C35.5 : Type {8,8}_34 Order 272 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-2 * R)^2, (R * S^-1)^4, S^-1 * R^-1 * S^2 * R^2 * S * R^-1 * S^-2 ] C35.6 : Type {8,8}_68 Order 272 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, R^-1 * S * R * S^-1 * R * S^-1 * R * S^-1 * R^2 * S^2 * R^-2 * S^-2 ] C35.7 : Type {12,12}_34 Order 204 mV = 3 mF = 3 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S^-2 * R^-1 * S * R^2 * S^-1 * R * S^-1 * R ] C35.8 : Type {21,21}_4 Order 168 mV = 3 mF = 3 Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^2 * R^-1, R^3 * S^-8 * R^8 * S^-2 ] C37.1 : Type {3,8}_12 Order 1728 mV = 1 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, S^8, (R * S^-2)^6, S^2 * R * S^-2 * R^-1 * S^2 * R * S^-2 * R^-1 * S * R^-1 * S^-2 * R * S^2 * R^-1 * S^-2 * R * S, S * R * S^-2 * R * S^-4 * R * S^-2 * R * S^4 * R^-1 * S^2 * R^-1 * S^-2 * R * S ] C37.2 : Type {4,8}_8 Order 576 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^8, S^-1 * R^-1 * S^2 * R * S^-1 * R * S^2 * R^-1 * S^-2, (R * S^-2)^4, S * R^-1 * S * R * S^-2 * R^2 * S^3 * R^-1 * S * R^-1 ] C37.3 : Type {8,8}_12 Order 288 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-2 * R)^2, (R * S^-1)^4, R^2 * S^-1 * R^4 * S * R^-1 * S^-1 * R * S^-1 ] C38.1 : Type {6,6}_74 Order 444 mV = 2 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^6, S^-1 * R^-2 * S^-2 * R^2 * S^-1 * R^-3 * S * R^-2 * S * R^-2 * S^-1 * R^2 * S^-1 * R ] C39.1 : Type {3,12}_152 Order 912 mV = 2 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, (R * S^-5)^2, S^-1 * R * S^-2 * R^-1 * S^2 * R * S^-2 * R * S^-2 * R * S^-1 * R * S^2 * R^-1 * S^-2 * R * S^2 * R^-1 * S^-2 * R * S^-2 ] C40.1 : Type {3,12}_78 Order 936 mV = 1 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, S^12, (S^2 * R^-1 * S^2)^3, S^-1 * R * S^-2 * R * S^-2 * R * S^-2 * R^-1 * S * R^-1 * S^-2 * R * S^2 * R^-1 * S^-2 ] C40.2 : Type {6,6}_78 Order 468 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, S^-1 * R^2 * S^-1 * R^3 * S^-1 * R^2 * S^-1 * R, S * R * S^-2 * R^3 * S^3 * R^-2, S^-2 * R^-1 * S * R * S^-1 * R^2 * S * R^-1 * S^2 * R^-1 * S^-1 ] C40.3 : Type {6,6}_78 Order 468 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-1 * R)^2, S^6, S^-1 * R^-1 * S * R * S^-1 * R^-1 * S * R * S^-2 * R * S^-2 * R^2 * S * R^-1 * S^-2 * R * S^-2 * R * S^-1 ] C40.4 : Type {6,12}_52 Order 312 mV = 2 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S * R * S^-1 * R^3 * S^2 * R^-2, S * R^2 * S^-1 * R^2 * S^4, S^-1 * R^-1 * S^2 * R * S^-1 * R * S^-2 * R * S^-2 ] C40.5 : Type {6,12}_52 Order 312 mV = 4 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^12, R^-1 * S * R^2 * S^-1 * R * S^-1 * R^-3 * S * R^-1 * S^-2 ] C40.6 : Type {9,18}_26 Order 234 mV = 3 mF = 3 Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S * R^-2, R^-9, S^2 * R^-3 * S^4, S * R * S^-2 * R * S^-1 * R * S^2 * R^-1 * S^2 ] C40.7 : Type {12,18}_36 Order 216 mV = 3 mF = 2 Defining relations for automorphism group: [ (R * S)^2, S * R^5 * S^2 * R^-1 * S, S^-1 * R^-1 * S * R^3 * S^-4 ] C41.1 : Type {4,8}_10 Order 640 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^8, S * R^-1 * S * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S, S^-2 * R^-1 * S^2 * R * S^-1 * R * S^3 * R^-1 * S^-2 ] C41.2 : Type {4,8}_20 Order 640 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^8, R * S^-2 * R * S^-1 * R^2 * S^3 * R^-1 * S ] C41.3 : Type {4,8}_20 Order 640 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^8, (S^-1 * R)^5, R * S^-2 * R * S^-2 * R^2 * S^-2 * R * S^-3 ] C41.4 : Type {4,8}_40 Order 640 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, R^2 * S^-1 * R * S^-1 * R * S^-1 * R * S^-2 * R * S^-1 * R^2 * S * R^-1 * S^-1 * R * S^-1 * R * S^2 * R^-1 * S ] C41.5 : Type {4,8}_40 Order 640 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^8, S * R * S^-3 * R^2 * S^4 * R^-1, S^-1 * R^-1 * S * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S * R^-1 * S * R^-1 * S^-1 ] C41.6 : Type {4,8}_20 Order 640 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^8, S * R * S^-3 * R^2 * S^4 * R^-1, S^-1 * R^-1 * S * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S^-2 * R * S^-1 * R ] C41.7 : Type {4,8}_40 Order 640 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, R^2 * S^-1 * R * S^-1 * R * S^-1 * R * S^-2 * R * S^-1 * R^2 * S * R^-1 * S^-1 * R * S^-1 * R * S^-1 * R * S^2 ] C41.8 : Type {4,12}_30 Order 480 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S * R^-1 * S * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S, S^-5 * R^2 * S^-2 * R * S^-1 * R ] C41.9 : Type {4,12}_60 Order 480 mV = 3 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^12, S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S * R^-1 * S^-1 * R * S^-1 ] C41.10 : Type {4,20}_20 Order 400 mV = 5 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, R * S^-2 * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S^-1, S^20 ] C41.11 : Type {4,36}_90 Order 360 mV = 9 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S^-1 * R * S^-1, S^-9 * R * S^2 * R^-1 * S^-2 * R * S * R^-1 * S^-4 ] C41.12 : Type {6,8}_12 Order 384 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-1)^4, S^8, S^-2 * R * S^-1 * R^3 * S^-1 * R * S * R^-1 * S^-1 ] C41.13 : Type {8,8}_10 Order 320 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S * R^-1 * S * R^2 * S^-1 * R * S, S^-1 * R * S^-1 * R^3 * S^-3 * R ] C41.14 : Type {8,8}_20 Order 320 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, S^-1 * R * S^-2 * R^-1 * S * R * S^-1 * R^-2 * S^-1 * R * S^-1 * R * S^-1 * R ] C41.15 : Type {8,8}_40 Order 320 mV = 2 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, (R * S^-3)^2, S^8, S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S^-1 * R * S^-1 ] C41.16 : Type {8,8}_40 Order 320 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, (R * S^-3)^2, S^8, S^-1 * R * S^-1 * R * S^-1 * R^2 * S^2 * R^-2 * S^-1 ] C41.17 : Type {8,8}_40 Order 320 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, (R * S^-3)^2, S^8, S^-1 * R * S^-1 * R * S^-1 * R^2 * S^-2 * R^2 * S^-1 ] C41.18 : Type {8,8}_40 Order 320 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, S^-1 * R * S^-1 * R * S^-2 * R * S^-1 * R^-2 * S^-1 * R * S^-1 * R * S^-1 * R ] C41.19 : Type {8,16}_8 Order 256 mV = 2 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, S * R * S^-2 * R^2 * S * R^-1 * S^2, S^-1 * R^-1 * S^2 * R^2 * S^-1 * R * S^-2 ] C41.20 : Type {8,24}_60 Order 240 mV = 6 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, (R * S^-3)^2, S^2 * R * S^-1 * R^2 * S^-2 * R * S ] C41.21 : Type {8,24}_30 Order 240 mV = 6 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, (R * S^-3)^2, S^-1 * R^-1 * S^2 * R^2 * S * R^-1 * S^-2 ] C41.22 : Type {12,12}_20 Order 240 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R * S^-1 * R^2 * S * R^-1 * S, S^-1 * R^5 * S * R^-1 * S^-1 * R ] C41.23 : Type {12,12}_20 Order 240 mV = 3 mF = 3 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, R^12, R * S^-2 * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S^-1 ] C41.24 : Type {14,14}_4 Order 224 mV = 2 mF = 2 Defining relations for automorphism group: [ (R * S)^2, S^-1 * R^-1 * S * R^2 * S * R^-1 * S^-1, S * R^5 * S^3 * R^-1, R^-14 ] C41.25 : Type {20,20}_10 Order 200 mV = 5 mF = 5 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S * R * S^-1 * R^2 * S * R^-1 * S, R * S^-3 * R * S^-1 * R^7 * S^-1 * R * S^-2 * R * S^-1 * R ] C41.26 : Type {36,36}_10 Order 180 mV = 9 mF = 9 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S * R^-1 * S * R^2 * S^-1 * R * S, R^-1 * S^3 * R^-10 * S^2 * R^-2 ] C42.1 : Type {5,10}_82 Order 410 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-5, (R * S^-3 * R)^2, (R * S^-2 * R * S^-1)^2, R^-1 * S * R^-1 * S * R^-2 * S * R^-1 * S^-3 ] C42.2 : Type {5,10}_82 Order 410 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-5, (R * S^-3 * R)^2, (R * S^-2 * R * S^-1)^2, S * R * S^-1 * R * S^-1 * R^-2 * S^5 * R^-1 ] C42.3 : Type {8,8}_82 Order 328 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-2 * R)^2, (R * S^-1)^4, R^2 * S^-1 * R^4 * S^-3 * R * S^-1 ] C43.1 : Type {3,9}_18 Order 1512 mV = 1 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, S^-9, S^-1 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S * R^-1 * S^2 * R^-1 * S^-2 * R * S^-2, S^-1 * R * S^-2 * R^-1 * S^3 * R * S^-3 * R * S^-4 * R * S^-3 * R * S^-1 ] C43.2 : Type {3,12}_168 Order 1008 mV = 2 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, (R * S^-5)^2, S^-1 * R * S^-2 * R * S^-2 * R^-1 * S^2 * R * S^-2 * R * S^-1 * R * S^2 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^-2 ] C43.3 : Type {6,9}_126 Order 378 mV = 3 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^-9, R^2 * S^-1 * R * S^-1 * R^-3 * S * R^-1 * S * R^-2 * S * R^-1 * S ] C43.4 : Type {6,9}_126 Order 378 mV = 3 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^-9, R * S^-1 * R^2 * S^-1 * R * S^-1 * R^3 * S^-1 * R^2 * S^-1 * R ] C43.5 : Type {6,9}_126 Order 378 mV = 3 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^-9, R^-1 * S * R * S^-1 * R^-1 * S * R^-3 * S * R^-2 * S * R^-2 * S^-2 ] C43.6 : Type {6,12}_56 Order 336 mV = 2 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-1 * R)^2, S^-2 * R^-3 * S^-4, S * R * S^-1 * R * S^-3 * R * S^-1 * R * S^2 * R^-1 * S^-2 * R * S^-1 * R * S ] C43.7 : Type {6,21}_14 Order 294 mV = 7 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^-1 * R^2 * S^-1 * R^-3 * S * R^-1 * S^-4 ] C43.8 : Type {6,45}_90 Order 270 mV = 15 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^-1 * R^2 * S^-1 * R^2 * S * R^-1 * S^-1 * R, S^-8 * R^3 * S * R^-1 * S^-6 ] C43.9 : Type {12,36}_18 Order 216 mV = 12 mF = 2 Defining relations for automorphism group: [ (R * S)^2, S * R^5 * S^2 * R^-1 * S, S * R * S^-1 * R^3 * S^4, R^12 ] C43.10 : Type {15,30}_14 Order 210 mV = 5 mF = 5 Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S * R^-2, S * R^2 * S^-1 * R^2 * S^4, S * R * S^-2 * R^2 * S * R^-1 * S^2, R^2 * S^-2 * R^8 * S^-1 * R * S^-1 ] C44.1 : Type {6,6}_86 Order 516 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-1 * R)^2, S^6, S * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^-1 * R * S * R^-1 * S ] C45.1 : Type {8,32}_32 Order 256 mV = 8 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R * S^-1 * R^2 * S^-1 * R * S^-1, S^-4 * R^3 * S * R^-1 * S^-3 ] C45.2 : Type {15,15}_4 Order 240 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, S^-1 * R^-1 * S * R^2 * S * R^-1 * S^-1, S * R^5 * S^2 * R^-2, R^-1 * S^2 * R^-9 * S * R^-1 * S ] C46.1 : Type {3,8}_30 Order 2160 mV = 1 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, S^8, S * R * S^-3 * R * S^-3 * R * S^-1 * R * S^3 * R^-1 * S^4 * R^-1 * S ] C46.2 : Type {4,12}_30 Order 540 mV = 3 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S * R * S^-3 * R * S^4, S^-1 * R * S^-3 * R^2 * S^-3 * R * S^-1, R^-1 * S * R^-1 * S * R * S^-1 * R * S^-1 * R^2 * S^2 * R^-1 * S * R^-1 * S * R^-1 * S ] C46.3 : Type {4,24}_24 Order 432 mV = 3 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S * R * S^-1 * R * S^-1 * R^2 * S^-1 * R * S * R^-1 * S, S^-1 * R * S^-3 * R^2 * S^-1 * R * S^-3, S * R * S^-4 * R^-2 * S^-5 * R * S^2 ] C46.4 : Type {6,8}_12 Order 432 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^8, (S * R^-1 * S)^3, S^-1 * R^-1 * S * R^-3 * S^-1 * R * S^-3 ] C46.5 : Type {6,18}_18 Order 324 mV = 3 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S * R^2 * S^-1 * R^2 * S * R^-1 * S * R^-1, R^-1 * S * R * S^-1 * R^2 * S^-4 ] C46.6 : Type {10,25}_50 Order 250 mV = 5 mF = 1 Defining relations for automorphism group: [ (R * S)^2, S^2 * R^-3 * S^-1 * R * S^2 ] C46.7 : Type {10,25}_50 Order 250 mV = 5 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R * S^-2 * R^-2 * S^-3 * R ] C46.8 : Type {24,24}_6 Order 216 mV = 3 mF = 3 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R * S^-1 * R^2 * S * R^-1 * S, S * R^5 * S^3 * R^-1, S^-1 * R^6 * S^-1 * R * S^-1 * R^2 ] C49.1 : Type {4,5}_12 Order 1920 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^-5, S * R^-1 * S * R * S^-1 * R * S^-1 * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S * R^-1 * S * R^-1 * S, (R * S^-2 * R * S^-1)^4 ] C49.2 : Type {4,6}_8 Order 1152 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^6, S * R * S^-1 * R^-1 * S * R * S^-1 * R^-2 * S^-1 * R * S * R^-1 * S^-1 * R * S, S^-1 * R * S^-1 * R^-1 * S * R^-1 * S^2 * R^-1 * S^-1 * R * S^2 * R^-1 * S^-2 ] C49.3 : Type {5,5}_12 Order 960 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^-5, S^-5, (R * S^-1)^6, S^-1 * R * S^-1 * R^2 * S^-1 * R^2 * S * R^-1 * S^-2 * R * S^-1 ] C49.4 : Type {6,6}_24 Order 576 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, S * R * S^-2 * R^3 * S^3 * R^-2, (R * S^-1 * R)^4, (R * S^-2 * R * S^-1 * R)^2, S^-2 * R^-1 * S * R * S^-1 * R^2 * S * R^-1 * S^-2 * R * S^-1 ] C49.5 : Type {6,6}_12 Order 576 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, (R * S^-1)^4, S^-1 * R^2 * S^-1 * R^3 * S^2 * R^-1 * S^-2 ] C49.6 : Type {6,12}_8 Order 384 mV = 2 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^-2 * R * S^-1 * R^2 * S * R^-1 * S^-2, R^2 * S^-2 * R^3 * S^-1 * R * S^3 ] C49.7 : Type {6,12}_8 Order 384 mV = 2 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^-2 * R * S^-1 * R^2 * S * R^-1 * S^-2, R^2 * S^-2 * R^3 * S^-1 * R * S^-3 ] C49.8 : Type {28,28}_4 Order 224 mV = 4 mF = 4 Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^2 * R^-1, R^-2 * S^12 * R^-1 * S * R^-9 * S^2 * R^-1 ] C49.9 : Type {28,28}_4 Order 224 mV = 4 mF = 4 Defining relations for automorphism group: [ (R * S)^2, S^-1 * R^-1 * S * R^2 * S * R^-1 * S^-1, S * R^5 * S * R^-1 * S^2, R^-10 * S^2 * R^-1 * S ] C50.1 : Type {4,6}_12 Order 1176 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^6, (R * S^-2)^4, S^-1 * R^-1 * S * R * S^-1 * R * S^-1 * R^-2 * S^-1 * R * S^-1 * R * S^-2 * R ] C50.2 : Type {6,6}_98 Order 588 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-1 * R)^2, S^6, S^-1 * R^-1 * S^2 * R * S^-2 * R * S^-2 * R * S^-1 * R * S^2 * R^-1 * S^2 * R^-1 * S^-2 * R * S^-2 ] C50.3 : Type {6,6}_14 Order 588 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, R * S^-1 * R * S^-1 * R^3 * S^-1 * R * S^3 ] C50.4 : Type {6,6}_14 Order 588 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, S * R * S^-2 * R^3 * S^3 * R^-2, (R * S^-2 * R * S^-1 * R)^2, S * R^-1 * S * R * S^-1 * R^2 * S * R^-1 * S^-1 * R * S ] C50.5 : Type {6,24}_56 Order 336 mV = 4 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^-2 * R^-1 * S * R^2 * S^-3 * R, S^-2 * R^2 * S^-1 * R^2 * S^-5 ] C50.6 : Type {6,24}_56 Order 336 mV = 8 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, R * S^-4 * R^-1 * S * R^-3 * S^-1 * R * S^2 ] C50.7 : Type {18,18}_14 Order 252 mV = 3 mF = 6 Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S * R^-2, S * R^2 * S^-1 * R^2 * S^4, S * R * S^-2 * R^2 * S^2 * R^-1 * S, S * R^-12 * S^5 ] C51.1 : Type {3,12}_8 Order 1200 mV = 1 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, (R * S^-2)^4, S^12, S^-1 * R * S^-6 * R^-1 * S^2 * R^-1 * S^-3 * R * S^-4 ] C51.2 : Type {4,8}_8 Order 800 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-1)^4, S^8, S^-1 * R * S^-3 * R * S^-1 * R * S^2 * R^-1 * S^-3, S * R * S^-1 * R^-1 * S * R * S^-1 * R^-2 * S^-1 * R * S * R^-1 * S^-1 * R * S ] C51.3 : Type {4,8}_200 Order 800 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, R^-1 * S * R^-1 * S * R * S^-1 * R^-1 * S * R^-1 * S * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S^-1 * R * S^-1 * R * S^-1 * R * S^2 * R * S^-1 ] C51.4 : Type {4,8}_200 Order 800 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, S * R^-1 * S * R^-1 * S * R^-1 * S * R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S * R^-1 * S * R^-1 * S^-1 * R * S^-2 * R^-1 ] C51.5 : Type {4,12}_6 Order 600 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^-3 * R * S^-1 * R^2 * S^3 * R^-1 * S^-1 ] C51.6 : Type {4,12}_150 Order 600 mV = 3 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^12, R^-1 * S * R^-1 * S * R^-1 * S * R^-1 * S * R^2 * S^2 * R^-1 * S^-2 * R * S^2 ] C51.7 : Type {4,24}_120 Order 480 mV = 6 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S^-1 * R * S^-1, S^24 ] C51.8 : Type {4,24}_120 Order 480 mV = 6 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^-1 * R^-1 * S * R^-1 * S * R * S^-1 * R^-2 * S^-1 * R * S^-1 * R * S^-1 * R * S^-1, R^-1 * S^5 * R * S^-1 * R^2 * S^-2 * R * S^2 * R^-1 * S^-2 ] C51.9 : Type {4,44}_110 Order 440 mV = 11 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, R * S^-2 * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S^-1, S^11 * R^2 * S * R^-1 * S^-2 * R * S^8 ] C51.10 : Type {8,8}_10 Order 400 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-2 * R)^2, (R * S^-1)^4, S * R * S^-1 * R^4 * S^4 * R^-1 ] C51.11 : Type {8,8}_50 Order 400 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, S^-1 * R * S^-1 * R * S^-2 * R^-1 * S * R^-2 * S^-1 * R * S^-1 * R * S^-1 * R ] C51.12 : Type {8,8}_4 Order 400 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^-1 * S * R^2 * S * R^-1 * S^-1, (R * S^-1)^4, S^8, R * S^-2 * R^4 * S^3 * R^-1 * S^-1 ] C51.13 : Type {8,8}_100 Order 400 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, S^2 * R * S^-1 * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S * R^-1 * S * R^-1 ] C51.14 : Type {8,16}_80 Order 320 mV = 4 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, (R * S^-3)^2, S^-3 * R^4 * S^-5, S * R^2 * S^-2 * R^2 * S^2 * R^-1 * S * R^-1 ] C51.15 : Type {8,16}_80 Order 320 mV = 4 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, (R * S^-3)^2, S^-3 * R^4 * S^-5, R * S^-2 * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S^-1 ] C51.16 : Type {12,12}_10 Order 300 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, (S^-1 * R)^3, S^-2 * R^4 * S * R^-1 * S^-2 ] C51.17 : Type {12,12}_50 Order 300 mV = 3 mF = 3 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, R^12, R^-2 * S^2 * R * S^-1 * R^-2 * S * R^-1 * S^-1 * R * S^2 ] C51.18 : Type {24,24}_10 Order 240 mV = 6 mF = 6 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S * R^-1 * S * R^2 * S^-1 * R * S, S^-1 * R^6 * S^-1 * R * S^-1 * R^9 * S^-1 * R^4 ] C51.19 : Type {24,24}_20 Order 240 mV = 6 mF = 6 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S^-1 * R^6 * S^-1 * R * S^-1 * R * S^-1 ] C51.20 : Type {44,44}_10 Order 220 mV = 11 mF = 11 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S * R * S^-1 * R^2 * S * R^-1 * S, R * S^-3 * R^2 * S^-2 * R^6 * S^-1 * R * S^-3 * R * S^-2 ] C52.1 : Type {6,54}_54 Order 324 mV = 18 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^-1 * R^2 * S^-1 * R^2 * S * R^-1 * S^-1 * R, S^9 * R * S^-1 * R * S^4 * R^-1 * S^-1 * R * S^3 ] C52.2 : Type {16,16}_34 Order 272 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R * S^-1 * R^3 * S^-2 * R ] C52.3 : Type {16,16}_34 Order 272 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, S^-1 * R^4 * S^-2 * R ] C53.1 : Type {4,8}_104 Order 832 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S * R^-1 * S^-1 * R * S^-1 * R * S^-1 * R * S^-2 * R^2 * S^-1 ] C53.2 : Type {4,8}_52 Order 832 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, R^-1 * S * R^-1 * S^2 * R * S^-1 * R * S^-1 * R * S^-1 * R * S * R^-1 * S^-1 * R * S^-1 * R * S^-1 * R * S^-2 * R * S^-1 * R^-1 * S ] C53.3 : Type {4,12}_156 Order 624 mV = 3 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^12, R * S^-1 * R^-1 * S * R * S^-1 * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S^-1 * R * S^-1 * R * S^-2 ] C53.4 : Type {4,20}_130 Order 520 mV = 5 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^-2 * R^-1 * S^2 * R * S^-1 * R^-2 * S^-2 * R * S^2 * R^-1 * S^-1 ] C53.5 : Type {6,6}_52 Order 624 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-1 * R)^2, S^6, S^-1 * R^-1 * S^2 * R * S^-2 * R * S^-2 * R * S^-1 * R * S * R^-1 * S^-2 * R * S^-1 * R * S * R^-1 * S^-1 * R * S^-2 ] C53.6 : Type {6,15}_130 Order 390 mV = 5 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^-1 * R^2 * S^-1 * R^-3 * S * R^-2 * S * R^-1 * S^-1 ] C53.7 : Type {8,8}_52 Order 416 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, R^2 * S * R^-1 * S^-2 * R^-1 * S * R * S^-1 * R^-2 * S * R^-1 * S * R^-1 * S^-1 * R * S^-2 ] C53.8 : Type {8,8}_52 Order 416 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, R^2 * S * R^-1 * S^-2 * R^-1 * S * R * S^-1 * R^-2 * S * R^-1 * S * R^-1 * S^-1 * R * S^2 ] C53.9 : Type {12,12}_26 Order 312 mV = 3 mF = 3 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, R^12, S^-1 * R * S^-1 * R * S^-1 * R^2 * S^-2 * R * S^-1 * R ] C53.10 : Type {12,12}_26 Order 312 mV = 2 mF = 4 Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S * R^-2, S * R^2 * S^-1 * R^2 * S^4, R^12, R * S^-3 * R * S^-1 * R * S^-2 * R * S^-2 ] C53.11 : Type {12,12}_26 Order 312 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, S^-1 * R^-1 * S * R^3 * S * R^-2 * S^-1, S^3 * R^3 * S^-1 * R * S^2, R^12 ] C53.12 : Type {16,32}_32 Order 256 mV = 8 mF = 4 Defining relations for automorphism group: [ (R * S)^2, (R * S^-1 * R^2)^2, (R * S^-1)^4, (R * S^-3)^2, S^-1 * R^6 * S * R^-1 * S^-1 * R * S^-1, S^-2 * R^-1 * S * R^3 * S^-5 ] C53.13 : Type {20,20}_26 Order 260 mV = 5 mF = 5 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S^-2 * R * S^-1 * R^2 * S^-1 * R * S^-1 * R ] C55.1 : Type {4,6}_18 Order 1296 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^6, S * R * S^-1 * R * S^-1 * R^2 * S^-1 * R * S * R^-1 * S, (R * S^-2)^6 ] C55.2 : Type {4,8}_24 Order 864 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^8, S * R^-1 * S * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S, (R * S^-1)^6 ] C55.3 : Type {4,16}_16 Order 576 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S * R * S^-1 * R * S^-1 * R^2 * S^-1 * R * S * R^-1 * S, S^-1 * R * S^-3 * R^2 * S^-1 * R * S^-3, S^16 ] C55.4 : Type {4,16}_16 Order 576 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S * R * S^-3 * R^2 * S^-1 * R * S^3 ] C55.5 : Type {6,6}_12 Order 648 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, S * R^-1 * S * R^2 * S^-1 * R * S, R^2 * S^-3 * R * S^-1 * R^3 * S * R^-1 * S * R^-1 * S * R^-1 * S^-2 ] C55.6 : Type {6,9}_18 Order 486 mV = 3 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^-9, S^-1 * R^-2 * S * R^2 * S^-1 * R^2 * S^-1 * R^3 * S * R^-1 * S * R^-1 * S * R ] C55.7 : Type {8,8}_6 Order 432 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S * R * S^-1 * R^2 * S * R^-1 * S, R^2 * S^-1 * R^4 * S^-1 * R * S * R^-1 * S^-1 ] C55.8 : Type {16,16}_6 Order 288 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R * S^-1 * R^2 * S * R^-1 * S, S * R^5 * S^3 * R^-1, R^-3 * S * R^-8 * S^2 * R^-1 * S ] C55.9 : Type {16,16}_12 Order 288 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, S^-2 * R^3 * S^-1 * R * S^-1 ] C56.1 : Type {5,10}_110 Order 550 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-5, (R * S^-3 * R)^2, (R * S^-2 * R * S^-1)^2, R * S^-2 * R^-1 * S * R^2 * S^2 * R^-2 * S^-1 ] C56.2 : Type {5,10}_110 Order 550 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-5, (R * S^-3 * R)^2, (R * S^-2 * R * S^-1)^2, S^-3 * R * S^-1 * R^-2 * S^-1 * R * S * R^-1 * S^-2 ] C56.3 : Type {10,15}_66 Order 330 mV = 3 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-5 * S * R^-1 * S^-2 ] C56.4 : Type {10,15}_66 Order 330 mV = 3 mF = 1 Defining relations for automorphism group: [ (R * S)^2, S^-3 * R^-2 * S^-1 * R * S^-1 * R ] C57.1 : Type {3,12}_56 Order 1344 mV = 2 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, (R * S^-5)^2, S^-1 * R * S^-3 * R^-1 * S^2 * R^-1 * S^2 * R * S^-2 * R * S^-2 * R * S^-1 * R * S^2 * R^-1 * S^-2 * R * S^-2 * R * S^-2 * R * S^-2 * R * S^-1 ] C57.2 : Type {6,6}_56 Order 672 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, S * R * S^-1 * R^3 * S^2 * R^-2, R^-1 * S^-3 * R^-1 * S * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^3 * R^-1 * S ] C57.3 : Type {12,12}_28 Order 336 mV = 2 mF = 2 Defining relations for automorphism group: [ (R * S)^2, S * R * S^-1 * R^3 * S^2 * R^-2, S * R^2 * S^-1 * R^2 * S^4, S * R * S^-2 * R^2 * S * R^-1 * S^2, R^12 ] C58.1 : Type {3,12}_114 Order 1368 mV = 1 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, S^12, (S^2 * R^-1 * S^2)^3, S^-2 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^2 * R * S^-1 * R * S^3 * R^-1 * S^2 * R^-1 * S^-3 * R * S^-1 ] C58.2 : Type {6,6}_114 Order 684 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, S^-1 * R^2 * S^-1 * R^3 * S^-1 * R^2 * S^-1 * R, S * R * S^-2 * R^3 * S^3 * R^-2, S * R * S^-1 * R * S^-2 * R^-2 * S^2 * R^-1 * S^3 * R^-1 * S ] C58.3 : Type {6,6}_114 Order 684 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-1 * R)^2, S^6, R^-1 * S^2 * R * S^-1 * R * S^-2 * R * S^-2 * R^-2 * S^-2 * R * S^-2 * R * S^-1 * R * S^3 * R^-1 * S ] C58.4 : Type {6,12}_76 Order 456 mV = 2 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S * R * S^-1 * R^3 * S^2 * R^-2, S * R^2 * S^-1 * R^2 * S^4, S * R * S^-2 * R * S^-1 * R^-2 * S^3 * R^-1 * S^2 * R^-1 * S ] C58.5 : Type {6,12}_76 Order 456 mV = 4 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^12, R * S^-1 * R^2 * S^-1 * R^-3 * S * R^-2 * S * R^-1 * S * R^-1 * S ] C58.6 : Type {9,18}_38 Order 342 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-9, R^-1 * S * R^-3 * S^3 * R^-1 ] C58.7 : Type {9,18}_38 Order 342 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, S * R^-1 * S * R^2 * S^-1 * R * S, R^-9, R^-2 * S * R^-2 * S * R^-1 * S^2 ] C58.8 : Type {9,18}_38 Order 342 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-9, S^3 * R^-2 * S * R^-1 * S^2 ] C58.9 : Type {9,18}_38 Order 342 mV = 3 mF = 3 Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S * R^-2, R^-9, S^2 * R^-3 * S^4, R^-1 * S * R * S^-2 * R * S^-2 * R^-1 * S^2 * R^-1 * S * R^-1 * S^-2 ] C59.1 : Type {4,8}_232 Order 928 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, R * S^-1 * R * S^-1 * R^-1 * S * R^-1 * S * R * S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S * R^-1 * S * R^-1 * S^-1 * R * S^-2 * R * S^-1 ] C59.2 : Type {4,8}_232 Order 928 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, R^-1 * S^-2 * R * S^-1 * R^-1 * S * R^-1 * S * R * S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S * R^-1 * S^-1 * R * S * R^-1 * S * R^-1 * S ] C59.3 : Type {4,12}_174 Order 696 mV = 3 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^12, R^-1 * S * R * S^-1 * R^-1 * S * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S * R^-1 * S * R^-1 * S^-2 ] C59.4 : Type {7,14}_58 Order 406 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-7, S * R^-1 * S * R^2 * S^-1 * R * S ] C59.5 : Type {7,14}_58 Order 406 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-7, S^2 * R^-1 * S * R^2 * S^-2 * R * S, S^3 * R^-3 * S^-1 * R * S * R^-1 * S ] C59.6 : Type {7,14}_58 Order 406 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-7, S * R * S^-1 * R^-3 * S * R^-3 * S ] C59.7 : Type {8,8}_58 Order 464 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, R * S^-1 * R * S^-1 * R^-1 * S * R^2 * S^-2 * R^-2 * S * R^-1 * S * R^-1 * S * R^-1 * S^-2 ] C59.8 : Type {8,8}_116 Order 464 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, R * S^-1 * R * S^-1 * R^-1 * S * R^-1 * S * R * S^-1 * R^-2 * S * R^-1 * S * R^-1 * S * R^-1 * S^-2 ] C59.9 : Type {12,12}_58 Order 348 mV = 3 mF = 3 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, R^12, R^-2 * S * R^-1 * S^2 * R^-2 * S * R^-1 * S^-2 * R * S^-1 ] C61.1 : Type {4,6}_10 Order 1440 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^6, S^-1 * R * S^-1 * R * S^-1 * R^-1 * S * R^-2 * S * R^-1 * S * R^-1 * S * R^-1 * S^-1, (R * S^-1)^8, S^-1 * R * S^-2 * R * S^-2 * R^-2 * S^-1 * R * S^2 * R^-1 * S * R^-1 * S^-1 * R ] C61.2 : Type {4,12}_20 Order 720 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S * R * S^-3 * R^2 * S^-3 * R * S, S^12, R^-1 * S * R^-1 * S * R^-1 * S * R^2 * S^-2 * R * S^3 ] C61.3 : Type {4,16}_80 Order 640 mV = 4 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^-1 * R^-1 * S * R^-1 * S * R * S^-1 * R^-2 * S^-1 * R * S^-1 * R * S^-1 * R * S^-1, S^16 ] C61.4 : Type {4,16}_80 Order 640 mV = 4 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, R * S^-1 * R^-1 * S^2 * R * S^-2 * R^2 * S^-1 * R * S^2 * R^-1 * S * R^-1 * S ] C61.5 : Type {4,28}_140 Order 560 mV = 7 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S^-1 * R * S^-1, S^28 ] C61.6 : Type {4,52}_130 Order 520 mV = 13 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, R * S^-2 * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S^-1, S^13 * R^2 * S * R^-1 * S^-2 * R * S^10 ] C61.7 : Type {6,6}_8 Order 720 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, (S^-1 * R)^5, S^-1 * R^-1 * S * R * S^-1 * R^2 * S^-1 * R * S^-2 * R ] C61.8 : Type {6,18}_36 Order 432 mV = 6 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, R^-1 * S * R^-2 * S * R^3 * S^-1 * R * S * R^-1 * S^-2 ] C61.9 : Type {6,63}_126 Order 378 mV = 21 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^-1 * R^2 * S^-1 * R^2 * S * R^-1 * S^-1 * R, S^-11 * R^3 * S^5 * R * S^-5 ] C61.10 : Type {12,12}_30 Order 360 mV = 3 mF = 3 Self-dual Defining relations for automorphism group: [ (R * S)^2, (R * S^-1 * R^2)^2, (R * S^-3)^2, R^12, S * R * S^-2 * R^3 * S * R^-1 * S^-1 * R * S ] C61.11 : Type {12,12}_30 Order 360 mV = 3 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-2 * S * R^3 * S * R^-1 * S^-2, S * R * S^-3 * R * S^4, R^12 ] C61.12 : Type {16,16}_40 Order 320 mV = 4 mF = 4 Defining relations for automorphism group: [ (R * S)^2, S^-1 * R^4 * S^-3, S^-1 * R^2 * S^-1 * R^3 * S * R^-1 * S^-1 * R^2, S^-1 * R^-1 * S * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S^-1 ] C61.13 : Type {16,16}_20 Order 320 mV = 4 mF = 4 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S^-1 * R^-1 * S * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S^-1 ] C61.14 : Type {16,16}_20 Order 320 mV = 4 mF = 4 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S * R^-1 * S * R * S^-1 * R^2 * S^-1 * R * S^2 * R^-1, R^-1 * S^3 * R^-9 * S^3 ] C61.15 : Type {28,28}_10 Order 280 mV = 7 mF = 7 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S * R^-1 * S * R^2 * S^-1 * R * S, R^-1 * S^4 * R^-1 * S * R^-3 * S * R^-9 * S * R^-1 * S^3 * R^-1 * S^2 ] C61.16 : Type {30,45}_18 Order 270 mV = 15 mF = 5 Defining relations for automorphism group: [ (R * S)^2, S * R^5 * S^2 * R^-1 * S, S * R * S^-1 * R^3 * S^4, R^-1 * S * R^-1 * S * R^-8 * S^3 ] C61.17 : Type {52,52}_10 Order 260 mV = 13 mF = 13 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S * R^-1 * S * R^2 * S^-1 * R * S, R^-2 * S^2 * R^-1 * S * R^-3 * S * R^-9 * S * R^-1 * S^3 * R^-1 * S ] C62.1 : Type {5,10}_122 Order 610 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-5, (R * S^-3 * R)^2, (R * S^-2 * R * S^-1)^2, R^2 * S^-1 * R * S^-1 * R^-2 * S^-1 * R * S * R^-1 * S^-2 ] C62.2 : Type {5,10}_122 Order 610 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-5, (R * S^-3 * R)^2, (R * S^-2 * R * S^-1)^2, S^-1 * R^-1 * S * R * S^-1 * R^-2 * S^-2 * R * S^-3 ] C62.3 : Type {6,6}_122 Order 732 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-1 * R)^2, S^6, R * S^-1 * R * S^-2 * R^-1 * S^2 * R^-1 * S^2 * R * S^-1 * R^-2 * S^2 * R^-1 * S^3 * R^-2 * S^-1 * R * S^-2 * R * S^2 ] C63.1 : Type {3,12}_248 Order 1488 mV = 2 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, (R * S^-5)^2, S * R^-1 * S^2 * R^-1 * S^3 * R^-1 * S^2 * R * S^-2 * R * S^-2 * R^-1 * S * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S ] C63.2 : Type {35,35}_4 Order 280 mV = 5 mF = 5 Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S * R^-1 * S, R^-22 * S^2 * R^-10 * S ] C64.1 : Type {3,12}_42 Order 1512 mV = 1 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, S^12, (S^2 * R^-1 * S^2)^3, S * R^-1 * S^2 * R * S^-2 * R * S^-2 * R * S^-2 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S ] C64.2 : Type {3,18}_42 Order 1134 mV = 3 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, S * R * S^-5 * R * S^6, (S^2 * R^-1 * S^2)^3, S^-2 * R^-1 * S^2 * R * S^-2 * R^-1 * S^2 * R * S^-2 * R * S^-1 * R * S^-2 * R * S^-2 * R * S^-2 * R * S^-1 ] C64.3 : Type {3,24}_84 Order 1008 mV = 2 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, S^-2 * R^-1 * S^2 * R^-1 * S^3 * R * S^-1 * R * S^-3 * R * S^-1, S * R * S^-5 * R^-1 * S * R^-1 * S^-5 * R * S^2 ] C64.4 : Type {6,6}_42 Order 756 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, S * R * S^-2 * R^3 * S^3 * R^-2, (R * S^-2 * R * S^-1 * R)^2, S^-1 * R^-1 * S * R * S^-1 * R^2 * S * R^-1 * S * R^-1 * S^-1 ] C64.5 : Type {6,6}_42 Order 756 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-1 * R)^2, S^6, S * R * S^-1 * R^-1 * S * R * S^-1 * R^-1 * S * R * S^-2 * R * S^-2 * R^-2 * S^-1 * R * S^3 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S ] C64.6 : Type {6,6}_42 Order 756 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, S^-1 * R^2 * S^-1 * R^3 * S^-1 * R^2 * S^-1 * R, S * R * S^-2 * R^3 * S^3 * R^-2, S^-1 * R * S^-3 * R * S^-1 * R^-2 * S^-2 * R * S^-2 * R * S^-1 ] C64.7 : Type {6,12}_84 Order 504 mV = 2 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, R * S^-3 * R^2 * S * R^-1 * S^-2, S^12 ] C64.8 : Type {6,12}_84 Order 504 mV = 4 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^12, R^-1 * S * R^2 * S^-1 * R^-3 * S * R^-2 * S * R^-2 * S^-2 ] C64.9 : Type {6,12}_84 Order 504 mV = 2 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S * R * S^-1 * R^3 * S^2 * R^-2, S * R^2 * S^-1 * R^2 * S^4, S^2 * R * S^-2 * R * S^-1 * R^-2 * S^2 * R^-1 * S^2 * R^-1 * S ] C64.10 : Type {6,12}_84 Order 504 mV = 2 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^-2 * R * S^-1 * R^3 * S^-1 * R^2 * S^-2 ] C64.11 : Type {6,30}_70 Order 420 mV = 5 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, R * S^-3 * R^2 * S * R^-1 * S^-2, S^-3 * R^-1 * S^2 * R^-2 * S^4 * R^-1 * S^-1 ] C64.12 : Type {6,30}_70 Order 420 mV = 10 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, R^-1 * S^3 * R^-2 * S * R^-2 * S * R^-1 * S^-5 ] C64.13 : Type {8,12}_24 Order 432 mV = 3 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-3)^2, S^-1 * R * S^-1 * R^4 * S^-1 * R^3 * S^-1, R^2 * S^-2 * R^3 * S^2 * R^-1 * S^-2 ] C64.14 : Type {8,12}_8 Order 432 mV = 3 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-3)^2, R * S^-2 * R^3 * S^-1 * R * S^-1 * R ] C64.15 : Type {8,12}_24 Order 432 mV = 3 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-3)^2, S^-1 * R^-1 * S * R^3 * S^-1 * R * S^-1 * R ] C64.16 : Type {9,18}_42 Order 378 mV = 3 mF = 3 Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S * R^-2, R^-9, S^2 * R^-3 * S^4, R^-1 * S * R * S^-1 * R * S^-3 * R^-1 * S^2 * R^-1 * S * R^-1 * S^-2 ] C64.17 : Type {12,24}_56 Order 336 mV = 4 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R * S^-2 * R^3 * S * R^-1 * S^-1 * R, S * R^-1 * S^2 * R^2 * S^3 * R^-1 ] C64.18 : Type {12,24}_56 Order 336 mV = 8 mF = 2 Defining relations for automorphism group: [ (R * S)^2, S * R^5 * S^2 * R^-1 * S, S^-1 * R^-1 * S * R^3 * S^-1 * R^2 * S^-1 ] C64.19 : Type {18,18}_18 Order 324 mV = 3 mF = 2 Defining relations for automorphism group: [ (R * S)^2, S * R^5 * S^3 * R^-1, S * R * S^-1 * R^3 * S^2 * R^-2, S^-1 * R^2 * S^-2 * R^9 * S^-2 * R * S^-1 ] C64.20 : Type {21,42}_14 Order 294 mV = 7 mF = 7 Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S * R^-2, S * R^2 * S^-1 * R^2 * S^4, S * R * S^-2 * R^2 * S * R^-1 * S^2, R^12 * S^-2 * R * S^-1 * R * S^-3 * R ] C65.1 : Type {4,6}_48 Order 1536 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^6, S * R^-1 * S * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S, S^2 * R * S^-1 * R * S^-1 * R^-1 * S * R * S^-1 * R * S^-1 * R^2 * S^2 * R^-1 * S^3 * R^-1 * S^2 * R^-1 ] C65.2 : Type {4,8}_16 Order 1024 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^8, (R * S^-2)^4, S * R * S^-3 * R * S^-1 * R * S^4 * R^-1 * S, S^-1 * R^-1 * S * R * S^-1 * R * S^-1 * R^-2 * S^-1 * R * S^-1 * R * S^-2 * R ] C65.3 : Type {4,8}_8 Order 1024 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^8, S^2 * R * S^-1 * R * S^-1 * R^2 * S^-2 * R * S * R^-1 * S, S * R * S^-1 * R^-1 * S * R * S^-1 * R^-2 * S^-1 * R * S * R^-1 * S^-1 * R * S ] C65.4 : Type {4,12}_12 Order 768 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-5)^2, S^12, S * R * S^-2 * R * S^-1 * R^2 * S^-2 * R * S * R^-1 * S, S * R^-1 * S * R * S^-2 * R^2 * S^-1 * R * S^3 * R^-1 ] C65.5 : Type {4,12}_12 Order 768 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S * R^-1 * S * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S, (R * S^-2)^4, (R * S^-5)^2, S^12 ] C65.6 : Type {4,12}_24 Order 768 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S * R^-1 * S * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S, (R * S^-5)^2, S^12, S^-1 * R * S^-2 * R * S^-2 * R * S^3 * R^-1 * S^-2 ] C65.7 : Type {5,6}_10 Order 960 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-5, S^6, (S^-1 * R)^5, (R * S^-2)^4, S * R * S^-2 * R * S^-1 * R^2 * S^3 * R^-2 * S ] C65.8 : Type {6,6}_16 Order 768 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, S * R * S^-2 * R^3 * S^3 * R^-2, (R * S^-2 * R * S^-1 * R)^2, (R * S^-2)^4, R^2 * S^-1 * R^2 * S^-1 * R^2 * S * R^-1 * S * R^-1 * S^-2 ] C65.9 : Type {6,6}_16 Order 768 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, S * R * S^-1 * R^2 * S * R^-1 * S, R^-1 * S * R^2 * S^-2 * R^-1 * S * R^-2 * S^-1 * R * S^-1 * R * S^2 ] C65.10 : Type {6,6}_8 Order 768 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, S^-1 * R^2 * S^-1 * R^3 * S^-2 * R * S^-2, (S^-1 * R^2 * S^-1)^3 ] C65.11 : Type {6,15}_10 Order 480 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^-2 * R^-3 * S^2 * R^-1 * S^-1, S * R^2 * S^-1 * R^3 * S^-1 * R^2 * S * R^-1 ] C65.12 : Type {8,8}_16 Order 512 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^8, S * R * S^-1 * R^4 * S^2 * R^-3, S * R^2 * S^-1 * R^3 * S^2 * R^-1 * S^2, S^-1 * R * S^-2 * R^3 * S * R^-1 * S^-2 * R ] C65.13 : Type {8,8}_8 Order 512 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1)^4, S^8, R^-2 * S * R^3 * S^-1 * R * S^2, S^2 * R^-1 * S * R^2 * S^-2 * R * S ] C65.14 : Type {8,8}_8 Order 512 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^8, S^8, R^-2 * S * R^3 * S^-1 * R * S^2, S * R * S^-2 * R^2 * S * R^-1 * S^2 ] C65.15 : Type {12,12}_8 Order 384 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R * S^-1 * R^2 * S * R^-1 * S, R^12, S^-1 * R^6 * S^-5, R^2 * S^-2 * R^3 * S^-1 * R * S^-3 ] C65.16 : Type {12,12}_8 Order 384 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R * S^-1 * R^2 * S * R^-1 * S, R^12, S^-1 * R^6 * S^-5, R^2 * S^-2 * R^3 * S^-1 * R * S^3 ] C65.17 : Type {12,12}_8 Order 384 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R * S^-1 * R^3 * S * R^-1 * S^2, S^-1 * R^-1 * S * R^3 * S^-1 * R * S^-2 ] C65.18 : Type {14,21}_12 Order 336 mV = 3 mF = 1 Defining relations for automorphism group: [ (R * S)^2, S * R * S^-1 * R^3 * S^4, S^-1 * R^-5 * S * R^-3 * S^-1 ] C67.1 : Type {9,12}_72 Order 432 mV = 2 mF = 3 Defining relations for automorphism group: [ (R * S)^2, (R * S^-1 * R)^2, R^-9, (R * S^-5)^2, R * S^-2 * R * S^-1 * R^-2 * S^3 * R^-1 * S^2 ] C67.2 : Type {15,30}_22 Order 330 mV = 3 mF = 3 Defining relations for automorphism group: [ (R * S)^2, S * R * S^-1 * R^3 * S^4, R^-2 * S * R^3 * S^-1 * R * S^2, R^-3 * S * R^-9 * S * R^-1 ] C67.3 : Type {15,30}_22 Order 330 mV = 3 mF = 3 Defining relations for automorphism group: [ (R * S)^2, S * R * S^-1 * R^2 * S * R^-1 * S, S^2 * R^-1 * S * R^2 * S^-2 * R * S, R^-2 * S * R^-9 * S * R^-2 ] C68.1 : Type {6,6}_134 Order 804 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-1 * R)^2, S^6, S * R * S^-1 * R^-1 * S * R * S^-1 * R^-1 * S * R^-1 * S^2 * R * S^-2 * R^-2 * S^-1 * R * S^3 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S ] C69.1 : Type {4,8}_136 Order 1088 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, R^-1 * S^-2 * R * S^-1 * R^-1 * S * R * S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S * R^-1 * S^-1 * R * S^-1 * R * S * R^-1 * S^-1 * R * S^-2 * R^2 * S ] C69.2 : Type {4,8}_68 Order 1088 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, R^-1 * S^-2 * R * S^-1 * R^-1 * S * R^-1 * S * R * S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S * R^-1 * S^-1 * R * S^-1 * R * S * R^-1 * S^2 * R^-2 * S ] C69.3 : Type {4,12}_204 Order 816 mV = 3 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^12, R^-1 * S^2 * R * S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S * R^-1 * S * R^-1 * S^-1 * R * S ] C69.4 : Type {4,20}_170 Order 680 mV = 5 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, R^-1 * S * R * S^-1 * R^-1 * S * R * S^-1 * R^2 * S^-2 * R * S^2 * R^-1 * S^-2 ] C69.5 : Type {8,8}_68 Order 544 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, R^-1 * S * R^-2 * S^-1 * R * S^-1 * R * S^-2 * R^2 * S^-1 * R * S^2 * R^-1 * S * R^-1 * S ] C69.6 : Type {8,8}_68 Order 544 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, R * S^-1 * R * S^-1 * R * S^-1 * R * S^-2 * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 ] C69.7 : Type {8,8}_68 Order 544 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-2 * R)^2, (R * S^-1)^4, S * R * S^-1 * R^4 * S^3 * R^-1 * S ] C69.8 : Type {12,12}_34 Order 408 mV = 3 mF = 3 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, R^12, R^-1 * S * R * S^-1 * R * S^-1 * R * S^-1 * R^2 * S^-1 * R * S^-2 * R * S^-1 ] C69.9 : Type {20,20}_34 Order 340 mV = 5 mF = 5 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S^-1 * R * S^-2 * R^2 * S^-1 * R * S^-1 * R ] C70.1 : Type {6,72}_72 Order 432 mV = 24 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^-1 * R^2 * S^-1 * R^2 * S * R^-1 * S^-1 * R, S^12 * R^3 * S^-1 * R * S^11 ] C71.1 : Type {4,32}_160 Order 640 mV = 8 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, R * S^-2 * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S^-1, S^32 ] C71.2 : Type {4,32}_160 Order 640 mV = 8 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^-1 * R^-1 * S * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S * R^-1 * S^-2 * R, S * R * S^-6 * R^-1 * S * R^2 * S * R^-1 * S^-5 * R * S^2 ] C71.3 : Type {4,60}_30 Order 600 mV = 15 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S^-1 * R * S^-1, S^15 * R * S^-1 * R * S^5 * R^-1 * S^-1 * R * S^8 ] C71.4 : Type {6,33}_154 Order 462 mV = 11 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, R^2 * S^-1 * R * S^-1 * R^-3 * S * R^-1 * S * R^-2 * S * R^-1 * S, R * S^-4 * R^-1 * S * R^-3 * S^-1 * R * S^5 ] C71.5 : Type {8,12}_120 Order 480 mV = 3 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, (R * S^-3)^2, R * S^-2 * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S^-1, S^12 ] C71.6 : Type {8,12}_120 Order 480 mV = 3 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, (R * S^-3)^2, S * R^2 * S^-2 * R^2 * S^2 * R^-1 * S * R^-1, S^12 ] C71.7 : Type {8,40}_10 Order 400 mV = 10 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, (R * S^-3)^2, S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S^-1 * R * S^-1, R^-1 * S^2 * R * S^-2 * R^2 * S^-6 ] C71.8 : Type {8,40}_20 Order 400 mV = 10 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, (R * S^-3)^2, S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S^-1 * R * S^-1, R * S^-2 * R^-1 * S * R * S^-1 * R^-1 * S^6 ] C71.9 : Type {24,24}_14 Order 336 mV = 4 mF = 8 Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S * R^-2, S * R^2 * S^-1 * R^2 * S^4, S * R * S^-2 * R^2 * S^2 * R^-1 * S, S^2 * R^-2 * S * R^-14 * S^5 ] C71.10 : Type {24,24}_28 Order 336 mV = 4 mF = 8 Defining relations for automorphism group: [ (R * S)^2, S * R * S^-1 * R^3 * S^2 * R^-2, S * R^2 * S^-1 * R^2 * S^4, S^2 * R^-1 * S * R^2 * S^-2 * R * S, R^8 * S^-1 * R^2 * S^-1 ] C71.11 : Type {32,32}_10 Order 320 mV = 8 mF = 8 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S * R^-1 * S * R^2 * S^-1 * R * S, S^14 * R^-11 * S * R^-3 * S^3 ] C71.12 : Type {32,32}_20 Order 320 mV = 8 mF = 8 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S^2 * R^-1, R^-1 * S^3 * R^-7 * S^2 * R^-1 * S * R^-1 ] C71.13 : Type {60,60}_10 Order 300 mV = 15 mF = 15 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S * R^-1 * S * R^2 * S^-1 * R * S, R^-1 * S^6 * R^-1 * S * R^-3 * S * R^-9 * S * R^-1 * S^3 * R^-1 * S * R^-1 ] C72.1 : Type {5,10}_142 Order 710 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-5, (R * S^-3 * R)^2, (R * S^-2 * R * S^-1)^2, S * R * S^-1 * R * S^-1 * R^-2 * S^4 * R^-1 * S ] C72.2 : Type {5,10}_142 Order 710 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-5, (R * S^-3 * R)^2, (R * S^-2 * R * S^-1)^2, S^-1 * R * S^-1 * R^2 * S^-1 * R^2 * S * R^-1 * S^-4 ] C73.1 : Type {3,10}_24 Order 2160 mV = 1 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, S^10, S^2 * R * S^-2 * R * S^-4 * R^-1 * S^4 * R^-1 * S^3 * R^-1 * S, S * R * S^-3 * R * S^-3 * R * S^-1 * R * S^-4 * R * S^-2 * R * S^2 ] C73.2 : Type {4,7}_8 Order 1344 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^-7, (R * S^-1)^6, S * R * S^-1 * R^-1 * S * R * S^-1 * R^-2 * S^-1 * R * S * R^-1 * S^-1 * R * S, S^-1 * R * S^-1 * R^-1 * S^2 * R * S^-1 * R * S * R^-1 * S^2 * R^-1 * S^-2, S^-2 * R^-1 * S^2 * R * S^-1 * R * S^-1 * R^2 * S^-1 * R * S^-3 * R ] C73.3 : Type {4,8}_12 Order 1152 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^8, (R * S^-2)^4, S^-2 * R * S^-3 * R^2 * S^-1 * R * S^-1 * R * S^-2 ] C73.4 : Type {4,8}_8 Order 1152 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^8, S^-1 * R^-1 * S^2 * R * S^-1 * R * S^2 * R^-1 * S^-2, (R * S^-2)^4, S * R^-1 * S * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S^-1 * R * S^-1 * R * S ] C73.5 : Type {8,8}_24 Order 576 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1)^4, S^8, S * R * S^-1 * R^4 * S^-1 * R^3 * S ] C73.6 : Type {8,8}_12 Order 576 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-2 * R)^2, (R * S^-1)^4, S^-1 * R^-1 * S * R^4 * S^-1 * R * S^-3 ] C73.7 : Type {8,8}_8 Order 576 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, S^8, S * R^2 * S^-2 * R^2 * S^-1 * R * S^-1 * R * S, R * S^-4 * R^2 * S * R^-1 * S^-3 ] C73.8 : Type {8,8}_8 Order 576 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, S^8, S^-3 * R * S^-1 * R^2 * S^-3 * R * S^-1 ] C73.9 : Type {8,24}_6 Order 432 mV = 3 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1)^4, S * R * S^-1 * R^3 * S^4 ] C73.10 : Type {21,42}_4 Order 336 mV = 6 mF = 3 Defining relations for automorphism group: [ (R * S)^2, S^-1 * R^-1 * S * R^2 * S * R^-1 * S^-1, S * R^5 * S * R^-1 * S^2, R * S^-1 * R * S^-4 * R * S^-1 * R^8 * S^-4 ] C74.1 : Type {6,6}_146 Order 876 mV = 2 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^6, R^-2 * S^-1 * R * S^-1 * R^2 * S^2 * R^2 * S^-1 * R * S^-1 * R^4 * S * R^-2 * S * R^-2 * S^-1 * R^2 * S^-2 * R^-2 * S ] C74.2 : Type {8,8}_146 Order 584 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-2 * R)^2, (R * S^-1)^4, R * S^-1 * R^-1 * S * R^3 * S^-1 * R^2 * S^2 ] C75.1 : Type {3,12}_296 Order 1776 mV = 2 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, (R * S^-5)^2, S * R^-1 * S^2 * R^-1 * S^2 * R * S^-2 * R^-1 * S^2 * R * S^-2 * R * S^-2 * R^-1 * S * R^-1 * S^2 * R^-1 * S^-2 * R * S^2 * R^-1 * S^3 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S ] C75.2 : Type {4,8}_296 Order 1184 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S * R^-1 * S * R^-1 * S^-1 * R * S^-2 * R * S^-1 * R * S^-1 ] C75.3 : Type {4,8}_296 Order 1184 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S * R^-1 * S * R^-1 * S^-1 * R * S^2 * R * S^-1 * R * S^-1 ] C75.4 : Type {4,12}_222 Order 888 mV = 3 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^12, R^-1 * S * R * S^-1 * R^-1 * S * R^-1 * S * R * S^-1 * R * S^-1 * R^-2 * S^-1 * R * S * R^-1 * S^-1 * R * S^-1 * R * S^-2 ] C75.5 : Type {8,8}_74 Order 592 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, R^-1 * S * R^-2 * S^-2 * R^-1 * S * R^-1 * S * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S^2 * R^-1 * S * R^-1 * S ] C75.6 : Type {8,8}_148 Order 592 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, R^-1 * S * R^-2 * S^-2 * R^-1 * S * R^-1 * S * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S^-1 * R * S^2 * R^-1 * S ] C75.7 : Type {12,12}_74 Order 444 mV = 3 mF = 3 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, R^12, R * S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S * R^-1 * S^-2 ] C75.8 : Type {12,12}_74 Order 444 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, (S^-1 * R)^3, R^12, (R * S^-2 * R^3)^2, S^-1 * R^-1 * S * R^4 * S * R^-3 * S^-1 ] C76.1 : Type {9,24}_36 Order 432 mV = 2 mF = 3 Defining relations for automorphism group: [ (R * S)^2, (R * S^-1 * R)^2, R^-9, S^4 * R^-2 * S^-3 * R * S ] C77.1 : Type {6,6}_76 Order 912 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-1 * R)^2, S^6, S^-1 * R * S^-1 * R^-1 * S * R^-1 * S^2 * R * S^-1 * R * S^-3 * R^-1 * S * R^2 * S^2 * R^-1 * S^2 * R^-1 * S^-1 * R * S * R^-1 * S^-1 * R * S * R^-1 * S^-2 ] C77.2 : Type {6,15}_190 Order 570 mV = 5 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, R * S^-1 * R^-1 * S * R * S^-1 * R^-3 * S * R^-2 * S * R^-1 * S * R^-1 * S ] C77.3 : Type {12,12}_38 Order 456 mV = 2 mF = 4 Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S * R^-2, S * R^2 * S^-1 * R^2 * S^4, R^12, S^-1 * R * S^-2 * R * S^-1 * R^-2 * S^3 * R^-1 * S * R^-1 * S^-2 ] C77.4 : Type {42,42}_4 Order 336 mV = 6 mF = 6 Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S * R^-1 * S, R^-28 * S^2 * R^-10 * S * R^-1 ] C78.1 : Type {10,20}_44 Order 440 mV = 2 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^10, R * S^-2 * R^3 * S^-1 * R^2 * S^-1, R * S^-1 * R * S^-1 * R^2 * S^-4 ] C78.2 : Type {10,20}_44 Order 440 mV = 2 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^10, S * R * S^-1 * R^3 * S * R^-2 * S, S^-3 * R^3 * S^-1 * R * S^-2 ] C78.3 : Type {10,20}_44 Order 440 mV = 4 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^10, R * S^-1 * R^4 * S^-3 * R ] C78.4 : Type {10,20}_44 Order 440 mV = 4 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^10, (R * S^-2 * R^2)^2, (R * S^-1 * R * S^-1 * R)^2, R * S^-3 * R^2 * S^-2 * R * S^-1 ] C79.1 : Type {3,12}_312 Order 1872 mV = 2 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, (R * S^-5)^2, S * R^-1 * S^3 * R^-1 * S^2 * R * S^-2 * R^-1 * S^2 * R * S^-2 * R * S^-2 * R^-1 * S * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^-2 * R * S^2 * R^-1 * S^2 * R^-1 * S ] C79.2 : Type {4,16}_208 Order 832 mV = 4 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^16, S^-1 * R^-1 * S * R * S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S^-1 * R * S * R^-1 * S^-1 * R * S^-1 ] C79.3 : Type {4,16}_208 Order 832 mV = 4 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^16, S^-1 * R^-1 * S * R * S^-1 * R * S^-1 * R * S^-1 * R^2 * S^-1 * R * S * R^-1 * S^-1 * R * S * R^-1 * S^-1 ] C79.4 : Type {4,28}_182 Order 728 mV = 7 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^2 * R^2 * S^-1 * R * S^-2 * R * S^-1 * R^-2 * S * R^-1 * S * R^-1 * S^-1 * R * S * R^-1, R * S^-2 * R^-1 * S^2 * R * S^-2 * R^2 * S^-1 * R * S^7 ] C79.5 : Type {6,9}_234 Order 702 mV = 3 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^-9, R^-1 * S * R^2 * S^-1 * R^2 * S^-1 * R^3 * S * R^-2 * S * R^-2 * S^-1 * R^2 * S^-2 ] C79.6 : Type {6,9}_234 Order 702 mV = 3 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^-9, S^-1 * R^2 * S^-1 * R^2 * S^-1 * R^3 * S * R^-2 * S * R^-2 * S^-1 * R^2 * S^-1 * R ] C79.7 : Type {6,9}_234 Order 702 mV = 3 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^-9, R^-1 * S * R * S^-1 * R^-1 * S * R^2 * S^-1 * R^3 * S * R^-2 * S * R^-2 * S^-1 * R^2 * S^-2 ] C79.8 : Type {6,12}_104 Order 624 mV = 2 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-1 * R)^2, S^-2 * R^-3 * S^-4, S * R * S^-1 * R^-1 * S * R * S^-2 * R^-1 * S^2 * R * S^-1 * R * S^2 * R^-1 * S^-2 * R * S^-1 * R * S * R^-1 * S^-1 * R * S ] C79.9 : Type {6,21}_182 Order 546 mV = 7 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, R * S^-1 * R^-1 * S * R^-2 * S * R^2 * S * R^-1 * S^-1 * R * S^2 ] C79.10 : Type {6,81}_162 Order 486 mV = 27 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^-1 * R^2 * S^-1 * R^2 * S * R^-1 * S^-1 * R, S^-14 * R^3 * S * R^-1 * S^-12 ] C79.11 : Type {12,18}_72 Order 432 mV = 6 mF = 2 Defining relations for automorphism group: [ (R * S)^2, (R * S^-2)^2, R^12, (R * S^-1 * R^4)^2, S * R^2 * S^-1 * R^-3 * S^-1 * R^2 * S^-1 * R * S ] C79.12 : Type {12,18}_18 Order 432 mV = 6 mF = 1 Defining relations for automorphism group: [ (R * S)^2, (R * S^-2)^2, S^-1 * R^2 * S^-1 * R^2 * S * R^-1 * S^-1 * R, R^12, S * R * S^-1 * R^5 * S * R^-2 * S^3 ] C79.13 : Type {15,30}_26 Order 390 mV = 5 mF = 5 Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S * R^-2, S * R^2 * S^-1 * R^2 * S^4, S * R^-1 * S^2 * R * S^-1 * R * S^-2 * R * S^2, R^-15 ] C79.14 : Type {16,16}_26 Order 416 mV = 4 mF = 4 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S * R^-1 * S * R^-1 * S * R^2 * S^-1 * R * S^-1 * R * S, S^-3 * R * S^-1 * R^8 * S^-2 * R ] C79.15 : Type {16,16}_52 Order 416 mV = 4 mF = 4 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, R * S^-2 * R^-1 * S * R^2 * S^-1 * R * S^-1 * R * S^-1 ] C79.16 : Type {28,28}_26 Order 364 mV = 7 mF = 7 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S * R^-1 * S, R * S^-1 * R^6 * S^-1 * R * S^-1 * R * S^-2 ] C80.1 : Type {6,6}_158 Order 948 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-1 * R)^2, S^6, S^-1 * R^-1 * S * R^2 * S^-3 * R^-1 * S * R^-1 * S^2 * R * S^-1 * R^-1 * S * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^-2 * R * S^3 * R * S^-1 ] C81.1 : Type {4,8}_10 Order 1280 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^8, S^-2 * R^-1 * S^2 * R * S^-1 * R * S^3 * R^-1 * S^-2 ] C81.2 : Type {4,8}_20 Order 1280 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^8, S^-1 * R * S^-1 * R^-1 * S * R * S^-1 * R^-2 * S^-3 * R * S^-3 ] C81.3 : Type {4,8}_20 Order 1280 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^8, S * R^-1 * S * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S, S^-1 * R^-1 * S * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S^-2 * R * S^-1 * R, S^-1 * R * S^-1 * R^-1 * S^2 * R * S^-1 * R * S * R^-1 * S^2 * R^-1 * S^-2 ] C81.4 : Type {4,8}_40 Order 1280 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^8, S * R * S^-3 * R^2 * S^4 * R^-1, R * S^-1 * R * S^-1 * R^-1 * S * R^-1 * S * R^-1 * S * R^-1 * S * R^2 * S * R^-1 * S^-1 * R * S^-1 * R * S^-1 * R * S^-2 ] C81.5 : Type {4,8}_40 Order 1280 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S * R^-1 * S^-1 * R * S * R^-1 * S^-1 * R * S^-2 * R^2 * S^-2 * R * S^-1 ] C81.6 : Type {4,8}_40 Order 1280 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^8, S * R * S^-3 * R^2 * S^4 * R^-1, R * S^-1 * R * S^-1 * R^-1 * S * R^-1 * S * R^-1 * S * R^-1 * S * R^2 * S^-1 * R * S^-1 * R * S * R^-1 * S^-1 * R * S^-2 ] C81.7 : Type {4,8}_80 Order 1280 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S * R^-1 * S^-1 * R * S * R^-1 * S^-1 * R * S * R^-1 * S^-1 * R * S^-2 * R * S^-1 ] C81.8 : Type {4,12}_60 Order 960 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S * R * S^-1 * R * S^-1 * R^2 * S^-1 * R * S * R^-1 * S, (R * S^-2)^4, S^12, S * R^-1 * S * R * S^-3 * R^-2 * S^-1 * R * S^-3 * R * S ] C81.9 : Type {4,12}_120 Order 960 mV = 3 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^12, R * S^-2 * R^-1 * S * R^-1 * S * R * S^-1 * R * S^-1 * R * S^-1 * R^-2 * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 ] C81.10 : Type {4,20}_20 Order 800 mV = 5 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^-1 * R^-1 * S * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S * R^-1 * S^-2 * R, S^20 ] C81.11 : Type {4,36}_180 Order 720 mV = 9 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S^-1 * R * S^-1, S^36 ] C81.12 : Type {4,68}_170 Order 680 mV = 17 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, R * S^-2 * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S^-1, S^17 * R^2 * S * R^-1 * S^-2 * R * S^14 ] C81.13 : Type {6,8}_12 Order 768 mV = 2 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-3)^2, S^8, S * R * S^-1 * R * S^-1 * R^3 * S * R^-1 * S^2 * R^-2, S * R^2 * S^-2 * R^3 * S^-1 * R * S^2 * R^-2 ] C81.14 : Type {6,8}_12 Order 768 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^8, S^-2 * R * S^-1 * R^3 * S^-1 * R * S * R^-1 * S^-1, (R * S^-1 * R)^4, S^-1 * R^2 * S^-2 * R^3 * S^-2 * R * S^-3 ] C81.15 : Type {6,8}_12 Order 768 mV = 2 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-3)^2, S^8, (R * S^-1 * R)^4, R * S^-2 * R * S^-1 * R^2 * S * R^-1 * S * R^-1 * S^-1 ] C81.16 : Type {6,8}_24 Order 768 mV = 2 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-3)^2, S^8, R * S^-2 * R * S^-1 * R^2 * S * R^-1 * S * R^-1 * S^-1, R^2 * S^-1 * R^2 * S^-1 * R^2 * S^2 * R^-1 * S^-1 * R * S^-1 ] C81.17 : Type {6,8}_24 Order 768 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^8, S^-1 * R^-1 * S * R * S^-1 * R^2 * S * R^-1 * S^-2 * R, (R * S^-1 * R * S^-2 * R)^2, S^-1 * R * S^-3 * R^2 * S^-3 * R * S^-1 ] C81.18 : Type {6,8}_24 Order 768 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-1)^4, S^8, S^2 * R^-1 * S * R^3 * S^-2 * R^2 * S ] C81.19 : Type {8,8}_10 Order 640 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^8, S^-1 * R * S^-1 * R^3 * S^-3 * R ] C81.20 : Type {8,8}_10 Order 640 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S * R^-1 * S * R^2 * S^-1 * R * S, S * R * S^-2 * R^3 * S * R^-2 * S^2, (R * S^-1 * R)^4 ] C81.21 : Type {8,8}_10 Order 640 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^8, S^-3 * R^3 * S^-2 * R^2 ] C81.22 : Type {8,8}_40 Order 640 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, R^-1 * S^2 * R * S^-1 * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S^-1 * R * S^-1 * R * S^-1 * R * S * R^-1 * S * R^-1 * S ] C81.23 : Type {8,8}_20 Order 640 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, (R * S^-3)^2, S^8, R^-1 * S * R^-1 * S * R * S^-1 * R^-2 * S^-1 * R * S^2 * R^-1 * S * R^-1 * S ] C81.24 : Type {8,8}_40 Order 640 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, (R * S^-3)^2, S^8, S^-1 * R * S^-1 * R * S^-2 * R^-2 * S * R^-1 * S^-1 * R * S^-1 * R * S^-1 * R ] C81.25 : Type {8,8}_40 Order 640 mV = 2 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, (R * S^-3)^2, S^8, R^-1 * S * R^2 * S^-2 * R^-2 * S^-1 * R * S^2 * R^-1 * S * R^-1 * S ] C81.26 : Type {8,8}_20 Order 640 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, S^8, S^3 * R^3 * S^3 * R^-1, R^-1 * S * R^-1 * S * R * S^-1 * R^-2 * S^-1 * R * S^-1 * R * S^-1 * R * S^2 ] C81.27 : Type {8,8}_40 Order 640 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, S^8, S^3 * R^3 * S^3 * R^-1, R^-1 * S * R^2 * S^-2 * R^-2 * S^-1 * R * S^-1 * R * S^-1 * R * S^2 ] C81.28 : Type {8,8}_40 Order 640 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, R * S^-1 * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S * R^-1 * S^-1 * R * S^-1 * R * S^-1 * R * S * R^-1 * S * R^-1 * S^-2 ] C81.29 : Type {8,16}_8 Order 512 mV = 2 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^8, S * R * S^-2 * R^2 * S * R^-1 * S^2, S * R * S^-1 * R * S^-1 * R * S^2 * R^-1 * S ] C81.30 : Type {8,16}_8 Order 512 mV = 2 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, S * R * S^-2 * R^2 * S * R^-1 * S^2 ] C81.31 : Type {8,16}_8 Order 512 mV = 4 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-3)^2, R^-2 * S * R^3 * S^-1 * R * S^2 ] C81.32 : Type {8,16}_8 Order 512 mV = 4 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^8, R^-2 * S * R^3 * S^-1 * R * S^2, S * R * S^-3 * R * S^4 ] C81.33 : Type {8,16}_8 Order 512 mV = 2 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, S^-1 * R^-1 * S^2 * R^2 * S^-1 * R * S^-2 ] C81.34 : Type {8,24}_60 Order 480 mV = 6 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, (R * S^-3)^2, S * R^2 * S^-2 * R^2 * S^2 * R^-1 * S * R^-1, S^-2 * R^-1 * S * R * S^-2 * R * S * R^-1 * S^-6 ] C81.35 : Type {8,24}_60 Order 480 mV = 6 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, (R * S^-3)^2, R * S^-2 * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S^-1, S^-2 * R^-1 * S * R * S^-2 * R * S * R^-1 * S^-6 ] C81.36 : Type {12,12}_20 Order 480 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R * S^-1 * R^2 * S * R^-1 * S, R^12, S^-2 * R^5 * S^-1 * R * S^-1 * R^2 ] C81.37 : Type {12,12}_20 Order 480 mV = 3 mF = 3 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, R^12, R * S^-1 * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S * R^-1 * S^-1 * R * S^2 ] C81.38 : Type {16,48}_24 Order 384 mV = 12 mF = 4 Defining relations for automorphism group: [ (R * S)^2, (R * S^-1 * R^2)^2, (R * S^-1)^4, (R * S^-3)^2, S^-1 * R^6 * S * R^-1 * S^-1 * R * S^-1, S^-3 * R^2 * S^-2 * R * S * R^-1 * S^-6 ] C81.39 : Type {20,20}_20 Order 400 mV = 5 mF = 5 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S^2 * R^-1, R^3 * S^-3 * R * S^-1 * R^6 * S^-2 * R * S^-1 * R * S^-1 ] C81.40 : Type {36,36}_10 Order 360 mV = 9 mF = 9 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S * R^-1 * S * R^2 * S^-1 * R * S, R^-2 * S^9 * R^-2 * S * R^-3 * S^2 * R^-8 * S * R^-3 * S^5 ] C81.41 : Type {68,68}_10 Order 340 mV = 17 mF = 17 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S * R^-1 * S * R^2 * S^-1 * R * S, R^-1 * S * R^-8 * S * R^-2 * S * R^-11 * S * R^-3 * S^5 ] C82.1 : Type {3,8}_12 Order 3888 mV = 1 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, S^8, (R * S^-2)^6, S * R * S^-2 * R^-1 * S^2 * R * S^-2 * R * S^-1 * R * S^-2 * R * S^2 * R^-1 * S^-2 * R * S^2, S^-1 * R^-1 * S^3 * R * S^-3 * R * S^-3 * R * S^-1 * R * S^3 * R^-1 * S^3 * R^-1 * S^3 * R^-1 * S^-2 ] C82.2 : Type {3,24}_12 Order 1296 mV = 3 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, S^-1 * R * S^-3 * R * S^-2 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^-2, S^-1 * R^-1 * S^7 * R^-1 * S^-8 ] C82.3 : Type {4,8}_8 Order 1296 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^8, S^-1 * R^-1 * S^2 * R * S^-1 * R * S^2 * R^-1 * S^-2, (R * S^-2)^4, S^-1 * R * S^-1 * R^-1 * S * R^-1 * S * R * S^-1 * R * S^-1 * R * S^-2 * R * S * R^-1 * S^-1 ] C82.4 : Type {4,12}_18 Order 972 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, R^-1 * S^2 * R * S^-1 * R^2 * S^-3 * R * S^-1 ] C82.5 : Type {4,12}_18 Order 972 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3 * R * S^-1)^2, S^-4 * R * S^-1 * R * S^2 * R^-1 * S^-2 ] C82.6 : Type {4,12}_18 Order 972 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3 * R * S^-1)^2, S^12, R * S^-2 * R * S^-2 * R^2 * S^-1 * R * S^-4 ] C82.7 : Type {4,40}_40 Order 720 mV = 5 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S * R * S^-1 * R * S^-1 * R^2 * S^-1 * R * S * R^-1 * S, S^-1 * R * S^-3 * R^2 * S^-1 * R * S^-3, S^-10 * R^2 * S^-5 * R * S^2 * R^-1 * S^-3 ] C82.8 : Type {6,6}_18 Order 972 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, S^-1 * R^2 * S^-1 * R^3 * S^2 * R^-1 * S^-2, (R * S^-1)^6, R * S^-3 * R^-1 * S * R^2 * S^3 * R^-2 * S^-1 ] C82.9 : Type {8,8}_18 Order 648 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-2 * R)^2, (R * S^-1)^4, S * R^2 * S^-1 * R^4 * S * R^-2 * S^-1 * R * S ] C82.10 : Type {9,18}_6 Order 486 mV = 1 mF = 3 Defining relations for automorphism group: [ (R * S)^2, (R * S^-1 * R)^2, R^-9, (S * R^-1 * S)^3, R^-1 * S * R * S^-5 * R^-1 * S^6 ] C82.11 : Type {9,18}_18 Order 486 mV = 1 mF = 3 Defining relations for automorphism group: [ (R * S)^2, (R * S^-1 * R)^2, R^-9, R^-1 * S * R * S^-1 * R^-2 * S^-2 * R * S^-2, R^-1 * S * R * S^-5 * R^-1 * S^6 ] C82.12 : Type {9,18}_18 Order 486 mV = 1 mF = 3 Defining relations for automorphism group: [ (R * S)^2, (R * S^-1 * R)^2, R^-9, S * R^-1 * S^2 * R^2 * S^2 * R^-1 * S, S^2 * R * S^-5 * R^-2 * S^5 ] C82.13 : Type {12,24}_8 Order 432 mV = 3 mF = 3 Defining relations for automorphism group: [ (R * S)^2, S * R^5 * S * R^-3, R^-1 * S^3 * R^2 * S^2 * R^-1 * S ] C82.14 : Type {40,40}_6 Order 360 mV = 5 mF = 5 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R * S^-1 * R^2 * S * R^-1 * S, S * R^5 * S^3 * R^-1, R^-2 * S^2 * R^-13 * S * R^-2 ] C83.1 : Type {4,8}_328 Order 1312 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, S^-1 * R^-1 * S * R * S^-1 * R^-1 * S * R * S^-1 * R^-1 * S * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S * R^-1 * S * R^-1 * S^-1 * R * S^-1 * R * S * R^-1 * S^2 * R^-1 * S * R^-1 * S * R ] C83.2 : Type {4,8}_328 Order 1312 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, S^-1 * R^-1 * S * R * S^-1 * R^-1 * S * R * S^-1 * R^-1 * S * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S * R^-1 * S * R^-1 * S^-1 * R * S * R^-1 * S^-1 * R * S^-1 * R * S^-1 * R * S^2 * R ] C83.3 : Type {4,12}_246 Order 984 mV = 3 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^12, R * S^3 * R * S^-1 * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S * R^-1 * S * R^-1 * S * R^-1 * S^-2 ] C83.4 : Type {8,8}_82 Order 656 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S * R^-1 * S * R^-1 * S^-2 * R ] C83.5 : Type {8,8}_164 Order 656 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S * R^-1 * S^-2 * R * S^-1 * R ] C83.6 : Type {8,8}_82 Order 656 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-2 * R)^2, (R * S^-1)^4, S^-1 * R * S^-3 * R^2 * S * R^-1 * S^-3 ] C83.7 : Type {12,12}_82 Order 492 mV = 3 mF = 3 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, R^12, R^2 * S^-2 * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S^-1 * R * S^-1 * R * S^2 ] C85.1 : Type {3,12}_84 Order 2016 mV = 1 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, S^12, (S^2 * R^-1 * S^2)^3, S^2 * R * S^-2 * R^-1 * S^2 * R * S^-2 * R * S^-2 * R^-1 * S * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S ] C85.2 : Type {6,6}_84 Order 1008 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, S * R * S^-2 * R^3 * S^3 * R^-2, (R * S^-2 * R * S^-1 * R)^2, S^-1 * R * S^-2 * R * S^-1 * R * S^-2 * R * S^-2, S^-1 * R^-2 * S * R^2 * S^-1 * R^-3 * S * R^-2 * S^-1 * R * S^-1 * R^2 ] C85.3 : Type {6,6}_84 Order 1008 mV = 2 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^6, R * S^2 * R^2 * S * R^-1 * S^-2 * R^-1 * S * R^2 * S^-1 * R * S^-1 * R^-3 * S * R^-2 * S * R^-1 * S * R^-2 * S * R^-1 * S * R^2 * S^-1 * R ] C85.4 : Type {6,12}_56 Order 672 mV = 2 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-1 * R)^2, (R * S^-5)^2, S * R * S^-2 * R^-1 * S^2 * R^-1 * S * R^-1 * S^3 * R^-1 * S^2 * R^-1 * S ] C85.5 : Type {6,12}_28 Order 672 mV = 2 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S * R * S^-1 * R^3 * S^2 * R^-2, S * R^2 * S^-1 * R^2 * S^4, S * R * S^-1 * R * S^-3 * R^-1 * S * R^-1 * S^3 * R^-1 * S^2 * R^-1 * S ] C85.6 : Type {6,12}_56 Order 672 mV = 4 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S * R * S^-2 * R * S^3, S^-1 * R * S^-2 * R^3 * S^-2 * R * S^-1 * R, S * R^-2 * S * R^2 * S^-1 * R^-3 * S * R^-1 * S * R^-2 * S * R^-2 ] C85.7 : Type {6,12}_28 Order 672 mV = 4 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^12, R^2 * S^-1 * R * S^-1 * R^2 * S^-1 * R^-3 * S * R^-1 * S * R^-2 * S^-1 * R * S^2 ] C85.8 : Type {6,15}_210 Order 630 mV = 5 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, R^2 * S^-1 * R * S^-1 * R^-3 * S * R^-1 * S * R^-2 * S * R^-1 * S, S^-15 ] C85.9 : Type {6,39}_182 Order 546 mV = 13 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, R^2 * S^-1 * R * S^-1 * R^-3 * S * R^-1 * S * R^-2 * S * R^-1 * S, S^-3 * R^-1 * S * R * S^-1 * R^2 * S^-1 * R^2 * S^-7 ] C85.10 : Type {9,18}_28 Order 504 mV = 3 mF = 3 Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S * R^-2, R^-9, S^2 * R^-3 * S^4, S^-1 * R * S^-2 * R * S^-2 * R^-1 * S * R^2 * S^2 * R^-1 * S^-2 * R * S^-2 ] C85.11 : Type {12,12}_42 Order 504 mV = 2 mF = 4 Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S * R^-2, S * R^2 * S^-1 * R^2 * S^4, R^12, S * R^-1 * S^2 * R * S^-1 * R^-2 * S^3 * R^-1 * S^2 * R^-1 * S ] C85.12 : Type {12,12}_42 Order 504 mV = 2 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^-2 * S * R^3 * S * R^-1 * S^-2, R^12, S^-1 * R^6 * S^-5 ] C85.13 : Type {12,36}_36 Order 432 mV = 6 mF = 2 Defining relations for automorphism group: [ (R * S)^2, S * R^5 * S^2 * R^-1 * S, S * R^2 * S^-1 * R^2 * S * R^-1 * S * R^-1, R^12, S^6 * R^-3 * S^-1 * R * S^5 ] C85.14 : Type {27,54}_14 Order 378 mV = 9 mF = 9 Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S * R^-2, S * R^2 * S^-1 * R^2 * S^4, S * R * S^-2 * R^2 * S^2 * R^-1 * S, R * S^-5 * R * S^-2 * R^11 * S^-4 * R * S^-1 * R ] C86.1 : Type {24,24}_34 Order 408 mV = 3 mF = 3 Defining relations for automorphism group: [ (R * S)^2, R^-2 * S * R^3 * S * R^-1 * S^-2, S^-1 * R^6 * S^-1 * R * S^-3 ] C87.1 : Type {3,12}_344 Order 2064 mV = 2 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, (R * S^-5)^2, S^-1 * R * S^-2 * R * S^-3 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^-2 * R * S^2 * R^-1 * S^-2 * R * S^-3 * R * S^-1 ] C87.2 : Type {7,14}_86 Order 602 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-7, R^-2 * S * R^3 * S * R^-1 * S^-2 ] C87.3 : Type {7,14}_86 Order 602 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-7, S^-1 * R^-1 * S * R^-3 * S^3 * R^-1 * S^-1 ] C87.4 : Type {7,14}_86 Order 602 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-7, R^-2 * S * R^3 * S^-1 * R * S^2 ] C88.1 : Type {6,90}_90 Order 540 mV = 30 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^-1 * R^2 * S^-1 * R^2 * S * R^-1 * S^-1 * R, S^15 * R^3 * S^-1 * R * S^14 ] C88.2 : Type {12,72}_72 Order 432 mV = 24 mF = 2 Defining relations for automorphism group: [ (R * S)^2, S * R^5 * S^2 * R^-1 * S, S * R^2 * S^-1 * R^2 * S * R^-1 * S * R^-1, R^12, R * S^-6 * R^2 * S^-1 * R * S^5 ] C88.3 : Type {18,24}_72 Order 432 mV = 4 mF = 3 Defining relations for automorphism group: [ (R * S)^2, R^-1 * S * R^4 * S^-2 * R * S^-1, S^-2 * R^2 * S^-1 * R^2 * S^-5 ] C88.4 : Type {18,24}_36 Order 432 mV = 2 mF = 6 Defining relations for automorphism group: [ (R * S)^2, (R * S^-1 * R)^2, R * S^-2 * R * S^-1 * R^-2 * S^-2 * R * S^3, S^-1 * R * S^-3 * R^-2 * S^-6 ] C88.5 : Type {42,63}_18 Order 378 mV = 21 mF = 7 Defining relations for automorphism group: [ (R * S)^2, S * R^5 * S^2 * R^-1 * S, S * R * S^-1 * R^3 * S^4, S^-1 * R^3 * S^-2 * R * S^-2 * R^8 * S^-1 * R^2 * S^-1 ] C89.1 : Type {4,48}_24 Order 768 mV = 6 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-2)^4, S^-1 * R * S^-1 * R * S^-2 * R^2 * S^2 * R^-1 * S^-1 * R * S^-1, S * R * S^-1 * R^-1 * S^4 * R^-1 * S^-5 * R * S ] C89.2 : Type {14,28}_4 Order 448 mV = 4 mF = 1 Defining relations for automorphism group: [ (R * S)^2, S^-1 * R^-1 * S * R^2 * S * R^-1 * S^-1, S * R^6 * S^3 * R^-2, R^14 ] C89.3 : Type {20,20}_22 Order 440 mV = 2 mF = 4 Defining relations for automorphism group: [ (R * S)^2, S * R * S^-1 * R^2 * S * R^-1 * S, S^2 * R^-1 * S * R^2 * S^-2 * R * S, R^-1 * S * R^-3 * S * R^-1 * S * R^-8 * S^3 * R^-1 ] C89.4 : Type {20,20}_22 Order 440 mV = 2 mF = 4 Defining relations for automorphism group: [ (R * S)^2, S * R * S^-1 * R^3 * S^4, R^-2 * S * R^3 * S^-1 * R * S^2, R^-1 * S^2 * R^-1 * S * R^-1 * S^3 * R^-9 * S^2 ] C89.5 : Type {48,48}_8 Order 384 mV = 12 mF = 12 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^2 * S^-1 * R^2 * S * R^-1 * S * R^-1, S * R * S^-1 * R * S^-1 * R * S^2 * R^-1 * S, S^-1 * R^6 * S^-1 * R^2 * S^-2 ] C90.1 : Type {8,8}_178 Order 712 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-2 * R)^2, (R * S^-1)^4, R * S^-3 * R^3 * S^-1 * R * S^-3 ] C91.1 : Type {4,8}_40 Order 1440 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^8, (R * S^-2)^4, S^-1 * R * S^-1 * R * S^-1 * R^-1 * S^2 * R^-1 * S^-1 * R * S * R^-1 * S^-3, S^-1 * R * S^-1 * R^-1 * S^2 * R * S^-1 * R * S * R^-1 * S^2 * R^-1 * S^-2 ] C91.2 : Type {4,8}_40 Order 1440 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^8, S * R * S^-1 * R * S^-1 * R^2 * S^-1 * R * S * R^-1 * S, (R * S^-2)^4 ] C91.3 : Type {4,8}_120 Order 1440 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, R * S^-1 * R * S^-2 * R^-1 * S * R^-1 * S * R^-1 * S * R^-1 * S * R^2 * S * R^-1 * S^-1 * R * S * R^-1 * S^-1 * R * S^-1 * R * S * R^-1 * S * R^-1 * S^-1 * R * S^2 * R^2 * S^-1 ] C91.4 : Type {4,8}_120 Order 1440 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, R * S^-1 * R * S^-2 * R^-1 * S * R^-1 * S * R^-1 * S * R^-1 * S * R^2 * S * R^-1 * S^-1 * R * S * R^-1 * S^-1 * R * S^-1 * R * S * R^-1 * S * R^-1 * S^2 * R^-1 * S * R^2 * S^-1 ] C91.5 : Type {4,12}_30 Order 1080 mV = 3 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S * R * S^-3 * R * S^4, S^-1 * R * S^-3 * R^2 * S^-3 * R * S^-1, S * R^-1 * S^-2 * R * S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S * R^-1 * S^-1 * R * S^-1 * R * S * R^-1 * S * R^-1 ] C91.6 : Type {4,12}_30 Order 1080 mV = 3 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^12, R * S^-1 * R * S^-1 * R^-1 * S * R * S^-1 * R^-1 * S * R * S^-1 * R^-2 * S * R^-1 * S * R^-1 * S * R^-1 * S * R^-1 * S^-2 ] C91.7 : Type {4,24}_24 Order 864 mV = 3 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S * R * S^-1 * R * S^-1 * R^2 * S^-1 * R * S * R^-1 * S, S^-1 * R * S^-3 * R^2 * S^-1 * R * S^-3, S^24 ] C91.8 : Type {4,40}_40 Order 800 mV = 10 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^-1 * R^-1 * S * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S * R^-1 * S^-2 * R, S^-9 * R^-1 * S * R^-2 * S * R^-1 * S^-1 * R * S^2 * R^-1 * S^-6 ] C91.9 : Type {4,40}_40 Order 800 mV = 10 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S^-1 * R * S^-1, S^40 ] C91.10 : Type {4,76}_190 Order 760 mV = 19 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S^-1 * R * S^-1, S^19 * R * S^-1 * R * S^5 * R^-1 * S^-1 * R * S^12 ] C91.11 : Type {6,8}_12 Order 864 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-1 * R)^2, S^8, R^-1 * S * R * S^-2 * R * S^-3 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^-2 ] C91.12 : Type {6,8}_12 Order 864 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^8, S^-2 * R * S^-1 * R^3 * S^-1 * R * S * R^-1 * S^-1, (S^-1 * R^2 * S^-1)^3 ] C91.13 : Type {8,8}_30 Order 720 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S * R^-1 * S * R^2 * S^-1 * R * S, R^-2 * S^2 * R^3 * S * R^-1 * S^-3 ] C91.14 : Type {8,8}_30 Order 720 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^8, S^-1 * R^-1 * S * R^4 * S^-1 * R * S^-3, S^-1 * R * S^-2 * R^3 * S * R^-1 * S^-1 * R * S^-1 ] C91.15 : Type {8,8}_30 Order 720 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S^-1 * R * S^2 * R^2 * S^-2 * R * S^-1 * R ] C91.16 : Type {8,8}_60 Order 720 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S * R^-1 * S * R^-1 * S^-1 * R * S^2 * R^2 * S^-1 * R * S^-1 * R ] C91.17 : Type {8,16}_16 Order 576 mV = 2 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, S^-3 * R^4 * S^-5, S * R * S^-1 * R * S^-1 * R^2 * S^-2 * R^2 * S, S * R * S^-3 * R^2 * S^-1 * R * S^3 ] C91.18 : Type {8,16}_16 Order 576 mV = 2 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, S^-3 * R^4 * S^-5, S * R * S^-1 * R * S^-1 * R^2 * S^-1 * R * S * R^-1 * S, S^-1 * R * S^-3 * R^2 * S^-1 * R * S^-3 ] C91.19 : Type {12,12}_30 Order 540 mV = 3 mF = 3 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, R^12, S^-1 * R * S^-1 * R * S^-2 * R * S^-1 * R^-2 * S^2 * R^-2 * S^-1 * R * S^-1 * R ] C91.20 : Type {12,12}_30 Order 540 mV = 3 mF = 3 Self-dual Defining relations for automorphism group: [ (R * S)^2, S^-1 * R^4 * S^-3, R^2 * S^-1 * R^3 * S^2 * R^-1 * S^-1, S^-1 * R * S^-2 * R^-1 * S * R * S^-1 * R^-2 * S^2 * R^-1 * S * R^-2 * S^-1 * R ] C91.21 : Type {12,24}_40 Order 480 mV = 6 mF = 3 Defining relations for automorphism group: [ (R * S)^2, S * R^5 * S * R^-3, S * R * S^-3 * R * S^4, R^12, S^-2 * R^5 * S^-3 * R * S^-1, S^-1 * R * S^-1 * R * S^-1 * R^2 * S^-1 * R * S^-2 * R ] C91.22 : Type {12,24}_40 Order 480 mV = 6 mF = 3 Defining relations for automorphism group: [ (R * S)^2, S * R^5 * S * R^-3, S * R * S^-3 * R * S^4, R^12, S^-2 * R^5 * S^-3 * R * S^-1, S^-1 * R * S^-1 * R * S^-1 * R^2 * S^-2 * R^2 * S^-1 ] C91.23 : Type {24,24}_6 Order 432 mV = 3 mF = 3 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^-1 * S * R^2 * S^-1 * R * S, S * R^5 * S * R^-1 * S^2, R^-1 * S^4 * R^-5 * S * R^-2 * S * R^-6 * S * R^-1 * S * R^-1 ] C91.24 : Type {40,40}_10 Order 400 mV = 10 mF = 10 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S * R^-1 * S * R^2 * S^-1 * R * S, S^-1 * R^13 * S^-1 * R * S^-3 * R^3 * S^-1 * R^9 * S^-1 * R^2 * S^-1 * R * S^-1 * R * S^-1 ] C91.25 : Type {40,40}_20 Order 400 mV = 10 mF = 10 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S * R^-1 * S * R * S^-1 * R^2 * S^-1 * R * S^2 * R^-1, R * S^-1 * R * S^-3 * R * S^-1 * R^6 * S^-1 * R * S^-1 * R^2 * S^-1 ] C91.26 : Type {49,49}_4 Order 392 mV = 7 mF = 7 Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S * R^-1 * S, R * S^-1 * R^31 * S^-2 * R^14 ] C91.27 : Type {76,76}_10 Order 380 mV = 19 mF = 19 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S * R^-1 * S * R^2 * S^-1 * R * S, R * S^-1 * R^11 * S^-1 * R * S^-3 * R^3 * S^-1 * R^10 * S^-2 * R^2 * S^-1 * R ] C92.1 : Type {6,6}_182 Order 1092 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, S * R * S^-2 * R^3 * S^3 * R^-2, (R * S^-2 * R * S^-1 * R)^2, R^-1 * S * R * S^-1 * R^-1 * S * R^2 * S^2 * R^-1 * S^3 ] C92.2 : Type {6,6}_182 Order 1092 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, S * R * S^-2 * R^3 * S^3 * R^-2, (R * S^-2 * R * S^-1 * R)^2, S * R^-1 * S^2 * R * S^-1 * R^2 * S * R^-1 * S^3 * R^-1 ] C92.3 : Type {6,6}_182 Order 1092 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-1 * R)^2, S^6, S * R * S^-1 * R^-1 * S * R * S^-1 * R^-1 * S * R * S^-1 * R * S^-2 * R^-1 * S * R * S^-1 * R * S^2 * R^-1 * S^-2 * R * S^-1 * R * S * R^-1 * S^-1 * R * S * R^-1 * S^-1 * R * S ] C92.4 : Type {6,6}_182 Order 1092 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-1 * R)^2, S^6, S^-1 * R^-1 * S * R * S^-1 * R * S^-1 * R^-1 * S * R * S^-1 * R^-1 * S * R * S^-2 * R * S^-2 * R^-1 * S * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^-1 * R * S * R^-1 * S^-1 * R * S * R^-1 * S^-2 ] C92.5 : Type {6,24}_104 Order 624 mV = 4 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^-1 * R^2 * S^-1 * R^3 * S^-1 * R^2 * S^-1 * R, S * R * S^-2 * R^3 * S^-2 * R * S * R^-1, S^-2 * R^2 * S^-1 * R^2 * S^-5, R * S^-3 * R * S^-1 * R^2 * S * R^-1 * S * R^-1 * S^-2 ] C92.6 : Type {6,24}_104 Order 624 mV = 8 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, R^2 * S^-1 * R^2 * S^-1 * R^-3 * S * R^-1 * S^-5 ] C92.7 : Type {6,42}_14 Order 588 mV = 14 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, R^-1 * S * R * S^-1 * R^-1 * S * R^-3 * S * R^-2 * S * R^-2 * S, S^4 * R * S^-1 * R^2 * S^-1 * R^-2 * S^-1 * R * S^7 ] C92.8 : Type {6,42}_14 Order 588 mV = 7 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^-2 * R^-1 * S * R^2 * S^-3 * R, S^-6 * R^2 * S^-1 * R^2 * S^-7 ] C92.9 : Type {18,18}_26 Order 468 mV = 3 mF = 6 Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S * R^-2, S * R^2 * S^-1 * R^2 * S^4, S * R^-1 * S^2 * R * S^-1 * R * S^-2 * R * S^2, S^-1 * R^12 * S^-5 ] C92.10 : Type {30,30}_14 Order 420 mV = 5 mF = 10 Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S * R^-2, S * R^2 * S^-1 * R^2 * S^4, S * R * S^-2 * R^2 * S * R^-1 * S^2, R^2 * S^-7 * R^12 * S^-3 * R^3 * S^-2 * R ] C93.1 : Type {8,64}_64 Order 512 mV = 16 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R * S^-1 * R^2 * S^-1 * R * S^-1, S^8 * R * S^-2 * R * S * R^-1 * S^-1 * R * S^4 ] C93.2 : Type {11,22}_46 Order 506 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, S^-2 * R^-1 * S * R^2 * S^2 * R^-1 * S^-1, R^-11, S * R^-5 * S * R^-2 * S^2 ] C93.3 : Type {11,22}_46 Order 506 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, S * R^5 * S * R^-1 * S^2, R^-11 ] C93.4 : Type {11,22}_46 Order 506 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, S * R^-1 * S * R^3 * S^-1 * R * S * R^-1, R^-11 ] C93.5 : Type {11,22}_46 Order 506 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, S * R * S^-2 * R^2 * S^2 * R^-1 * S, R^-11 ] C93.6 : Type {11,22}_46 Order 506 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-11, S * R^-5 * S^2 * R^-1 * S * R^-1 ] C94.1 : Type {3,12}_186 Order 2232 mV = 1 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, S^12, (S^2 * R^-1 * S^2)^3, S * R^-1 * S^2 * R * S^-2 * R^-1 * S^2 * R * S^-2 * R * S^-2 * R * S^-1 * R * S^-2 * R * S^3 * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S ] C94.2 : Type {6,6}_186 Order 1116 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, S^-1 * R^2 * S^-1 * R^3 * S^-1 * R^2 * S^-1 * R, S * R * S^-2 * R^3 * S^3 * R^-2, R * S^-1 * R^-1 * S * R * S^-1 * R * S^-3 * R^-1 * S * R^-1 * S^-2 * R * S^-1 * R * S^2 ] C94.3 : Type {6,6}_186 Order 1116 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-1 * R)^2, S^6, S^-1 * R^-1 * S * R * S^-1 * R * S^-2 * R^-1 * S^2 * R^-1 * S^2 * R * S^-2 * R * S^-1 * R * S * R^-1 * S^-2 * R * S^-1 * R * S^3 * R^-1 * S^2 * R^-2 * S^-1 ] C94.4 : Type {6,12}_124 Order 744 mV = 2 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S * R * S^-1 * R^3 * S^2 * R^-2, S * R^2 * S^-1 * R^2 * S^4, R * S^-1 * R^-1 * S * R * S^-2 * R * S^-2 * R^-2 * S^-2 * R * S^-2 * R * S^-2 ] C94.5 : Type {6,12}_124 Order 744 mV = 4 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^12, R * S^-1 * R^2 * S^-1 * R * S^-1 * R^-3 * S^-1 * R^2 * S^-1 * R^2 * S^-1 * R ] C94.6 : Type {9,18}_62 Order 558 mV = 3 mF = 3 Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S * R^-2, R^-9, S^2 * R^-3 * S^4, S * R^-1 * S^2 * R^-1 * S^2 * R * S^-1 * R * S^3 * R^-1 * S * R^-1 * S^-1 * R * S ] C94.7 : Type {10,10}_62 Order 620 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^10, (R * S^-1 * R^3)^2, (R * S^-3 * R)^2, S^-1 * R^-1 * S^2 * R^2 * S * R^-1 * S^-2 ] C94.8 : Type {10,10}_62 Order 620 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^10, (R * S^-1 * R^3)^2, (R * S^-3 * R)^2, (R * S^-2 * R * S^-1)^2, S * R^-1 * S * R * S^-1 * R^2 * S * R^-1 * S^-1 * R * S ] C94.9 : Type {24,36}_72 Order 432 mV = 6 mF = 4 Defining relations for automorphism group: [ (R * S)^2, S^-1 * R^-1 * S * R^3 * S^-4 ] C96.1 : Type {10,50}_50 Order 500 mV = 10 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^10, R * S^-1 * R^4 * S^-1 * R * S^-2, S * R * S^-3 * R^3 * S^6 ] C96.2 : Type {10,50}_50 Order 500 mV = 10 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^10, R * S^-1 * R^4 * S^-1 * R * S^-2, S^-2 * R^-1 * S * R * S^-1 * R^2 * S^-6 ] C97.1 : Type {3,12}_48 Order 2304 mV = 1 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, S^12, (R * S^-4 * R * S^-3)^2, S * R^-1 * S^3 * R * S^-2 * R * S^-2 * R^-1 * S * R^-1 * S^-2 * R * S^-2 * R * S^-2 * R * S ] C97.2 : Type {3,24}_16 Order 1536 mV = 2 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, S^2 * R^-1 * S^4 * R * S^-1 * R^-1 * S^2 * R^-1 * S^4 * R^-1 * S, S * R^-1 * S^2 * R^-1 * S^3 * R * S^-1 * R * S^-4 * R * S^3 ] C97.3 : Type {4,5}_12 Order 3840 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^-5, S^-2 * R^-1 * S * R * S^-1 * R^-1 * S * R^-1 * S * R^-1 * S * R^-1 * S * R^-1 * S^-2 * R * S^-1 * R * S^-1 * R ] C97.4 : Type {4,6}_16 Order 2304 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^6, S^-1 * R * S^-3 * R * S^-1 * R^-2 * S^-1 * R * S^-1 * R * S^-1 * R * S * R^-1 * S^-1, S^-1 * R^-1 * S * R * S^-2 * R * S^-1 * R^-2 * S * R^-1 * S^2 * R^-1 * S^-2 * R ] C97.5 : Type {4,16}_16 Order 1024 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^2 * R * S^-1 * R * S^-1 * R^2 * S^-2 * R * S * R^-1 * S, S * R * S^-3 * R * S^-1 * R * S^-3 * R * S^2 ] C97.6 : Type {4,16}_16 Order 1024 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S * R * S^-3 * R^2 * S^-3 * R * S, S^-1 * R^-1 * S * R * S^-1 * R * S^-1 * R^-2 * S^-1 * R * S^-1 * R * S^-2 * R ] C97.7 : Type {5,5}_24 Order 1920 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^-5, S^-5, (R * S^-1)^6, S^-1 * R^-2 * S^2 * R * S^-1 * R^2 * S * R^-1 * S * R^-1 * S^-2 * R ] C97.8 : Type {6,6}_12 Order 1152 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, R * S^-3 * R^-2 * S * R^-1 * S^-2 * R ] C97.9 : Type {6,6}_24 Order 1152 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, (R * S^-1 * R)^4, (R * S^-2 * R * S^-1 * R)^2, (R * S^-1 * R * S^-2 * R)^2, R * S^-2 * R * S^-2 * R^2 * S * R^-1 * S^-1 * R * S^2 ] C97.10 : Type {6,6}_24 Order 1152 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^6, S^6, R^-1 * S * R^2 * S^-1 * R^2 * S^-2 * R * S^-2, S^-1 * R^-1 * S * R * S^-1 * R^3 * S * R^-1 * S^-2 * R^2 ] C97.11 : Type {6,9}_72 Order 864 mV = 3 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^-9, R^-1 * S * R^-2 * S * R^2 * S^-1 * R^2 * S^-1 * R^-3 * S * R^-2 * S^-1 * R^2 * S^-1 * R^2 * S^-2 ] C97.12 : Type {6,12}_16 Order 768 mV = 2 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^-2 * R * S^-1 * R^2 * S * R^-1 * S^-2, S^-2 * R^2 * S^-1 * R^2 * S^-1 * R * S^-2 * R ] C97.13 : Type {6,12}_8 Order 768 mV = 2 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S^-2 * R * S^-1 * R^2 * S * R^-1 * S^-2, (R * S^-1 * R)^4 ] C97.14 : Type {6,12}_16 Order 768 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, R * S^-3 * R^-2 * S * R^-1 * S * R^-1 * S, (R * S^-2 * R * S^-1 * R)^2, S^-1 * R * S^-2 * R^-1 * S * R^2 * S^2 * R^-1 * S * R^-1 * S^-1 ] C97.15 : Type {6,27}_108 Order 648 mV = 9 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, R * S^-1 * R^-1 * S * R * S^-1 * R^-1 * S * R^-2 * S * R^-2 * S^4 ] C97.16 : Type {6,99}_198 Order 594 mV = 33 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-2)^2, S^-1 * R^2 * S^-1 * R^2 * S * R^-1 * S^-1 * R, S^-17 * R^3 * S * R^-1 * S^-15 ] C97.17 : Type {15,30}_4 Order 480 mV = 2 mF = 1 Defining relations for automorphism group: [ (R * S)^2, S^-1 * R^-1 * S * R^2 * S * R^-1 * S^-1, S * R^6 * S * R^-1 * S * R^-1 * S, R^-15 ] C97.18 : Type {16,16}_16 Order 512 mV = 4 mF = 4 Self-dual Defining relations for automorphism group: [ (R * S)^2, (R * S^-1 * R^2)^2, (R * S^-3)^2, S^-1 * R * S^-2 * R^3 * S * R^-1 * S^-2 * R ] C97.19 : Type {16,16}_8 Order 512 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^-2 * S * R^3 * S^-1 * R * S^2, S^2 * R^-1 * S * R^2 * S^-2 * R * S, R * S^-1 * R^5 * S * R^-1 * S^-2 * R ] C97.20 : Type {16,16}_8 Order 512 mV = 2 mF = 2 Defining relations for automorphism group: [ (R * S)^2, (R * S^-1)^4, S * R * S^-1 * R^3 * S * R^-2 * S, S^2 * R^-1 * S * R^2 * S^-2 * R * S ] C97.21 : Type {16,16}_16 Order 512 mV = 2 mF = 4 Defining relations for automorphism group: [ (R * S)^2, (R * S^-1 * R^2)^2, S^-2 * R * S^-1 * R^2 * S^2 * R^-1 * S^-1, R^-1 * S * R^6 * S^-2 * R * S^3 ] C97.22 : Type {24,72}_18 Order 432 mV = 24 mF = 4 Defining relations for automorphism group: [ (R * S)^2, S * R^5 * S^2 * R^-1 * S, S * R * S^-1 * R^3 * S^4, S^3 * R^-1 * S^3 * R^-1 * S^2 * R^-9 * S * R^-2 * S * R^-1 ] C97.23 : Type {24,72}_36 Order 432 mV = 24 mF = 4 Defining relations for automorphism group: [ (R * S)^2, S * R^5 * S^2 * R^-1 * S, S * R^2 * S^-1 * R^2 * S * R^-1 * S * R^-1, R^2 * S^-1 * R^4 * S^-5 ] C97.24 : Type {28,28}_4 Order 448 mV = 4 mF = 4 Defining relations for automorphism group: [ (R * S)^2, S^-1 * R^-1 * S * R^2 * S * R^-1 * S^-1, S * R^5 * S * R^-1 * S^2, R^-4 * S^9 * R^-2 * S * R^-9 * S * R^-1 * S ] C98.1 : Type {6,6}_194 Order 1164 mV = 1 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^6, (R * S^-1 * R)^2, S^6, S^-1 * R^-1 * S * R * S^-1 * R^-1 * S^2 * R^-1 * S * R * S^-1 * R * S^-2 * R^-1 * S * R * S^-1 * R * S^-1 * R * S^2 * R^-1 * S^-2 * R * S^2 * R^-1 * S^2 * R^-1 * S^-2 ] C98.2 : Type {8,8}_194 Order 776 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-2 * R)^2, (R * S^-1)^4, S * R * S^-3 * R^2 * S * R^-1 * S^-1 * R * S ] C99.1 : Type {3,12}_392 Order 2352 mV = 2 mF = 1 Defining relations for automorphism group: [ R^-3, (R * S)^2, (R * S^-5)^2, S^-1 * R * S^-3 * R^-1 * S^2 * R^-1 * S^2 * R * S^-2 * R^-1 * S^2 * R * S^-2 * R * S^-2 * R^-1 * S * R^-1 * S^2 * R^-1 * S^2 * R^-1 * S^-2 * R * S^-2 * R * S^-2 * R * S^-2 * R * S^-2 * R * S^-1 ] C99.2 : Type {12,12}_14 Order 588 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, (S^-1 * R)^3, R^12, (R * S^-2 * R^3)^2, S^-1 * R^-1 * S * R^4 * S^3 * R^-1 * S^-1 ] C100.1 : Type {6,36}_36 Order 648 mV = 6 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6, S * R^2 * S^-1 * R^2 * S * R^-1 * S * R^-1, S * R * S^-2 * R^3 * S^-2 * R * S * R^-1, S^-5 * R^-1 * S * R^-2 * S^3 * R^-1 * S^-3 ] C100.2 : Type {18,27}_54 Order 486 mV = 3 mF = 3 Defining relations for automorphism group: [ (R * S)^2, S * R^5 * S^2 * R^-1 * S, S * R^2 * S^-1 * R^2 * S * R^-1 * S * R^-1, S^2 * R * S^-1 * R^-3 * S^6 ] C100.3 : Type {18,27}_54 Order 486 mV = 3 mF = 1 Defining relations for automorphism group: [ (R * S)^2, S^3 * R^-2 * S * R^-1 * S * R^-1 ] C100.4 : Type {18,27}_54 Order 486 mV = 3 mF = 1 Defining relations for automorphism group: [ (R * S)^2, S * R^-4 * S * R^-2 * S ] C100.5 : Type {18,27}_54 Order 486 mV = 3 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^-1 * S * R^-3 * S^4 ] C101.1 : Type {4,8}_200 Order 1600 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S * R^-1 * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S * R^-1 * S^-1 * R * S^-1 * R * S^-1 ] C101.2 : Type {4,8}_100 Order 1600 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^8, R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S^-1 * R * S * R^-1 * S^-1 * R * S^-1 * R * S^-1 * R * S * R^-1 * S^-1 * R * S^-1 * R * S^-1 ] C101.3 : Type {4,8}_10 Order 1600 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^8, (S^-1 * R)^5, S * R^-1 * S * R * S^-3 * R^-2 * S^-1 * R * S^4 * R^-1, R^-1 * S * R^-1 * S^2 * R * S^-1 * R^2 * S^-2 * R * S^-2 * R * S^-1 ] C101.4 : Type {4,8}_50 Order 1600 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S^8, S * R * S^-1 * R * S^-1 * R^-1 * S * R^-2 * S^-2 * R * S^3 * R^-1, S^-1 * R^-1 * S * R * S^-1 * R * S^-2 * R * S^-2 * R * S^-1 * R * S^-2 ] C101.5 : Type {4,8}_8 Order 1600 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-1)^4, S^8, S^-1 * R^-1 * S * R * S^-1 * R^-1 * S * R^-2 * S * R^-1 * S^-1 * R * S * R^-1 * S^-1, S^-2 * R * S^-4 * R^-2 * S^2 * R^-1 * S^-2 * R * S^-2 * R ] C101.6 : Type {4,12}_12 Order 1200 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-2)^4, S^12, S^-1 * R^-1 * S * R * S^-1 * R * S^-1 * R^-2 * S^-1 * R * S^-1 * R * S^-2 * R, S^-1 * R * S^-1 * R^-1 * S^2 * R^-1 * S * R^-1 * S * R^-1 * S^-1 * R * S^-3 ] C101.7 : Type {4,12}_300 Order 1200 mV = 3 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^12, S^-1 * R^-1 * S * R^-1 * S * R * S^-1 * R^-1 * S * R^-1 * S * R * S^-1 * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S * R^-1 * S * R^-1 * S^-1 * R * S^-1 ] C101.8 : Type {4,12}_10 Order 1200 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3 * R * S^-1)^2, S^12, S^-1 * R^-1 * S * R * S^-1 * R * S^-2 * R^-2 * S^3 * R^-1 * S^-2, S * R * S^-1 * R^-1 * S * R * S^-2 * R^-1 * S * R^-1 * S^-1 * R * S^2 * R^-1 ] C101.9 : Type {4,20}_50 Order 1000 mV = 5 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, R * S^-2 * R^-1 * S^2 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S^-2 * R * S^3 ] C101.10 : Type {4,20}_10 Order 1000 mV = 1 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S * R * S^-1 * R * S^-1 * R^2 * S^-1 * R * S * R^-1 * S, (R * S^-2)^4, S^-1 * R^-1 * S^3 * R * S^-1 * R * S^2 * R^-1 * S^-3 ] C101.11 : Type {4,24}_30 Order 960 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, R * S^-1 * R * S^-2 * R^2 * S^-5 ] C101.12 : Type {4,24}_60 Order 960 mV = 2 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, S * R * S^-2 * R * S^-1 * R^2 * S^2 * R^-1 * S^-1 * R * S, S * R * S^-1 * R * S^-2 * R^2 * S^6 ] C101.13 : Type {4,24}_120 Order 960 mV = 6 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^-1 * R^-1 * S * R^-1 * S * R * S^-1 * R^-2 * S^-1 * R * S^-1 * R * S^-1 * R * S^-1, S^24 ] C101.14 : Type {4,24}_60 Order 960 mV = 6 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, R^-1 * S^2 * R * S^-2 * R^-1 * S * R * S^-1 * R^2 * S^-1 * R * S^2 * R^-1 * S^-3 ] C101.15 : Type {4,44}_220 Order 880 mV = 11 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, R * S^-2 * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S^-1, S^44 ] C101.16 : Type {4,84}_210 Order 840 mV = 21 mF = 1 Defining relations for automorphism group: [ R^4, (R * S)^2, (R * S^-3)^2, S^-1 * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S^-1 * R * S^-1, S^21 * R^2 * S^2 * R^-1 * S^-2 * R * S^17 ] C101.17 : Type {8,8}_20 Order 800 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-2 * R)^2, (R * S^-1)^4, R^-3 * S * R^4 * S^-1 * R^2 * S * R^-1 * S ] C101.18 : Type {8,8}_4 Order 800 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^-1 * S * R^2 * S * R^-1 * S^-1, (R * S^-1)^4, S^8, R^-3 * S * R^4 * S^-1 * R^2 * S * R^-1 * S ] C101.19 : Type {8,8}_100 Order 800 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, S^2 * R^-2 * S^-2 * R^-1 * S * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S^-1 * R * S^-1 * R * S^-1 * R * S * R^-1 * S * R^-1 * S * R^-1 ] C101.20 : Type {8,8}_100 Order 800 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^8, S^-1 * R^4 * S^-3, R * S^2 * R^-2 * S^-1 * R * S^-2 * R^-1 * S * R * S^-1 * R^2 * S * R^-1 * S^-1 * R * S^-1 * R * S^-1 * R * S * R^-1 * S * R^-1 * S^-1 ] C101.21 : Type {8,16}_80 Order 640 mV = 4 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^8, S * R * S^-3 * R * S^4, S * R * S^-1 * R^4 * S^2 * R^-3, S * R^2 * S^-1 * R^3 * S^2 * R^-1 * S^2, S * R^-1 * S * R * S^-1 * R^2 * S^-1 * R * S^2 * R^-1 ] C101.22 : Type {8,16}_80 Order 640 mV = 4 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^8, S * R * S^-3 * R * S^4, S * R * S^-1 * R^4 * S^2 * R^-3, S * R^2 * S^-1 * R^3 * S^2 * R^-1 * S^2, S^-1 * R^-1 * S * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S^-1 ] C101.23 : Type {8,16}_80 Order 640 mV = 4 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, (R * S^-3)^2, S * R^2 * S^-2 * R^2 * S^2 * R^-1 * S * R^-1, S^16 ] C101.24 : Type {8,16}_80 Order 640 mV = 4 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, (R * S^-3)^2, S^-2 * R^2 * S^-2 * R^2 * S^-1 * R * S^2 * R^-1 * S^-1 ] C101.25 : Type {8,16}_80 Order 640 mV = 4 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, (R * S^-3)^2, S^-2 * R^-1 * S * R * S^-1 * R^2 * S^-1 * R * S^2 * R^-1 * S^-1 ] C101.26 : Type {8,16}_80 Order 640 mV = 4 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, (R * S^-3)^2, R * S^-2 * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S^-1, S^16 ] C101.27 : Type {8,16}_80 Order 640 mV = 4 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, (R * S^-3)^2, S^-3 * R^4 * S^-5, R * S^-1 * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S^2 * R^-2 * S^-2 ] C101.28 : Type {8,16}_80 Order 640 mV = 4 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, (R * S^-3)^2, S^-3 * R^4 * S^-5, R * S^-1 * R * S^-1 * R * S^-1 * R^-2 * S * R^-1 * S * R^-1 * S^-1 * R * S^-2 ] C101.29 : Type {8,56}_70 Order 560 mV = 14 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, (R * S^-3)^2, S * R^2 * S^-2 * R^2 * S^2 * R^-1 * S * R^-1, R^-1 * S^5 * R * S^-2 * R^-1 * S * R^-1 * S^-6 ] C101.30 : Type {8,56}_140 Order 560 mV = 14 mF = 2 Defining relations for automorphism group: [ (R * S)^2, R^8, (R * S^-1 * R^2)^2, (R * S^-3)^2, S * R^2 * S^-2 * R^2 * S^2 * R^-1 * S * R^-1, S^6 * R * S^-2 * R * S^2 * R^-1 * S^-2 * R * S^2 ] C101.31 : Type {12,12}_10 Order 600 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, R^12, S^-2 * R^5 * S^-1 * R * S^-3, S * R * S^-1 * R^4 * S^3 * R^-1 * S, R * S^-3 * R^3 * S^-2 * R * S^-1 * R ] C101.32 : Type {12,12}_50 Order 600 mV = 3 mF = 3 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, R^12, R^-1 * S * R^-1 * S * R^-1 * S * R * S^-1 * R^-1 * S * R^-1 * S * R^-1 * S * R^-1 * S ] C101.33 : Type {16,48}_30 Order 480 mV = 12 mF = 4 Defining relations for automorphism group: [ (R * S)^2, S * R^5 * S * R^-3, S^-1 * R^-1 * S^2 * R^2 * S * R^-1 * S^-2, R^-1 * S^3 * R^-9 * S^3 ] C101.34 : Type {16,48}_60 Order 480 mV = 12 mF = 4 Defining relations for automorphism group: [ (R * S)^2, S * R^5 * S * R^-3, S * R^2 * S^-1 * R^3 * S^2 * R^-1 * S^2, R * S^-3 * R^3 * S * R^-1 * S^-2 * R ] C101.35 : Type {20,20}_50 Order 500 mV = 5 mF = 5 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, R * S^-1 * R * S^-1 * R * S^-1 * R^2 * S^-1 * R * S^-1 * R * S^2 ] C101.36 : Type {20,20}_50 Order 500 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R^6 * S^-1 * R * S^-2 ] C101.37 : Type {20,20}_50 Order 500 mV = 1 mF = 1 Defining relations for automorphism group: [ (R * S)^2, R * S^-1 * R^4 * S^-1 * R^2 * S^-1 ] C101.38 : Type {20,20}_10 Order 500 mV = 1 mF = 1 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R * S^-1 * R^2 * S * R^-1 * S, R * S^-2 * R^3 * S^-3 * R, S^-2 * R^-1 * S * R^3 * S^2 * R^-2 * S^-1 ] C101.39 : Type {24,24}_40 Order 480 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^5 * S^-1 * R^2 * S ] C101.40 : Type {24,24}_40 Order 480 mV = 2 mF = 2 Self-dual Defining relations for automorphism group: [ (R * S)^2, S^-1 * R^-1 * S * R^3 * S^-1 * R * S^-2, R^7 * S^-1 * R * S * R^-1 * S ] C101.41 : Type {24,24}_20 Order 480 mV = 6 mF = 6 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S * R * S^-1 * R * S^-1 * R^2 * S * R^-1 * S^2 * R^-1, R^-1 * S^3 * R^-1 * S * R^-9 * S^7 * R^-1 * S ] C101.42 : Type {24,24}_20 Order 480 mV = 6 mF = 6 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S^-1 * R * S^-1 * R * S^-1 * R^2 * S^-1 * R * S^-2 * R ] C101.43 : Type {44,44}_10 Order 440 mV = 11 mF = 11 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S * R * S^-1 * R^2 * S * R^-1 * S, R^2 * S^-13 * R^3 * S^-5 * R^11 * S^-1 * R * S^-1 * R^3 * S^-1 * R * S^-1 * R ] C101.44 : Type {84,84}_10 Order 420 mV = 21 mF = 21 Self-dual Defining relations for automorphism group: [ (R * S)^2, S * R^4 * S^3, S * R^-1 * S * R^2 * S^-1 * R * S, S^-1 * R^15 * S^-1 * R * S^-3 * R^3 * S^-1 * R^9 * S^-1 * R^2 * S^-1 * R * S^-1 * R^2 ] Total number of maps in list above: 594