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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 418346############################################################################# ## #W perf6.grp GAP Groups Library Volkmar Felsch ## Alexander Hulpke ## ## #Y Copyright (C) 1997, Lehrstuhl D für Mathematik, RWTH Aachen, Germany ## ## This file contains the perfect groups of sizes 43200-87480 ## All data is based on Holt/Plesken: Perfect Groups, OUP 1989 ## PERFGRP[81]:=[# 43200.1 [[1,"abcde", function(a,b,c,d,e) return [[a^2,b^3,(a*b)^5,c^4,d^3,e^3,(d*e)^4*c^2,(d*e^-1) ^5,c^2*d*c^2*d^-1,c^2*e*c^2*e^-1, c^-1*d^-1*e*d*e*d^-1*e*d*e^-1, a^-1*d^-1*a*d,a^-1*e^-1*a*e, b^-1*d^-1*b*d,b^-1*e^-1*b*e], [[b,a*b*a*b^-1*a,d,e],[a,b,e*d*c^-1,d]]]; end, [5,80]], "A5 x A6 2^1",[33,1,1],2, [1,3],[5,80]], # 43200.2 [[1,"abcde", function(a,b,c,d,e) return [[a^4,b^3,(a*b)^5,a^2*b*a^2*b^-1,c^2,d^3,e^3,(d*e) ^4,(d*e^-1)^5, c^-1*d^-1*e*d*e*d^-1*e*d*e^-1, a^-1*d^-1*a*d,a^-1*e^-1*a*e, b^-1*d^-1*b*d,b^-1*e^-1*b*e], [[a*b,d,e],[a,b,c,d]]]; end, [24,6]], "A5 2^1 x A6",[33,1,2],2, [1,3],[24,6]], # 43200.3 [[1,"abcde", function(a,b,c,d,e) return [[a^4,b^3,(a*b)^5,c^2*a^2,d^3,e^3,(d*e)^4*c^2,(d*e ^-1)^5,c^-1*d^-1*e*d*e*d^-1*e*d *e^-1,a^-1*d^-1*a*d, a^-1*e^-1*a*e,b^-1*d^-1*b*d, b^-1*e^-1*b*e],[[a*b,e*d*c^-1,d]]]; end, [960]], "( A5 x A6 ) 2^1",[33,1,3],2, [1,3],960] ]; PERFGRP[82]:=[# 43320.1 [[1,"abyz", function(a,b,y,z) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,y^19,z^19,y^-1 *z^-1*y*z,a^-1*y*a*z^-1, a^-1*z*a*y, b^-1*y*b*(y^(-1*6)*z^(-1*9))^-1, b^-1*z*b*(y^(-1*5)*z^5)^-1],[[a,b]]]; end, [361],[0,0,2,2,2,2]], "A5 2^1 19^2",[5,2,1],1, 1,361], # 43320.2 (otherpres.) [[1,"abdyz", function(a,b,d,y,z) return [[a^2*d^-1,b^3,(a*b)^5,d^2,d^-1*b^-1*d*b, y^19,z^19,y^-1*z^-1*y*z, a^-1*y*a*z^-1,a^-1*z*a*y, b^-1*y*b*(y^(-1*6)*z^(-1*9))^-1, b^-1*z*b*(y^(-1*5)*z^5)^-1],[[a,b]]]; end, [361],[0,0,2,2,2,2]]] ]; PERFGRP[83]:=[# 43740.1 [[1,"abuvwxyz", function(a,b,u,v,w,x,y,z) return [[a^2,b^3,(a*b)^5,u^3,v^3,w^3,x^3,y^3,z^3,u^-1*v ^-1*u*v,u^-1*w^-1*u*w, u^-1*x^-1*u*x,u^-1*y^-1*u*y, u^-1*z^-1*u*z, a^-1*u*a*(u^-1*v*w^-1*x^-1*y)^-1 ,a^-1*v*a*(u*v*w^-1*z)^-1, a^-1*w*a*(u^-1*w*x*y^-1*z^-1)^-1 ,a^-1*x*a*(v^-1*w*y^-1)^-1, a^-1*y*a*(u*v^-1*w^-1*y^-1*z)^-1 ,a^-1*z*a*(u^-1*v^-1*x^-1*y*z) ^-1,b^-1*u*b*(u*w^-1*y)^-1, b^-1*v*b*(v*x^-1*z)^-1, b^-1*w*b*(w*y)^-1,b^-1*x*b*(x*z)^-1, b^-1*y*b*y^-1,b^-1*z*b*z^-1], [[a*b,b*a*b*a*b^-1*a*b^-1,z]]]; end, [18]], "A5 3^6",[2,6,1],1, 1,18] ]; PERFGRP[84]:=[# 46080.1 [[1,"abcdstuve", function(a,b,c,d,s,t,u,v,e) return [[a^2*d^-1,b^3,c^3,(b*c)^4*d^-1,(b*c^-1)^5, a^-1*b^-1*c*b*c*b^-1*c*b*c^-1,d^2, d^-1*b^-1*d*b,d^-1*c^-1*d*c, d^-1*e^-1*d*e,e^4,e^-1*s^-1*e*s, e^-1*t^-1*e*t,e^-1*u^-1*e*u, e^-1*v^-1*e*v,s^2,t^2,u^2,v^2, s^-1*t^-1*s*t,s^-1*u^-1*s*u*e^2, s^-1*v^-1*s*v,t^-1*u^-1*t*u, t^-1*v^-1*t*v*e^2,u^-1*v^-1*u*v, a^-1*s*a*u^-1,a^-1*t*a*v^-1, a^-1*u*a*s^-1,a^-1*v*a*t^-1, b^-1*s*b*(t*v*e)^-1, b^-1*t*b*(s*t*u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, c^-1*s*c*(t*u)^-1,c^-1*t*c*t^-1, c^-1*u*c*(s*u*e)^-1, c^-1*v*c*(s*t*u*v*e^2)^-1], [[b,c],[c*b*a*d,b,s,e]]]; end, [64,80]], "A6 2^1 x ( 2^4 E 2^1 A ) C 2^1",[13,7,1],8, 3,[64,80]] ]; PERFGRP[85]:=[# 48000.1 [[4,1920,3,3000,2,120,3,1], "A5 # 2^5 5^2 [1]",6,1, 1,[16,24,25]], # 48000.2 [[4,1920,4,3000,2,120,4,1], "A5 # 2^5 5^2 [2]",6,1, 1,[80,25]], # 48000.3 [[4,1920,5,3000,2,120,5,1], "A5 # 2^5 5^2 [3]",6,1, 1,[10,24,25]] ]; PERFGRP[86]:=[# 50616.1 [[1,"abc", function(a,b,c) return [[c^18*a^2,c*b^4*c^-1*b^-1,b^37,a^4,a^2*b^(-1 *1)*a^2*b,a^2*c^-1*a^2*c, c*a*c*a^-1,(b*a)^3, c^(-1*2)*b*c^2*b^3*a*b^2*a*c*b^2*a],[[b,c^4]]] ; end, [152]], "L2(37) 2^1 = SL(2,37)",22,-2, 21,152] ]; PERFGRP[87]:=[# 51840.1 [[1,"abd", function(a,b,d) return [[a^2,b^5,(a*b)^9,(a^-1*b^-1*a*b)^3,(b*a*b*a *b^-1*a*b^-1*a)^2*d^-1,d^2, a^-1*d*a*d^-1,b^-1*d*b*d^-1], [[b^-1*a*b*a*(b^3*a)^2*b*a*b^3*a*b^-1, a*b^3*a*b*a*b^2*a*b*a*b^3*(a*b^-1)^2*d] ]]; end, [80]], "U4(2) 2^1",28,-2, 22,80] ]; PERFGRP[88]:=[# 51888.1 [[1,"abc", function(a,b,c) return [[c^23,c*b^(-1*22)*c^-1*b^-1,b^47,a^2,c*a*c*a ^-1,(b*a)^3],[[b,c]]]; end, [48],[0,2,2]], "L2(47)",22,-1, 27,48] ]; PERFGRP[89]:=[# 56448.1 [[2,168,1,336,1], "( L3(2) x L3(2) ) 2^1 [1]",[34,1,1],2, [2,2],[7,16]], # 56448.2 [[3,336,1,336,1,"d1","d2"], "( L3(2) x L3(2) ) 2^1 [2]",[34,1,2],2, [2,2],128] ]; PERFGRP[90]:=[# 57600.1 [[2,960,1,60,1], "A5 x A5 # 2^4 [1]",[29,4,1],1, [1,1],[16,5]], # 57600.2 [[2,960,2,60,1], "A5 x A5 # 2^4 [2]",[29,4,2],1, [1,1],[10,5]] ]; PERFGRP[91]:=[# 57624.1 [[1,"abxyz", function(a,b,x,y,z) return [[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4,x^7,y^7, z^7,x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,a^-1*x*a*z^-1, a^-1*y*a*y,a^-1*z*a*x^-1, b^-1*x*b*z^-1, b^-1*y*b*(y^-1*z^-1)^-1, b^-1*z*b*(x*y^2*z)^-1], [[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,y]]]; end, [56]], "L3(2) 7^3",[10,3,1],1, 2,56], # 57624.2 [[1,"abxyz", function(a,b,x,y,z) return [[a^2,b^3,(a*b)^7*z^-1,(a^-1*b^-1*a*b)^4, x^7,y^7,z^7,x^-1*y^-1*x*y, x^-1*z^-1*x*z,y^-1*z^-1*y*z, a^-1*x*a*z^-1,a^-1*y*a*y, a^-1*z*a*x^-1,b^-1*x*b*z^-1, b^-1*y*b*(y^-1*z^-1)^-1, b^-1*z*b*(x*y^2*z)^-1], [[a*b*x^2,b*a*b^-1*a*b^-1*a*b*a*b^-1,y ]]]; end, [56]], "L3(2) N 7^3",[10,3,2],1, 2,56] ]; PERFGRP[92]:=[# 58240.1 [[1,"abd", function(a,b,d) return [[a^2,b^4,(a*b)^5,(a^-1*b^-1*a*b)^7*d,(a*b^2) ^13, a*b^-1*a*b^2*a*b^2*(a*b^-1*a*b*a*b^2)^2 *a*b^2*a*b*(a*b^2)^4,d^2, a^-1*d*a*d^-1,b^-1*d*b*d^-1], [[a*b^2,(a*b*a*b^2)^2*a*b^2*a*b^-1 *(a*b^2*a*b*a*b^2)^2]]]; end, [1120]], "Sz(8) 2^1",28,-2, 23,1120] ]; PERFGRP[93]:=[# 58320.1 [[1,"abcwxyz", function(a,b,c,w,x,y,z) return [[a^4,b^3,c^3,(b*c)^4*a^2,(b*c^-1)^5,a^2*b*a^2 *b^-1,a^2*c*a^2*c^-1, a^-1*b^-1*c*b*c*b^-1*c*b*c^-1,w^3, x^3,y^3,z^3,w^-1*x^-1*w*x, w^-1*y^-1*w*y,w^-1*z^-1*w*z, x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,a^-1*w*a*z^-1, a^-1*x*a*x^-1, a^-1*y*a*(w^-1*x^-1*y^-1*z^-1) ^-1,a^-1*z*a*w^-1, b^-1*w*b*x^-1,b^-1*x*b*y^-1, b^-1*y*b*w^-1,b^-1*z*b*z^-1, c^-1*w*c*(w^-1*x*y^-1*z^-1)^-1, c^-1*x*c*(x^-1*z)^-1, c^-1*y*c*(w*x^-1)^-1, c^-1*z*c*x], [[c*b*a^-1,b,w],[b,c*a*b*c,z]]]; end, [80,30]], "A6 2^1 x 3^4'",[14,4,1],2, 3,[80,30]], # 58320.2 [[1,"abcstuv", function(a,b,c,s,t,u,v) return [[a^4,b^3,c^3,(b*c)^4*a^(-1*2),(b*c^-1)^5,a^-1 *b^-1*c*b*c*b^-1*c*b*c^-1, a^(-1*2)*b^-1*a^2*b,a^(-1*2)*c^-1*a^2*c, s^3,t^3,u^3,v^3,s^-1*t^-1*s*t, s^-1*u^-1*s*u,s^-1*v^-1*s*v, t^-1*u^-1*t*u,t^-1*v^-1*t*v, u^-1*v^-1*u*v,a^-1*s*a*u^-1, a^-1*t*a*v^-1,a^-1*u*a*s, a^-1*v*a*t,b^-1*s*b*(s*v^-1)^-1, b^-1*t*b*(t*u^-1*v)^-1, b^-1*u*b*u^-1,b^-1*v*b*v^-1, c^-1*s*c*(s^-1*t*u^-1*v)^-1, c^-1*t*c*(s*t*u*v)^-1, c^-1*u*c*(s^-1*v^-1)^-1, c^-1*v*c*(t^-1*u^-1*v)^-1], [[a,b,c]]]; end, [81]], "A6 2^1 3^4",[14,4,2],1, 3,81], # 58320.3 (otherpres.) [[1,"abcdstuv", function(a,b,c,d,s,t,u,v) return [[a^2*d^-1,b^3,c^3,(b*c)^4*d^-1,(b*c^-1)^5, a^-1*b^-1*c*b*c*b^-1*c*b*c^-1,d^2, d^-1*b^-1*d*b,d^-1*c^-1*d*c,s^3, t^3,u^3,v^3,s^-1*t^-1*s*t, s^-1*u^-1*s*u,s^-1*v^-1*s*v, t^-1*u^-1*t*u,t^-1*v^-1*t*v, u^-1*v^-1*u*v,a^-1*s*a*u^-1, a^-1*t*a*v^-1,a^-1*u*a*s, a^-1*v*a*t,b^-1*s*b*(s*v^-1)^-1, b^-1*t*b*(t*u^-1*v)^-1, b^-1*u*b*u^-1,b^-1*v*b*v^-1, c^-1*s*c*(s^-1*t*u^-1*v)^-1, c^-1*t*c*(s*t*u*v)^-1, c^-1*u*c*(s^-1*v^-1)^-1, c^-1*v*c*(t^-1*u^-1*v)^-1], [[a,b,c]]]; end, [81]]] ]; PERFGRP[94]:=[# 58800.1 [[1,"abc", function(a,b,c) return [[c^24,b^7,c^(-1*8)*b^2*c^8*b^-1,c*b^3*c*b^2*c ^(-1*2)*b^(-1*3),a^2,c*a*c*a^-1,(b*a)^3, c^2*b*c*b^2*a*b*a*c*a*b^2*a*b^-1*c^(-1*3) *b^-1*a],[[b,c]]]; end, [50]], "L2(49)",22,-1, 28,50] ]; PERFGRP[95]:=[# 60480.1 [[1,"abd", function(a,b,d) return [[a^2,b^4,(a*b)^7*d^-1,(a^-1*b^-1*a*b)^5, (a*b^2)^5,(a*b*a*b*a*b^3)^5, (a*b*a*b*a*b^2*a*b^-1)^5*d^(-1*2),d^3, a^-1*d*a*d^-1,b^-1*d*b*d^-1], [[a*b*a,b^2*a*b^-1*a*b*a*b^2*a*b*d]]]; end, [63]], "L3(4) 3^1",[27,0,1],-3, 20,63], # 60480.2 [[2,120,1,504,1], "A5 2^1 x L2(8)",[35,1,1],2, [1,4],[24,9]], # 60480.3 [[2,168,1,360,1], "L3(2) x A6",[37,0,1],1, [2,3],[7,6]] ]; PERFGRP[96]:=fail; PERFGRP[97]:=[# 62400.1 [[1,"ab", function(a,b) return [[a^2,b^3,(a*b)^15,(a^-1*b^-1*a*b)^5,(a*b*a*b*a *b*a*b^-1*a*b^-1*a*b^-1)^3, (a*b^-1*a*b*a*b*a*b*a*b*a*b)^4], [[(a*b)^5*a,b*a*b^-1*(a*b)^6]]]; end, [65]], "U3(4)",28,-1, 29,65] ]; PERFGRP[98]:=[# 64512.1 [[1,"abcuvwxyzd", function(a,b,c,u,v,w,x,y,z,d) return [[a^2,b^3,(a*b)^7,b^-1*(a*b)^3*c^-1,c*b^-1 *c*b*a^-1*b^-1*c^-1*b *c^-1*a,u^2,v^2,w^2,x^2,y^2,z^2,d^2, u^-1*v^-1*u*v,u^-1*w^-1*u*w, u^-1*x^-1*u*x,u^-1*y^-1*u*y, u^-1*z^-1*u*z,u^-1*d^-1*u*d, v^-1*w^-1*v*w,v^-1*x^-1*v*x, v^-1*y^-1*v*y,v^-1*z^-1*v*z, v^-1*d^-1*v*d,w^-1*x^-1*w*x, w^-1*y^-1*w*y,w^-1*z^-1*w*z, w^-1*d^-1*w*d,x^-1*y^-1*x*y, x^-1*z^-1*x*z,x^-1*d^-1*x*d, y^-1*z^-1*y*z,y^-1*d^-1*y*d, z^-1*d^-1*z*d,a^-1*u*a*(u*x)^-1, a^-1*v*a*(v*y)^-1,a^-1*w*a*(w*z)^-1, a^-1*x*a*x^-1,a^-1*y*a*y^-1, a^-1*z*a*z^-1,a^-1*d*a*d^-1, b^-1*u*b*(x*y*d)^-1, b^-1*v*b*(y*z)^-1, b^-1*w*b*(x*y*z)^-1, b^-1*x*b*(v*w*x)^-1, b^-1*y*b*(u*v*w*y)^-1, b^-1*z*b*(u*w*z)^-1,b^-1*d*b*d^-1, c^-1*u*c*(v*d)^-1,c^-1*v*c*(w*d)^-1, c^-1*w*c*(u*v)^-1, c^-1*x*c*(x*z*d)^-1,c^-1*y*c*x^-1, c^-1*z*c*y^-1,c^-1*d*c*d^-1], [[b^-1*c,u*d]]]; end, [112]], "L2(8) 2^6 E 2^1",[16,7,1],2, 4,112], # 64512.2 [[1,"abcuvwxyzf", function(a,b,c,u,v,w,x,y,z,f) return [[a^2*f,b^3,(a*b)^7,b^-1*(a*b)^3*c^-1,b^-1 *c^-1*b*c^-1*a^-1*c *b^-1*c*b*a*(y*z)^-1,f^2,u^2,v^2, w^2,x^2,y^2,z^2,u^-1*v^-1*u*v, u^-1*w^-1*u*w,u^-1*x^-1*u*x, u^-1*y^-1*u*y,u^-1*z^-1*u*z, u^-1*f^-1*u*f,v^-1*w^-1*v*w, v^-1*x^-1*v*x,v^-1*y^-1*v*y, v^-1*z^-1*v*z,v^-1*f^-1*v*f, w^-1*x^-1*w*x,w^-1*y^-1*w*y, w^-1*z^-1*w*z,w^-1*f^-1*w*f, x^-1*y^-1*x*y,x^-1*z^-1*x*z, x^-1*f^-1*x*f,y^-1*z^-1*y*z, y^-1*f^-1*y*f,z^-1*f^-1*z*f, a^-1*u*a*(u*x)^-1,a^-1*v*a*(v*y)^-1, a^-1*w*a*(w*z)^-1,a^-1*x*a*x^-1, a^-1*y*a*y^-1,a^-1*z*a*z^-1, a^-1*f*a*f^-1, b^-1*u*b*(x*y*f^-1)^-1, b^-1*v*b*(y*z)^-1, b^-1*w*b*(x*y*z)^-1, b^-1*x*b*(v*w*x)^-1, b^-1*y*b*(u*v*w*y)^-1, b^-1*z*b*(u*w*z*f^-1)^-1, b^-1*f*b*f^-1, c^-1*u*c*(v*f^-1)^-1, c^-1*v*c*(w*f^-1)^-1, c^-1*w*c*(u*v*f)^-1, c^-1*x*c*(x*z*f)^-1, c^-1*y*c*(x*f)^-1, c^-1*z*c*(y*f^-1)^-1, c^-1*f*c*f^-1],[[b^-1*c,u*f]]]; end, [112]], "L2(8) N 2^6 E 2^1 I",[16,7,2],2, 4,112], # 64512.3 [[1,"abcuvwxyzd", function(a,b,c,u,v,w,x,y,z,d) return [[a^2,b^3,(a*b)^7,b^-1*(a*b)^3*c^-1,b^-1*c ^-1*b*c^-1*a^-1*c*b^-1 *c*b*a*(y*z*d)^-1,d^2,u^2,v^2,w^2,x^2, y^2,z^2,u^-1*v^-1*u*v,u^-1*w^-1*u*w ,u^-1*x^-1*u*x,u^-1*y^-1*u*y, u^-1*z^-1*u*z,u^-1*d^-1*u*d, v^-1*w^-1*v*w,v^-1*x^-1*v*x, v^-1*y^-1*v*y,v^-1*z^-1*v*z, v^-1*d^-1*v*d,w^-1*x^-1*w*x, w^-1*y^-1*w*y,w^-1*z^-1*w*z, w^-1*d^-1*w*d,x^-1*y^-1*x*y, x^-1*z^-1*x*z,x^-1*d^-1*x*d, y^-1*z^-1*y*z,y^-1*d^-1*y*d, z^-1*d^-1*z*d,a^-1*u*a*(u*x)^-1, a^-1*v*a*(v*y)^-1,a^-1*w*a*(w*z)^-1, a^-1*x*a*x^-1,a^-1*y*a*y^-1, a^-1*z*a*z^-1,a^-1*d*a*d^-1, b^-1*u*b*(x*y)^-1,b^-1*v*b*(y*z)^-1, b^-1*w*b*(x*y*z*d)^-1, b^-1*x*b*(v*w*x)^-1, b^-1*y*b*(u*v*w*y*d)^-1, b^-1*z*b*(u*w*z)^-1,b^-1*d*b*d^-1, c^-1*u*c*(v*d)^-1,c^-1*v*c*(w*d)^-1, c^-1*w*c*(u*v)^-1, c^-1*x*c*(x*z*d)^-1, c^-1*y*c*(x*d)^-1,c^-1*z*c*y^-1, c^-1*d*c*d^-1],[[b^-1*c*d,u*d]]]; end, [112]], "L2(8) N 2^6 E 2^1 II",[16,7,3],2, 4,112], # 64512.4 [[1,"abcuvwxyzd", function(a,b,c,u,v,w,x,y,z,d) return [[a^2*d,b^3,(a*b)^7,b^-1*(a*b)^3*c^-1,b^-1 *c^-1*b*c^-1*a^-1*c *b^-1*c*b*a*(y*z*d)^-1,d^2,u^2,v^2, w^2,x^2,y^2,z^2,u^-1*v^-1*u*v, u^-1*w^-1*u*w,u^-1*x^-1*u*x, u^-1*y^-1*u*y,u^-1*z^-1*u*z, u^-1*d^-1*u*d,v^-1*w^-1*v*w, v^-1*x^-1*v*x,v^-1*y^-1*v*y, v^-1*z^-1*v*z,v^-1*d^-1*v*d, w^-1*x^-1*w*x,w^-1*y^-1*w*y, w^-1*z^-1*w*z,w^-1*d^-1*w*d, x^-1*y^-1*x*y,x^-1*z^-1*x*z, x^-1*d^-1*x*d,y^-1*z^-1*y*z, y^-1*d^-1*y*d,z^-1*d^-1*z*d, a^-1*u*a*(u*x)^-1,a^-1*v*a*(v*y)^-1, a^-1*w*a*(w*z)^-1,a^-1*x*a*x^-1, a^-1*y*a*y^-1,a^-1*z*a*z^-1, a^-1*d*a*d^-1,b^-1*u*b*(x*y*d)^-1, b^-1*v*b*(y*z)^-1, b^-1*w*b*(x*y*z*d)^-1, b^-1*x*b*(v*w*x)^-1, b^-1*y*b*(u*v*w*y*d)^-1, b^-1*z*b*(u*w*z*d)^-1,b^-1*d*b*d^-1 ,c^-1*u*c*v^-1,c^-1*v*c*w^-1, c^-1*w*c*(u*v*d)^-1, c^-1*x*c*(x*z)^-1,c^-1*y*c*x^-1, c^-1*z*c*(y*d)^-1,c^-1*d*c*d^-1], [[b^-1*c*d,u]]]; end, [112]], "L2(8) N 2^6 E 2^1 III",[16,7,4],2, 4,112] ]; PERFGRP[99]:=[# 64800.1 [[2,60,1,1080,1], "A5 x A6 3^1",[33,0,1],3, [1,3],[5,18]] ]; PERFGRP[100]:=[# 65520.1 [[2,60,1,1092,1], "A5 x L2(13)",40,1, [1,6],[5,14]] ]; PERFGRP[101]:=[# 68880.1 [[1,"abc", function(a,b,c) return [[c^20*a^2,c*b^8*c^-1*b^-1,b^41,a^4,a^2*b^(-1 *1)*a^2*b,a^2*c^-1*a^2*c, c*a*c*a^-1,(b*a)^3,c^-1*(b*c*a)^4*b*a], [[b,c^8]]]; end, [336]], "L2(41) 2^1 = SL(2,41)",22,-2, 25,336] ]; PERFGRP[102]:=[# 69120.1 [[4,23040,1,1080,2,360,1,1], "A6 3^1 x ( 2^4 E 2^1 A ) C 2^1",[13,6,1],12, 3,[64,18]], # 69120.2 [[4,23040,2,1080,2,360,2,1], "A6 3^1 x ( 2^4 E 2^1 A ) C N 2^1",[13,6,2],12, 3,[384,18]], # 69120.3 [[4,23040,3,1080,2,360,3,1], "A6 3^1 x 2^1 x ( 2^4 E 2^1 )",[13,6,3],12, 3,[12,80,18]], # 69120.4 [[1,"abcuvwxyz", function(a,b,c,u,v,w,x,y,z) return [[a^6,b^3,c^3,(b*c)^4,(b*c^-1)^5,a^-1*b^-1*c *b*c*b^-1*c*b*c^-1,u^2,v^2,w^2, x^2,y^2,z^2,u^-1*v^-1*u*v, u^-1*w^-1*u*w,u^-1*x^-1*u*x, u^-1*y^-1*u*y,u^-1*z^-1*u*z, v^-1*w^-1*v*w,v^-1*x^-1*v*x, v^-1*y^-1*v*y,v^-1*z^-1*v*z, w^-1*x^-1*w*x,w^-1*y^-1*w*y, w^-1*z^-1*w*z,x^-1*y^-1*x*y, x^-1*z^-1*x*z,y^-1*z^-1*y*z, a^-1*u*a*(v*x)^-1, a^-1*v*a*(u*v*w*x)^-1,a^-1*w*a*x^-1 ,a^-1*x*a*(w*x)^-1, a^-1*y*a*(x*z)^-1, a^-1*z*a*(w*x*y*z)^-1,b^-1*u*b*u^-1 ,b^-1*v*b*v^-1,b^-1*w*b*(u*x)^-1, b^-1*x*b*(v*w*x)^-1, b^-1*y*b*(u*y*z)^-1, b^-1*z*b*(v*y)^-1,c^-1*u*c*w^-1, c^-1*v*c*x^-1,c^-1*w*c*(y*z)^-1, c^-1*x*c*y^-1,c^-1*y*c*v^-1, c^-1*z*c*(u*v)^-1],[[b,c]]]; end, [64]], "A6 3^1 # 2^6 [4]",[13,6,4],1, 3,64] ]; PERFGRP[103]:=[# 74412.1 [[1,"abc", function(a,b,c) return [[c^26,c*b^4*c^-1*b^-1,b^53,a^2,c*a*c*a^-1, (b*a)^3,c^(-1*3)*b*c*b*c^2*a*b^2*a*c*b^2*a], [[b,c]]]; end, [54]], "L2(53)",22,-1, 30,54] ]; PERFGRP[104]:=[# 75000.1 [[1,"abxyzd", function(a,b,x,y,z,d) return [[a^4,b^3,(a*b)^5,a^2*b*a^2*b^-1,x^5,y^5,z^5,d^5, x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,x^-1*d^-1*x*d, y^-1*d^-1*y*d,z^-1*d^-1*z*d, a^-1*d^-1*a*d,b^-1*d^-1*b*d, a^-1*x*a*z^-1*d,a^-1*y*a*y*d^-1, a^-1*z*a*x^-1*d^-1, b^-1*x*b*z^-1, b^-1*y*b*(y^-1*z)^-1, b^-1*z*b*(x*y^(-1*2)*z)^-1], [[a*b,x],[b,a*b*a*b^-1*a,x]]]; end, [24,25]], "A5 2^1 x 5^3 E 5^1",[3,4,1],10, 1,[24,25]], # 75000.2 [[1,"abwxyz", function(a,b,w,x,y,z) return [[w^5,x^5,y^5,z^5,w^-1*x^-1*w*x,w^-1*y^(-1 *1)*w*y,w^-1*z^-1*w*z, x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,a^-1*w*a*z^-1, a^-1*x*a*y,a^-1*y*a*x^-1, a^-1*z*a*w,b^-1*w*b*z, b^-1*x*b*(y*z^-1)^-1, b^-1*y*b*(x^-1*y^2*z^-1)^-1, b^-1*z*b*(w*x^2*y^(-1*2)*z^-1)^-1,a^4, b^3,(a*b)^5,a^2*b^-1*a^2*b], [[a*b,b*a*b*a*b^-1*a*b^-1,x]]]; end, [30]], "A5 2^1 5^4",[3,4,2],1, 1,30], # 75000.3 [[1,"abyzYZ", function(a,b,y,z,Y,Z) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,y^5,z^5,Y^5,Z^5, y^-1*z^-1*y*z,y^-1*Y^-1*y*Y, y^-1*Z^-1*y*Z,z^-1*Y^-1*z*Y, z^-1*Z^-1*z*Z,Y^-1*Z^-1*Y*Z, a^-1*y*a*z^-1,a^-1*z*a*y, a^-1*Y*a*Z^-1,a^-1*Z*a*Y, b^-1*y*b*z,b^-1*z*b*(y*z^-1)^-1, b^-1*Y*b*Z,b^-1*Z*b*(Y*Z^-1)^-1], [[a,b,y],[a,b,Y]]]; end, [25,25]], "A5 2^1 5^2 x 5^2",[3,4,3],1, 1,[25,25]], # 75000.4 [[1,"abyzYZ", function(a,b,y,z,Y,Z) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,y^5,z^5,Y^5,Z^5, y^-1*z^-1*y*z,y^-1*Y^-1*y*Y, y^-1*Z^-1*y*Z,z^-1*Y^-1*z*Y, z^-1*Z^-1*z*Z,Y^-1*Z^-1*Y*Z, a^-1*y*a*(z*Y^-1)^-1, a^-1*z*a*(y^-1*Z)^-1, a^-1*Y*a*Z^-1,a^-1*Z*a*Y, b^-1*y*b*(z^-1*Y^-1*Z)^-1, b^-1*z*b*(y*z^-1*Z)^-1,b^-1*Y*b*Z, b^-1*Z*b*(Y*Z^-1)^-1], [[b,a*b*a*b^-1*a,y*Y^-1*Z^-1]]]; end, [125]], "A5 2^1 5^2 E 5^2",[3,4,4],1, 1,125] ]; PERFGRP[105]:=[# 77760.1 [[4,960,1,4860,1,60], "A5 # 2^4 3^4 [1]",6,1, 1,[16,15]], # 77760.2 [[4,960,2,4860,1,60], "A5 # 2^4 3^4 [2]",6,1, 1,[10,15]], # 77760.3 [[4,960,1,4860,2,60], "A5 # 2^4 3^4 [3]",6,1, 1,[16,60]], # 77760.4 [[4,960,2,4860,2,60], "A5 # 2^4 3^4 [4]",6,1, 1,[10,60]] ]; PERFGRP[106]:=[# 79200.1 [[2,120,1,660,1], "( A5 x L2(11) ) 2^1 [1]",[36,1,1],2, [1,5],[24,11]], # 79200.2 [[2,60,1,1320,1], "( A5 x L2(11) ) 2^1 [2]",[36,1,2],2, [1,5],[5,24]], # 79200.3 [[3,120,1,1320,1,"d1","d2"], "( A5 x L2(11) ) 2^1 [3]",[36,1,3],2, [1,5],288] ]; PERFGRP[107]:=[# 79464.1 [[1,"abc", function(a,b,c) return [[c^21*a^2,c*b^9*c^-1*b^-1,b^43,a^4,a^2*b^(-1 *1)*a^2*b,a^2*c^-1*a^2*c, c*a*c*a^-1,(b*a)^3],[[b,c^2]]]; end, [88],[0,0,2]], "L2(43) 2^1 = SL(2,43)",22,-2, 26,88] ]; PERFGRP[108]:=[# 79860.1 [[1,"abxyz", function(a,b,x,y,z) return [[a^2,b^3,(a*b)^5,x^11,y^11,z^11,x^-1*y^-1*x*y, x^-1*z^-1*x*z,y^-1*z^-1*y*z, a^-1*x*a*z^-1,a^-1*y*a*y, a^-1*z*a*x^-1, b^-1*x*b*(x*y^(-1*5)*z^(-1*2))^-1, b^-1*y*b*(x^(-1*4)*y^-1)^-1, b^-1*z*b*x^(-1*5)], [[a*b,b*a*b*a*b^-1*a*b^-1,y*z^5]]]; end, [66]], "A5 11^3",[5,3,1],1, 1,66] ]; PERFGRP[109]:=[# 80640.1 [[1,"abdwxyz", function(a,b,d,w,x,y,z) return [[a^2*d^-1,b^4*d^-1,(a*b)^7,(a*b)^2*a*b^2*( a*b*a*b^-1)^2*(a*b)^2 *(a*b^-1)^2*a*b*a*b^-1,d^2, d^-1*a^-1*d*a,d^-1*b^-1*d*b,w^2, x^2,y^2,z^2,w*x*w*x,w*y*w*y,w*z*w*z,x*y*x*y, x*z*x*z,y*z*y*z,a^-1*w*a*y^-1, a^-1*x*a*z^-1,a^-1*y*a*w^-1, a^-1*z*a*x^-1,b^-1*w*b*(w*x*y*z)^-1 ,b^-1*x*b*y^-1,b^-1*y*b*(w*x)^-1, b^-1*z*b*(w*z)^-1], [[a,b],[a*b,b*a*b*a*b^2*a*b^-1*a*b*a*b^-1 *a*b*a*b^2*d,w]]]; end, [16,240]], "A7 2^1 x 2^4",[23,5,1],2, 8,[16,240]], # 80640.2 [[1,"abef", function(a,b,e,f) return [[a^2,b^4,(a*b)^7*e,(a*b^2)^5*(e*f)^-1,(a^-1*b ^-1*a*b)^5,(a*b*a*b*a*b^3)^5*f, (a*b*a*b*a*b^2*a*b^-1)^5,e^2,f^2, e^-1*f^-1*e*f,a^-1*e*a*e^-1, a^-1*f*a*f^-1,b^-1*e*b*e^-1, b^-1*f*b*f^-1], [[a*e,b*a*b*a*b^-1*a*b^2*f^-1]]]; end, [224]], "L3(4) 2^1 x 2^1",[27,2,1],-4, 20,224], # 80640.3 [[1,"abf", function(a,b,f) return [[a^2,b^4*f^(-1*2),(a*b)^7,(a*b^2)^5*f^-1,(a^-1 *b^-1*a*b)^5*f^(-1*2),(a*b*a*b*a*b^3)^5 *f,(a*b*a*b*a*b^2*a*b^-1)^5,f^4, a^-1*f*a*f^-1,b^-1*f*b*f^-1], [[a,b*a*b*a*b^-1*a*b^2*f^-1]]]; end, [224]], "L3(4) 2^1 A 2^1 I",[27,2,2],-4, 20,224], # 80640.4 [[1,"abe", function(a,b,e) return [[a^2,b^4*e^(-1*2),(a*b)^7*e,(a*b^2)^5*e^-1,(a^(-1 *1)*b^-1*a*b)^5*e^(-1*2), (a*b*a*b*a*b^3)^5*e^(-1*2), (a*b*a*b*a*b^2*a*b^-1)^5, a^-1*e*a*e^-1,b^-1*e*b*e^-1], [[a*e^2,b^-1*a*b^-1*a*b*a*b^2]]]; end, [224]], "L3(4) 2^1 A 2^1 II",[27,2,3],-4, 20,224], # 80640.5 [[2,60,1,1344,1], "( A5 x L3(2) ) # 2^3 [1]",[31,3,1],1, [1,2],[5,8]], # 80640.6 [[2,60,1,1344,2], "( A5 x L3(2) ) # 2^3 [2]",[31,3,2],1, [1,2],[5,14]] ]; PERFGRP[110]:=[# 84672.1 [[2,168,1,504,1], "L3(2) x L2(8)",[38,0,1],1, [2,4],[7,9]] ]; PERFGRP[111]:=[fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail, fail]; PERFGRP[112]:=[# 86400.1 [[2,120,1,720,1], "( A5 x A6 ) 2^2",[33,2,1],4, [1,3],[24,80]] ]; PERFGRP[113]:=[# 87480.1 [[1,"abuvwxyz", function(a,b,u,v,w,x,y,z) return [[a^4,b^3,(a*b)^5,a^2*b*a^2*b^-1,u^3,v^3,w^3,x^3, y^3,z^3,u^-1*v^-1*u*v,u^-1*w^-1*u*w ,u^-1*x^-1*u*x,u^-1*y^-1*u*y, u^-1*z^-1*u*z, a^-1*u*a*(u^-1*v*w^-1*x^-1*y)^-1 ,a^-1*v*a*(u*v*w^-1*z)^-1, a^-1*w*a*(u^-1*w*x*y^-1*z^-1)^-1 ,a^-1*x*a*(v^-1*w*y^-1)^-1, a^-1*y*a*(u*v^-1*w^-1*y^-1*z)^-1 ,a^-1*z*a*(u^-1*v^-1*x^-1*y*z) ^-1,b^-1*u*b*(u*w^-1*y)^-1, b^-1*v*b*(v*x^-1*z)^-1, b^-1*w*b*(w*y)^-1,b^-1*x*b*(x*z)^-1, b^-1*y*b*y^-1,b^-1*z*b*z^-1], [[a*b,u,v],[a*b,b*a*b*a*b^-1*a*b^-1,z]]]; end, [24,18]], "A5 2^1 x 3^6",[2,6,1],2, 1,[24,18]], # 87480.2 [[1,"abuvwxyz", function(a,b,u,v,w,x,y,z) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,u^3,v^3,w^3,x^3, y^3,z^3,u^-1*v^-1*u*v,u^-1*w^-1*u*w ,u^-1*x^-1*u*x,u^-1*y^-1*u*y, u^-1*z^-1*u*z,v^-1*w^-1*v*w, v^-1*x^-1*v*x,v^-1*y^-1*v*y, v^-1*z^-1*v*z,w^-1*x^-1*w*x, w^-1*y^-1*w*y,w^-1*z^-1*w*z, x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,a^-1*u*a*v^-1, a^-1*v*a*u,a^-1*w*a*(u^-1*x)^-1, a^-1*x*a*(v*w^-1)^-1, a^-1*y*a*(u*w^-1*x^-1*y^-1*z^-1) ^-1,a^-1*z*a*(w^-1*y^-1*z)^-1, b^-1*u*b*(u^-1*v^-1*w)^-1, b^-1*v*b*(u^-1*v*w)^-1, b^-1*w*b*u^-1,b^-1*x*b*(w*y)^-1, b^-1*y*b*(u^-1*w*x*y*z)^-1, b^-1*z*b*(w*y*z^-1)^-1],[[a^2,a*b,u]]]; end, [36]], "A5 2^1 3^6'",[2,6,2],1, 1,36], # 87480.3 [[1,"abstuvde", function(a,b,s,t,u,v,d,e) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,d^3,d^-1*a ^-1*d*a,d^-1*b^-1*d*b, d^-1*s^-1*d*s,e^3,e^-1*a^-1*e*a, e^-1*b^-1*e*b,e^-1*s^-1*e*s, d^-1*e^-1*d*e,s^3,t^3,u^3,v^3, s^-1*t^-1*s*t,s^-1*u^-1*s*u *d^-1,s^-1*v^-1*s*v*e^-1, t^-1*u^-1*t*u*e^-1, t^-1*v^-1*t*v*(d*e^-1)^-1, u^-1*v^-1*u*v, a^-1*s*a*(u*e^-1)^-1, a^-1*t*a*(v*e)^-1, a^-1*u*a*(s^-1*d)^-1, a^-1*v*a*(t^-1*d)^-1, b^-1*s*b*(s*v^-1*d^-1)^-1, b^-1*t*b*(t*u^-1*v*d*e^-1)^-1, b^-1*u*b*u^-1,b^-1*v*b*v^-1], [[a,b,d],[a,b,e]]]; end, [243,243]], "A5 2^1 3^4 C ( 3^1 x 3^1 )",[2,6,3],9, 1,[243,243]], # 87480.4 [[1,"abcdwxyz", function(a,b,c,d,w,x,y,z) return [[a^2*d^-1,b^3,c^3*(w*x*y^-1)^-1,(b*c)^4, (b*c^-1)^5,a^-1*b^-1*c*b*c*b^-1*c*b *c^-1,d^3,w^3,x^3,y^3,z^3,d^-1*w^-1*d *w,d^-1*x^-1*d*x,d^-1*y^-1*d*y, d^-1*z^-1*d*z,w^-1*x^-1*w*x, w^-1*y^-1*w*y,w^-1*z^-1*w*z, x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,a^-1*d*a*d^-1, a^-1*w*a*z^-1,a^-1*x*a*x^-1, a^-1*y*a*(w^-1*x^-1*y^-1*z^-1) ^-1,a^-1*z*a*w^-1, b^-1*d*b*(d*w*y^-1*z)^-1, b^-1*w*b*x^-1,b^-1*x*b*y^-1, b^-1*y*b*w^-1,b^-1*z*b*z^-1, c^-1*d*c*(d*x^-1*z^-1)^-1, c^-1*w*c*(w^-1*x*y^-1*z^-1)^-1, c^-1*x*c*(x^-1*z)^-1, c^-1*y*c*(w*x^-1)^-1,c^-1*z*c*x], [[b,c*a*b*c,d*y^-1*z]]]; end, [30]], "A6 3^1 E 3^4' I",[14,5,1],1, 3,30], # 87480.5 [[1,"abcdwxyz", function(a,b,c,d,w,x,y,z) return [[a^2*d^-1,b^3*(w*x*y*z^-1)^-1,c^3*(w*y ^-1*z^-1)^-1,(b*c)^4,(b*c^-1)^5, a^-1*b^-1*c*b*c*b^-1*c*b*c^-1,d^3, w^3,x^3,y^3,z^3,d^-1*w^-1*d*w, d^-1*x^-1*d*x,d^-1*y^-1*d*y, d^-1*z^-1*d*z,w^-1*x^-1*w*x, w^-1*y^-1*w*y,w^-1*z^-1*w*z, x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,a^-1*d*a*d^-1, a^-1*w*a*z^-1,a^-1*x*a*x^-1, a^-1*y*a*(w^-1*x^-1*y^-1*z^-1) ^-1,a^-1*z*a*w^-1, b^-1*d*b*(d*w*x^-1*z)^-1, b^-1*w*b*x^-1,b^-1*x*b*y^-1, b^-1*y*b*w^-1,b^-1*z*b*z^-1, c^-1*d*c*(d*x)^-1, c^-1*w*c*(w^-1*x*y^-1*z^-1)^-1, c^-1*x*c*(x^-1*z)^-1, c^-1*y*c*(w*x^-1)^-1,c^-1*z*c*x], [[b*w^-1,c*a*b*c]]]; end, [30]], "A6 3^1 E 3^4' II",[14,5,2],1, 3,30], # 87480.6 [[1,"abcwxyzf", function(a,b,c,w,x,y,z,f) return [[a^2,b^3,c^3,(b*c)^4,(b*c^-1)^5,a^-1*b^-1*c *b*c*b^-1*c*b*c^-1,w^3,x^3,y^3, z^3,f^3,w^-1*f^-1*w*f,x^-1*f^-1*x*f ,y^-1*f^-1*y*f,z^-1*f^-1*z*f, w^-1*x^-1*w*x,w^-1*y^-1*w*y, w^-1*z^-1*w*z,x^-1*y^-1*x*y, x^-1*z^-1*x*z,y^-1*z^-1*y*z, a^-1*w*a*z^-1,a^-1*x*a*x^-1, a^-1*y*a*(w^-1*x^-1*y^-1*z^-1) ^-1,a^-1*z*a*w^-1, a^-1*f*a*f^-1,b^-1*w*b*x^-1, b^-1*x*b*y^-1,b^-1*y*b*w^-1, b^-1*z*b*z^-1,b^-1*f*b*f^-1, c^-1*w*c*(w^-1*x*y^-1*z^-1*f)^-1 ,c^-1*x*c*(x^-1*z*f)^-1, c^-1*y*c*(w*x^-1*f)^-1, c^-1*z*c*(x^-1*f^-1)^-1, c^-1*f*c*f^-1],[[a,b,w]]]; end, [18]], "A6 3^4' E 3^1 I",[14,5,3],3, 3,18], # 87480.7 [[1,"abcwxyze", function(a,b,c,w,x,y,z,e) return [[a^2,b^3,c^3,(b*c)^4,(b*c^-1)^5,a^-1*b^-1*c *b*c*b^-1*c*b*c^-1,w^3,x^3,y^3, z^3,e^3,w^-1*e^-1*w*e,x^-1*e^-1*x*e ,y^-1*e^-1*y*e,z^-1*e^-1*z*e, w^-1*x^-1*w*x,w^-1*y^-1*w*y, w^-1*z^-1*w*z,x^-1*y^-1*x*y, x^-1*z^-1*x*z,y^-1*z^-1*y*z, a^-1*w*a*z^-1,a^-1*x*a*x^-1, a^-1*y*a*(w^-1*x^-1*y^-1*z^-1) ^-1,a^-1*z*a*w^-1, a^-1*e*a*e^-1,b^-1*w*b*x^-1, b^-1*x*b*(y*e^-1)^-1, b^-1*y*b*(w*e)^-1,b^-1*z*b*(z*e)^-1, b^-1*e*b*e^-1, c^-1*w*c*(w^-1*x*y^-1*z^-1*e^-1) ^-1,c^-1*x*c*(x^-1*z*e^-1)^-1, c^-1*y*c*(w*x^-1*e^-1)^-1, c^-1*z*c*(x^-1*e)^-1, c^-1*e*c*e^-1], [[a*b,b*a*b*a*b^-1*a*b^-1,w*e]]]; end, [108]], "A6 3^4' E 3^1 II",[14,5,4],3, 3,108], # 87480.8 [[1,"abcwxyzd", function(a,b,c,w,x,y,z,d) return [[a^2*d^-1,b^3,c^3,(b*c)^4,(b*c^-1)^5,a^-1 *b^-1*c*b*c*b^-1*c*b*c^-1, d^3,b^-1*d*b*d^-1,c^-1*d*c*d^-1, w^3,x^3,y^3,z^3,w^-1*d^-1*w*d, x^-1*d^-1*x*d,y^-1*d^-1*y*d, z^-1*d^-1*z*d,w^-1*x^-1*w*x, w^-1*y^-1*w*y,w^-1*z^-1*w*z, x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,a^-1*w*a*z^-1, a^-1*x*a*x^-1, a^-1*y*a*(w^-1*x^-1*y^-1*z^-1) ^-1,a^-1*z*a*w^-1, b^-1*w*b*x^-1,b^-1*x*b*y^-1, b^-1*y*b*w^-1,b^-1*z*b*z^-1, c^-1*w*c*(w^-1*x*y^-1*z^-1)^-1, c^-1*x*c*(x^-1*z)^-1, c^-1*y*c*(w*x^-1)^-1, c^-1*z*c*x], [[a*d,c*d,w],[b,c*a*b*c,z]]]; end, [18,30]], "A6 3^1 x 3^4'",[14,5,5],3, 3,[18,30]] ]; ############################################################################# ## #E perf6.grp . . . . . . . . . . . . . . . . . . . . . . . . . ends here ##