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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 perf12.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 787320-987840 ## All data is based on Holt/Plesken: Perfect Groups, OUP 1989 ## PERFGRP[296]:=[# 787320.1 [[1,"abwxyzWXYZ", function(a,b,w,x,y,z,W,X,Y,Z) return [[a^4,b^3,(a*b)^5,a^2*b*a^2*b^-1,w^3,x^3,y^3,z^3, 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,w^-1*W*w*W^-1, w^-1*X*w*X^-1,w^-1*Y*w*Y^-1, w^-1*Z*w*Z^-1,x^-1*W*x*W^-1, x^-1*X*x*X^-1,x^-1*Y*x*Y^-1, x^-1*Z*x*Z^-1,y^-1*W*y*W^-1, y^-1*X*y*X^-1,y^-1*Y*y*Y^-1, y^-1*Z*y*Z^-1,z^-1*W*z*W^-1, z^-1*X*z*X^-1,z^-1*Y*z*Y^-1, z^-1*Z*z*Z^-1,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, a^-1*W*a*Z^-1,a^-1*X*a*X^-1, a^-1*Y*a*(W^2*X^2*Y^2*Z^2)^-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], [[a*b,w,W],[b,a*b*a*b^-1*a,w*x^-1,W], [b,a*b*a*b^-1*a,W*X^-1,w]]]; end, [24,15,15]], "A5 2^1 x 3^4' x 3^4'",[2,8,1],2, 1,[24,15,15]], # 787320.2 [[1,"abwxyz", function(a,b,w,x,y,z) return [[a^4,b^3,(a*b)^5,a^2*b*a^2*b^-1,w^9,x^9,y^9,z^9, 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], [[a*b,w],[b,a*b*a*b^-1*a,w*x^-1]]]; end, [24,45]], "A5 2^1 x 3^4' A 3^4'",[2,8,2],2, 1,[24,45]], # 787320.3 [[1,"abwxyzWXYZ", function(a,b,w,x,y,z,W,X,Y,Z) return [[a^4,b^3*Z^-1,(a*b)^5,a^2*b*a^2*b^-1,w^3,x^3, y^3,z^3,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,w^-1*W*w*W^-1, w^-1*X*w*X^-1,w^-1*Y*w*Y^-1, w^-1*Z*w*Z^-1,x^-1*W*x*W^-1, x^-1*X*x*X^-1,x^-1*Y*x*Y^-1, x^-1*Z*x*Z^-1,y^-1*W*y*W^-1, y^-1*X*y*X^-1,y^-1*Y*y*Y^-1, y^-1*Z*y*Z^-1,z^-1*W*z*W^-1, z^-1*X*z*X^-1,z^-1*Y*z*Y^-1, z^-1*Z*z*Z^-1,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, a^-1*W*a*Z^-1,a^-1*X*a*X^-1, a^-1*Y*a*(W^2*X^2*Y^2*Z^2)^-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], [[a*b,w,W],[b,a*b*a*b^-1*a,w*x^-1,W], [a^2,b,z,W*X^-1,w]]]; end, [24,15,60]], "A5 2^1 3^4' x N 3^4",[2,8,3],2, 1,[24,15,60]], # 787320.4 [[1,"abwxyz", function(a,b,w,x,y,z) return [[a^4,b^3*z^-1,(a*b)^5,a^2*b*a^2*b^-1,w^9,x^9, y^9,z^9,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], [[a*b,w],[a^2,b,w*x^-1]]]; end, [24,180]], "A5 2^1 x N 3^4' A 3^4'",[2,8,4],2, 1,[24,180]], # 787320.5 [[1,"abstuvwxyz", function(a,b,s,t,u,v,w,x,y,z) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,s^3,t^3,u^3,v^3, w^3,x^3,y^3,z^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,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,s^-1*w*s*w^-1, s^-1*x*s*x^-1,s^-1*y*s*y^-1, s^-1*z*s*z^-1,t^-1*w*t*w^-1, t^-1*x*t*x^-1,t^-1*y*t*y^-1, t^-1*z*t*z^-1,u^-1*w*u*w^-1, u^-1*x*u*x^-1,u^-1*y*u*y^-1, u^-1*z*u*z^-1,v^-1*w*v*w^-1, v^-1*x*v*x^-1,v^-1*y*v*y^-1, v^-1*z*v*z^-1,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, a^-1*w*a*z^-1,a^-1*x*a*x^-1, a^-1*y*a*(w^2*x^2*y^2*z^2)^-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], [[b,a*b*a*b^-1*a,w*x^-1,s], [b,a*b*a*b^-1*a,u,w]]]; end, [15,45]], "A5 2^1 3^4 x 3^4'",[2,8,5],1, 1,[15,45]], # 787320.6 [[1,"abstuvwxyz", function(a,b,s,t,u,v,w,x,y,z) return [[a^4,b^3*z^-1,(a*b)^5,a^2*b^-1*a^2*b,s^3,t^3, u^3,v^3,w^3,x^3,y^3,z^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,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,s^-1*w*s*w^-1, s^-1*x*s*x^-1,s^-1*y*s*y^-1, s^-1*z*s*z^-1,t^-1*w*t*w^-1, t^-1*x*t*x^-1,t^-1*y*t*y^-1, t^-1*z*t*z^-1,u^-1*w*u*w^-1, u^-1*x*u*x^-1,u^-1*y*u*y^-1, u^-1*z*u*z^-1,v^-1*w*v*w^-1, v^-1*x*v*x^-1,v^-1*y*v*y^-1, v^-1*z*v*z^-1,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, a^-1*w*a*z^-1,a^-1*x*a*x^-1, a^-1*y*a*(w^2*x^2*y^2*z^2)^-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], [[b,a^2,w*x^-1,s,t],[b,a*b*a*b^-1*a,u,w]]]; end, [60,45]], "A5 2^1 3^4 x N 3^4'",[2,8,6],1, 1,[60,45]], # 787320.7 [[1,"abstuvwxyz", function(a,b,s,t,u,v,w,x,y,z) return [[a^4,b^3*z^-1,(a*b)^5,a^2*b^-1*a^2*b,s^3,t^3, u^3,v^3,w^3,x^3,y^3,z^3,s^-1*t^-1*s*t *(w*y)^-1,s^-1*u^-1*s*u *(w*x^-1*z)^-1,s^-1*v^-1*s*v *(w*x*y*z^-1)^-1,t^-1*u^-1*t*u *(w*y^-1)^-1,t^-1*v^-1*t*v *(w^-1*x*z^-1)^-1,u^-1*v^-1*u*v *(w^-1*x^-1*y^-1)^-1, s^-1*w^-1*s*w,s^-1*x^-1*s*x, s^-1*y^-1*s*y,s^-1*z^-1*s*z, a^-1*s*a*(u*w)^-1, a^-1*t*a*(v*x^-1*z)^-1, a^-1*u*a*(s^-1*y^-1*z^-1)^-1, a^-1*v*a*(t^-1*z^-1)^-1, b^-1*s*b*(s*v^-1*w*x*y*z^-1)^-1, b^-1*t*b*(t*u^-1*v*y^-1)^-1, b^-1*u*b*(u*w*x^-1)^-1, b^-1*v*b*(v*w^-1*x^-1*y^-1)^-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*w*b*x^-1,b^-1*x*b*y^-1, b^-1*y*b*w^-1,b^-1*z*b*z^-1], [[b,s,u,v]]]; end, [360]], "A5 2^1 3^4 C N 3^4'",[2,8,7],1, 1,360], # 787320.8 [[1,"abstuvwxyz", function(a,b,s,t,u,v,w,x,y,z) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,s^3,t^3,u^3,v^3, w^3,x^3,y^3,z^3,s^-1*t^-1*s*t*(w*y)^-1, s^-1*u^-1*s*u*(w*x^-1*z)^-1, s^-1*v^-1*s*v*(w*x*y*z^-1)^-1, t^-1*u^-1*t*u*(w*y^-1)^-1, t^-1*v^-1*t*v*(w^-1*x*z^-1)^-1, u^-1*v^-1*u*v*(w^-1*x^-1*y^-1) ^-1,s^-1*w^-1*s*w,s^-1*x^-1*s *x,s^-1*y^-1*s*y,s^-1*z^-1*s*z, a^-1*s*a*(u*w)^-1, a^-1*t*a*(v*x^-1*z)^-1, a^-1*u*a*(s^-1*y^-1*z^-1)^-1, a^-1*v*a*(t^-1*z^-1)^-1, b^-1*s*b*(s*v^-1*w*x*y*z^-1)^-1, b^-1*t*b*(t*u^-1*v*y^-1)^-1, b^-1*u*b*(u*w*x^-1)^-1, b^-1*v*b*(v*w^-1*x^-1*y^-1)^-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*w*b*x^-1,b^-1*x*b*y^-1, b^-1*y*b*w^-1,b^-1*z*b*z^-1], [[b,s,u,v]]]; end, [360]], "A5 2^1 3^4 C 3^4'",[2,8,8],1, 1,360], # 787320.9 [[1,"abstuvSTUV", function(a,b,s,t,u,v,S,T,U,V) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,s^3*T^-1,t^3 *(S*T^-1)^-1,u^3*V^-1, v^3*(U*V^-1)^-1,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*T^-1*V)^-1, b^-1*t*b *(t*u^-1*v*S^-1*T^-1*V^-1)^-1, b^-1*u*b*(u*S*U*V^-1)^-1, b^-1*v*b*(v*T*V)^-1],[[a^2,s,t,u]]]; end, [540]], "A5 2^1 3^4 A 3^4 I",[2,8,9],1, 1,540], # 787320.10 [[1,"abstuvSTUV", function(a,b,s,t,u,v,S,T,U,V) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,s^3*S^-1,t^3 *T^-1,u^3*U^-1,v^3*V^-1,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*S^-1*T^-1*V)^-1 , b^-1*t*b*(t*u^-1*v*S^-1*T^-1*U^(-1 *1)*V)^-1,b^-1*u*b*(u*S*T*V)^-1, b^-1*v*b*(v*S*U)^-1],[[a^2,s,t,u]]]; end, [540]], "A5 2^1 3^4 A 3^4 II",[2,8,10],1, 1,540], # 787320.11 [[1,"abstuvSTUV", function(a,b,s,t,u,v,S,T,U,V) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,s^3*S^-1,t^3 *T^-1,u^3*U^-1,v^3*V^-1,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*S*T^-1)^-1, b^-1*t*b*(t*u^-1*v*V)^-1, b^-1*u*b*(u*S*T*V)^-1, b^-1*v*b*(v*S*U)^-1],[[a^2,s,t,u]]]; end, [540]], "A5 2^1 3^4 A 3^4 III",[2,8,11],1, 1,540], # 787320.12 [[1,"abstuvSTUV", function(a,b,s,t,u,v,S,T,U,V) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,s^3,t^3,u^3,v^3, 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,s^-1*S^-1*s*S, s^-1*T^-1*s*T,s^-1*U^-1*s*U, s^-1*V^-1*s*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*S*V)^-1 , b^-1*t*b*(t*u^-1*v*S^-1*T^-1*U^(-1 *1))^-1,b^-1*u*b*u^-1, b^-1*v*b*v^-1,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], [[a^2,s,t,u,v,S,T,U]]]; end, [180]], "A5 2^1 3^4 E 3^4",[2,8,12],1, 1,180], # 787320.13 [[1,"abstuvSTUV", function(a,b,s,t,u,v,S,T,U,V) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,s^3,t^3,u^3,v^3, 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,s^-1*S^-1*s*S, s^-1*T^-1*s*T,s^-1*U^-1*s*U, s^-1*V^-1*s*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, 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], [[b,a*b*a*b^-1*a,u,S],[b,a*b*a*b^-1*a,U,s]]] ; end, [45,45]], "A5 2^1 3^4 x 3^4",[2,8,13],1, 1,[45,45]], # 787320.14 [[1,"abcduvwxyz", function(a,b,c,d,u,v,w,x,y,z) 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,d^-1*b^-1*d*b,d^-1*c^-1*d*c, u^3,v^3,w^3,x^3,y^3,z^3,d^-1*u^-1*d*u, d^-1*v^-1*d*v,d^-1*w^-1*d*w, d^-1*x^-1*d*x,d^-1*y^-1*d*y, d^-1*z^-1*d*z,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*(u^2*v*w^2*x^2*y)^-1, a^-1*v*a*(u*v*w^2*z)^-1, a^-1*w*a*(u^2*w*x*y^2*z^2)^-1, a^-1*x*a*(v^2*w*y^2)^-1, a^-1*y*a*(u*v^2*w^2*y^2*z)^-1, a^-1*z*a*(u^2*v^2*x^2*y*z)^-1, b^-1*u*b*(u*w^2*y)^-1, b^-1*v*b*(v*x^2*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, c^-1*u*c*u^-1,c^-1*v*c*v^-1, c^-1*w*c*(v*w)^-1, c^-1*x*c*(u*v^2*x)^-1, c^-1*y*c*(u*v^2*x^2*y)^-1, c^-1*z*c*(u^2*v^2*w^2*x*z)^-1], [[b,c*a*b*c,y,z,w,x],[a*d,c*d,u]]]; end, [90,18]], "A6 3^1 x 3^6",[14,7,1],3, 3,[90,18]], # 787320.15 [[1,"abcduvwxyz", function(a,b,c,d,u,v,w,x,y,z) return [[a^2*(d*v^2*w*x*y^2)^-1,b^3*z^-1,c^3*v^(-1 *2),(b*c)^4*(v*x^2*y^2)^-1, (b*c^-1)^5*(v*x^2*y)^-1, a^-1*b^-1*c*b*c*b^-1*c*b*c^-1,d^3, d^-1*b^-1*d*b,d^-1*c^-1*d*c,u^3, v^3,w^3,x^3,y^3,z^3,d^-1*u^-1*d*u, d^-1*v^-1*d*v,d^-1*w^-1*d*w, d^-1*x^-1*d*x,d^-1*y^-1*d*y, d^-1*z^-1*d*z,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*(u^2*v*w^2*x^2*y)^-1, a^-1*v*a*(u*v*w^2*z)^-1, a^-1*w*a*(u^2*w*x*y^2*z^2)^-1, a^-1*x*a*(v^2*w*y^2)^-1, a^-1*y*a*(u*v^2*w^2*y^2*z)^-1, a^-1*z*a*(u^2*v^2*x^2*y*z)^-1, b^-1*u*b*(u*w^2*y)^-1, b^-1*v*b*(v*x^2*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, c^-1*u*c*u^-1,c^-1*v*c*v^-1, c^-1*w*c*(v*w)^-1, c^-1*x*c*(u*v^2*x)^-1, c^-1*y*c*(u*v^2*x^2*y)^-1, c^-1*z*c*(u^2*v^2*w^2*x*z)^-1], [[b,c*a*b*c,y,z,w,x],[a*d,c*d,u]]]; end, [90,18],[0,[2,3]]], "A6 3^1 x N 3^6",[14,7,2],3, 3,[90,18]], # 787320.16 [[1,"abcdwxyzef", function(a,b,c,d,w,x,y,z,e,f) 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,d^-1*b^-1*d*b,d^-1*c^-1*d*c, w^3,x^3,y^3,z^3,e^3,f^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,d^-1*e^-1*d*e, d^-1*f^-1*d*f,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*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*e*a*e^-1,a^-1*f*a*f^-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,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*e*c*e^-1,c^-1*f*c*f^-1], [[a,b,w,d],[a,c,w,d],[a*d,c*d,w,e]]]; end, [18,18,18]], "A6 3^1 x ( 3^4' E ( 3^1 x 3^1 ) )",[14,7,3],27, 3,[18,18,18]] ]; PERFGRP[297]:=[# 806736.1 [[1,"abyzYZ", function(a,b,y,z,Y,Z) return [[a^4,b^3,(a*b)^7,a^2*b^-1*a^2*b,(a^-1*b^-1 *a*b)^4*a^2,y^7,z^7,Y^7,Z^7, y^-1*z^-1*y*z,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, a^-1*y*a*z,a^-1*z*a*y^-1, b^-1*y*b*z^-1, b^-1*z*b*(y^-1*z^-1)^-1, a^-1*Y*a*Z,a^-1*Z*a*Y^-1, b^-1*Y*b*Z^-1, b^-1*Z*b*(Y^-1*Z^-1)^-1], [[a,b,y],[a,b,Y]]]; end, [49,49]], "L3(2) 2^1 7^2 x 7^2",[10,4,1],1, 2,[49,49]], # 806736.2 [[1,"abwxyz", function(a,b,w,x,y,z) return [[a^4,b^3,(a*b)^7,a^2*b^-1*a^2*b,(a^-1*b^-1 *a*b)^4*a^2,w^7,x^7,y^7,z^7, 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,a^-1*x*a*y^-1, a^-1*y*a*x,a^-1*z*a*w^-1, b^-1*w*b*z^-1, b^-1*x*b*(y^-1*z^-1)^-1, b^-1*y*b*(x*y^2*z)^-1, b^-1*z*b*(w^-1*x^(-1*3)*y^(-1*3)*z^-1) ^-1], [[a^2,a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,x] ]]; end, [56]], "L3(2) 2^1 7^4",[10,4,2],1, 2,56] ]; PERFGRP[298]:=[# 816480.1 [[2,4860,1,168,1], "( A5 x L3(2) ) # 3^4 [1]",[32,4,1],1, [1,2],[15,7]], # 816480.2 [[2,4860,2,168,1], "( A5 x L3(2) ) # 3^4 [2]",[32,4,2],1, [1,2],[60,7]] ]; PERFGRP[299]:=[# 820800.1 [[2,120,1,6840,1], "( A5 x L2(19) ) 2^2",40,4, [1,9],[24,40]] ]; PERFGRP[300]:=[# 822528.1 [[2,168,1,4896,1], "( L3(2) x L2(17) ) 2^1 [1]",40,2, [2,7],[7,288]], # 822528.2 [[2,336,1,2448,1], "( L3(2) x L2(17) ) 2^1 [2]",40,2, [2,7],[16,18]], # 822528.3 [[3,336,1,4896,1,"d1","d2"], "( L3(2) x L2(17) ) 2^1 [3]",40,2, [2,7],2304] ]; PERFGRP[301]:=[# 823080.1 [[1,"abxyz", function(a,b,x,y,z) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,x^19,y^19,z^19, 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^(-1*2)*y^(-1*6)*z^5)^-1, b^-1*y*b*(x^(-1*8)*y^(-1*4)*z^(-1*7))^-1, b^-1*z*b*(x^6*y^7*z^6)^-1], [[a*b,z],[a*b,b*a*b*a*b^-1*a*b^-1, y*z^(-1*2)]]]; end, [24,114],[0,0,2,2,2,2,2,2]], "A5 2^1 19^3",[5,3,1],2, 1,[24,114]], # 823080.2 [[1,"abyzd", function(a,b,y,z,d) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,d^19,d^-1*y ^-1*d*y,d^-1*z^-1*d*z,y^19,z^19, y^-1*z^-1*y*z*d^-1, a^-1*y*a*z^-1,a^-1*z*a*y, a^-1*d*a*d^-1, b^-1*y*b*(y^(-1*6)*z^(-1*9)*d^(-1*8))^-1, b^-1*z*b*(y^(-1*5)*z^5*d^3)^-1],[[a,b]]]; end, [6859],[0,0,2,2,2,2,2,2,0,2]], "A5 2^1 19^2 C 19^1",[5,3,2],19, 1,6859] ]; PERFGRP[302]:=[# 846720.1 [[2,336,1,2520,1], "( L3(2) x A7 ) 2^1 [1]",40,2, [2,8],[16,7]], # 846720.2 [[2,168,1,5040,1], "( L3(2) x A7 ) 2^1 [2]",40,2, [2,8],[7,240]], # 846720.3 [[3,336,1,5040,1,"d1","d2"], "( L3(2) x A7 ) 2^1 [3]",40,2, [2,8],1920] ]; PERFGRP[303]:=[# 864000.1 [[2,120,1,7200,1], "( A5 x A5 x A5 ) 2^2 [1]",40,4, [1,1,1],[24,5,24]], # 864000.2 [[2,120,1,7200,2], "( A5 x A5 x A5 ) 2^2 [2]",40,4, [1,1,1],[24,288]], # 864000.3 [[3,120,1,14400,1,"d1","a2","a2","c2","c2"], "( A5 x A5 x A5 ) 2^2 [3]",40,4, [1,1,1],[288,288]] ]; PERFGRP[304]:=[# 871200.1 [[2,660,1,1320,1], "( L2(11) x L2(11) ) 2^1 [1]",40,2, [5,5],[11,24]], # 871200.2 [[3,1320,1,1320,1,"d1","d2"], "( L2(11) x L2(11) ) 2^1 [2]",40,2, [5,5],288] ]; PERFGRP[305]:=[# 874800.1 [[2,60,1,14580,1], "( A5 x A5 ) # 3^5",[30,5,1],3, [1,1],[5,18]] ]; PERFGRP[306]:=[# 878460.1 [[1,"abxyz", function(a,b,x,y,z) return [[a^2,b^3,(a*b)^11,(a*b)^4*(a*b^-1)^5*(a*b)^4*(a *b^-1)^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*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*a*(b^-1*a)^4*b^-1,y]]]; end, [132]], "L2(11) 11^3",[19,3,1],1, 5,132], # 878460.2 [[1,"abxyz", function(a,b,x,y,z) return [[a^2,b^3,(a*b)^11*z^-1,(a*b)^4*(a*b^-1)^5*(a*b) ^4*(a*b^-1)^5*(x^2*y^3*z^5)^-1,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*z^-1, b^-1*y*b*(y^-1*z^-1)^-1, b^-1*z*b*(x*y^2*z)^-1], [[a*b*x^(-1*3),b*a*b*a*(b^-1*a)^4*b^-1,y]]]; end, [132]], "L2(11) N 11^3",[19,3,2],1, 5,132] ]; PERFGRP[307]:=[# 881280.1 [[2,360,1,2448,1], "A6 x L2(17)",40,1, [3,7],[6,18]] ]; PERFGRP[308]:=[# 885720.1 [[1,"abc", function(a,b,c) return [[c^60,b^11,c^(-1*6)*b*c^6*b^(-1*6),c^(-1*29)*b*c*b*c ^28*b^(-1*4),a^2,c*a*c*a^-1,(b*a)^3, c*b^4*c*b^2*c*a*b^3*c*b*a*b^-1*c^-1*a *b^-1*a],[[b,c]]]; end, [122]], "L2(121)",22,-1, 54,122] ]; PERFGRP[309]:=[# 887040.1 [[1,"abe", function(a,b,e) return [[a^2,b^4,(a*b)^11,(a*b*a*b^2)^7,(a*b*a*b^-1*a*b ^-1*a*b^2*a*b)^2*b*a*b^-1 *e^-1,e^2,a^-1*e*a*e^-1, b^-1*e*b*e^-1], [[a*b*a*b^2,a*b^-1*a*b*a*b^-1*a*b*a*e]]]; end, [352]], "M22 2^1",28,-2, 46,352], # 887040.2 [[2,1344,1,660,1], "( L3(2) x L2(11) ) # 2^3 [1]",[39,3,1],1, [2,5],[8,11]], # 887040.3 [[2,1344,2,660,1], "( L3(2) x L2(11) ) # 2^3 [2]",[39,3,2],1, [2,5],[14,11]] ]; PERFGRP[310]:=[# 892800.1 [[2,60,1,14880,1], "A5 x L2(31)",40,1, [1,18],[5,32]] ]; PERFGRP[311]:=[# 900000.1 [[2,60,1,15000,1], "( A5 x A5 ) 2^1 # 5^3 [1]",[30,3,1],2, [1,1],[5,24,30]], # 900000.2 [[2,120,1,7500,1], "( A5 x A5 ) 2^1 # 5^3 [2]",[30,3,1],2, [1,1],[24,30]], # 900000.3 [[3,120,1,15000,1,"d1","a2","a2"], "( A5 x A5 ) 2^1 # 5^3 [3]",[30,3,1],2, [1,1],[288,360]], # 900000.4 [[2,60,1,15000,2], "( A5 x A5 ) 2^1 # 5^3 [4]",[30,3,2],2, [1,1],[5,24,30]], # 900000.5 [[2,120,1,7500,2], "( A5 x A5 ) 2^1 # 5^3 [5]",[30,3,2],2, [1,1],[24,30]], # 900000.6 [[3,120,1,15000,2,"d1","a2","a2"], "( A5 x A5 ) 2^1 # 5^3 [6]",[30,3,2],2, [1,1],[288,360]], # 900000.7 [[2,60,1,15000,3], "( A5 x A5 ) 2^1 # 5^3 [7]",[30,3,3],5, [1,1],[5,125]] ]; PERFGRP[312]:=[# 903168.1 [[2,168,1,5376,1], "( L3(2) x L3(2) ) # 2^5 [1]",[34,5,1],4, [2,2],[7,16,16]], # 903168.2 [[2,336,1,2688,1], "( L3(2) x L3(2) ) # 2^5 [2]",[34,5,2],4, [2,2],[16,8,16]], # 903168.3 [[2,336,1,2688,2], "( L3(2) x L3(2) ) # 2^5 [3]",[34,5,3],4, [2,2],[16,16]], # 903168.4 [[2,336,1,2688,3], "( L3(2) x L3(2) ) # 2^5 [4]",[34,5,4],4, [2,2],[16,16,14]], # 903168.5 [[3,336,1,5376,1,"d1","d2"], "( L3(2) x L3(2) ) # 2^5 [5]",[34,5,5],4, [2,2],[128,128]], # 903168.6 [[3,336,1,5376,1,"d1","e2"], "( L3(2) x L3(2) ) # 2^5 [6]",[34,5,6],4, [2,2],[128,128]] ]; PERFGRP[313]:=[# 907200.1 [[2,60,1,15120,1], "( A5 x A7 3^1 ) 2^1 [1]",40,6, [1,8],[5,45,240]], # 907200.2 [[2,120,1,7560,1], "( A5 x A7 3^1 ) 2^1 [2]",40,6, [1,8],[24,45]], # 907200.3 [[3,120,1,15120,1,"d1","d2"], "( A5 x A7 3^1 ) 2^1 [3]",40,6, [1,8],[540,2880]], # 907200.4 [[2,360,1,2520,1], "A6 x A7",40,1, [3,8],[6,7]] ]; PERFGRP[314]:=[# 912576.1 [[1,"abc", function(a,b,c) return [[c^48*a^2,c*b^25*c^-1*b^-1,b^97,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^10*(b*c)^2*a*b*c^2*a*b*a*b^2*c*b*a], [[b,c^32]]]; end, [3136],[0,5,2,2,3,3]], "L2(97) 2^1 = SL(2,97)",22,-2, 47,3136] ]; PERFGRP[315]:=[# 921600.1 [[1,"abcdstuvwxyz", function(a,b,c,d,s,t,u,v,w,x,y,z) return [[a^2,b^3,(a*b)^5,c^2,d^3,(c*d)^5,a^-1*c^-1*a*c ,a^-1*d^-1*a*d,b^-1*c^-1*b*c, b^-1*d^-1*b*d,s^2,t^2,u^2,v^2,w^2,x^2,y^2, z^2,s^-1*t^-1*s*t,s^-1*u^-1*s*u, s^-1*v^-1*s*v,s^-1*w^-1*s*w, s^-1*x^-1*s*x,s^-1*y^-1*s*y, s^-1*z^-1*s*z,t^-1*u^-1*t*u, t^-1*v^-1*t*v,t^-1*w^-1*t*w, t^-1*x^-1*t*x,t^-1*y^-1*t*y, t^-1*z^-1*t*z,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*s*a*w^-1,a^-1*t*a*x^-1, a^-1*u*a*y^-1,a^-1*v*a*z^-1, a^-1*w*a*s^-1,a^-1*x*a*t^-1, a^-1*y*a*u^-1,a^-1*z*a*v^-1, b^-1*s*b*(t*x)^-1, b^-1*t*b*(s*t*w*x)^-1, b^-1*u*b*(v*z)^-1, b^-1*v*b*(u*v*y*z)^-1, b^-1*w*b*(w*x)^-1,b^-1*x*b*w^-1, b^-1*y*b*(y*z)^-1,b^-1*z*b*y^-1, c^-1*s*c*u^-1,c^-1*t*c*v^-1, c^-1*u*c*s^-1,c^-1*v*c*t^-1, c^-1*w*c*y^-1,c^-1*x*c*z^-1, c^-1*y*c*w^-1,c^-1*z*c*x^-1, d^-1*s*d*(t*v)^-1, d^-1*t*d*(s*t*u*v)^-1, d^-1*u*d*(u*v)^-1,d^-1*v*d*u^-1, d^-1*w*d*(x*z)^-1, d^-1*x*d*(w*x*y*z)^-1, d^-1*y*d*(y*z)^-1,d^-1*z*d*y^-1], [[a*b*a*b^-1*a,b,c,d,w]]]; end, [80]], "A5 x A5 2^8",[29,8,1],1, [1,1],80], # 921600.2 [[1,"abcdstuvwxyz", function(a,b,c,d,s,t,u,v,w,x,y,z) return [[a^2,b^3,(a*b)^5,c^2,d^3,(c*d)^5,a^-1*c^-1*a*c ,a^-1*d^-1*a*d,b^-1*c^-1*b*c, b^-1*d^-1*b*d*y^-1,s^2,t^2,u^2,v^2, w^2,x^2,y^2,z^2,s^-1*t^-1*s*t, s^-1*u^-1*s*u,s^-1*v^-1*s*v, s^-1*w^-1*s*w,s^-1*x^-1*s*x, s^-1*y^-1*s*y,s^-1*z^-1*s*z, t^-1*u^-1*t*u,t^-1*v^-1*t*v, t^-1*w^-1*t*w,t^-1*x^-1*t*x, t^-1*y^-1*t*y,t^-1*z^-1*t*z, 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*s*a*w^-1, a^-1*t*a*x^-1,a^-1*u*a*y^-1, a^-1*v*a*z^-1,a^-1*w*a*s^-1, a^-1*x*a*t^-1,a^-1*y*a*u^-1, a^-1*z*a*v^-1,b^-1*s*b*(t*x)^-1, b^-1*t*b*(s*t*w*x)^-1, b^-1*u*b*(v*z)^-1, b^-1*v*b*(u*v*y*z)^-1, b^-1*w*b*(w*x)^-1,b^-1*x*b*w^-1, b^-1*y*b*(y*z)^-1,b^-1*z*b*y^-1, c^-1*s*c*u^-1,c^-1*t*c*v^-1, c^-1*u*c*s^-1,c^-1*v*c*t^-1, c^-1*w*c*y^-1,c^-1*x*c*z^-1, c^-1*y*c*w^-1,c^-1*z*c*x^-1, d^-1*s*d*(t*v)^-1, d^-1*t*d*(s*t*u*v)^-1, d^-1*u*d*(u*v)^-1,d^-1*v*d*u^-1, d^-1*w*d*(x*z)^-1, d^-1*x*d*(w*x*y*z)^-1, d^-1*y*d*(y*z)^-1,d^-1*z*d*y^-1], [[a*b*a*b^-1*a,b,c,d,w]]]; end, [80]], "A5 x A5 N 2^8",[29,8,2],1, [1,1],80], # 921600.3 [[2,960,1,960,1], "( A5 x A5 ) # 2^8 [3]",[29,8,3],1, [1,1],[16,16]], # 921600.4 [[2,960,1,960,2], "( A5 x A5 ) # 2^8 [4]",[29,8,4],1, [1,1],[16,10]], # 921600.5 [[2,960,2,960,2], "( A5 x A5 ) # 2^8 [5]",[29,8,5],1, [1,1],[10,10]], # 921600.6 [[2,7680,1,120,1], "( A5 x A5 ) # 2^8 [6]",[29,8,6],16, [1,1],[12,64,24]], # 921600.7 [[2,7680,2,120,1], "( A5 x A5 ) # 2^8 [7]",[29,8,7],16, [1,1],[24,64,24]], # 921600.8 [[2,7680,3,120,1], "( A5 x A5 ) # 2^8 [8]",[29,8,8],16, [1,1],[24,64,24]], # 921600.9 [[2,7680,4,120,1], "( A5 x A5 ) # 2^8 [9]",[29,8,9],16, [1,1],[24,64,24]], # 921600.10 [[2,7680,5,120,1], "( A5 x A5 ) # 2^8 [10]",[29,8,10],16, [1,1],[24,24,24]], # 921600.11 [[2,15360,1,60,1], "( A5 x A5 ) # 2^8 [11]",[29,8,11],16, [1,1],[64,64,5]], # 921600.12 [[2,15360,2,60,1], "( A5 x A5 ) # 2^8 [12]",[29,8,12],16, [1,1],[24,12,64,5]], # 921600.13 [[2,15360,3,60,1], "( A5 x A5 ) # 2^8 [13]",[29,8,13],1, [1,1],[16,16,5]], # 921600.14 [[2,15360,4,60,1], "( A5 x A5 ) # 2^8 [14]",[29,8,14],1, [1,1],[40,5]], # 921600.15 [[2,15360,5,60,1], "( A5 x A5 ) # 2^8 [15]",[29,8,15],1, [1,1],[16,10,5]], # 921600.16 [[2,15360,6,60,1], "( A5 x A5 ) # 2^8 [16]",[29,8,16],1, [1,1],[10,10,5]], # 921600.17 [[2,15360,7,60,1], "( A5 x A5 ) # 2^8 [17]",[29,8,17],1, [1,1],[20,5]], # 921600.18 [[3,15360,1,120,1,"e1","e1","d2"], "( A5 x A5 ) # 2^8 [18]",[29,8,18],16, [1,1],[768,768]], # 921600.19 [[3,15360,2,120,1,"d1","d2"], "( A5 x A5 ) # 2^8 [19]",[29,8,19],16, [1,1],[288,144,768]], # 921600.20 [[3,15360,2,120,1,"d1","f1","d2"], "( A5 x A5 ) # 2^8 [20]",[29,8,20],16, [1,1],[288,144,768]], # 921600.21 [[3,15360,2,120,1,"d1","e1","e1","f1","d2"], "( A5 x A5 ) # 2^8 [21]",[29,8,21],16, [1,1],[288,144,768]], # 921600.22 [[3,15360,2,120,1,"f1","d2"], "( A5 x A5 ) # 2^8 [22]",[29,8,22],16, [1,1],[288,144,768]], # 921600.23 [[3,15360,2,120,1,"e1","e1","d2"], "( A5 x A5 ) # 2^8 [23]",[29,8,23],16, [1,1],[288,144,768]] ]; PERFGRP[316]:=[# 921984.1 [[4,2688,1,57624,1,168], "L3(2) # 2^4 7^3 [1]",12,2, 2,[8,16,56]], # 921984.2 [[4,2688,2,57624,1,168], "L3(2) # 2^4 7^3 [2]",12,2, 2,[16,56]], # 921984.3 [[4,2688,3,57624,1,168], "L3(2) # 2^4 7^3 [3]",12,2, 2,[16,14,56]], # 921984.4 [[4,2688,1,57624,2,168], "L3(2) # 2^4 7^3 [4]",12,2, 2,[8,16,56]], # 921984.5 [[4,2688,2,57624,2,168], "L3(2) # 2^4 7^3 [5]",12,2, 2,[16,56]], # 921984.6 [[4,2688,3,57624,2,168], "L3(2) # 2^4 7^3 [6]",12,2, 2,[16,14,56]], # 921984.7 [[4,2688,1,115248,4,336,1,3], "L3(2) # 2^4 7^3 [7]",12,7, 2,[8,16,343]], # 921984.8 [[4,2688,3,115248,4,336,3,3], "L3(2) # 2^4 7^3 [8]",12,7, 2,[16,14,343]] ]; PERFGRP[317]:=[# 929280.1 [[4,7680,4,14520,2,120,4,1], "A5 # 2^7 11^2 [1]",6,4, 1,[24,64,121]], # 929280.2 [[4,7680,5,14520,2,120,5,1], "A5 # 2^7 11^2 [2]",6,4, 1,[24,24,121]] ]; PERFGRP[318]:=[# 933120.1 [[1,"abdwxyzstuve", function(a,b,d,w,x,y,z,s,t,u,v,e) return [[a^4,b^3,(a*b)^5,a^2*b*a^2*b^-1,d^2,a^-1*d ^-1*a*d,b^-1*d^-1*b*d,w^2,x^2,y^2, z^2,(w*x)^2*d,(w*y)^2*d,(w*z)^2*d,(x*y)^2*d, (x*z)^2*d,(y*z)^2*d,a^-1*w*a*z^-1, a^-1*x*a*x^-1,a^-1*y*a*(w*x*y*z)^-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,d^-1*w^-1*d*w, d^-1*x^-1*d*x,d^-1*y^-1*d*y, d^-1*z^-1*d*z,s^3,t^3,u^3,v^3,e^3, s^-1*t^-1*s*t*e^-1, s^-1*u^-1*s*u*e,s^-1*v^-1*s*v, t^-1*u^-1*t*u*e,t^-1*v^-1*t*v*e, u^-1*v^-1*u*v*e,s^-1*e*s*e^-1, t^-1*e*t*e^-1,u^-1*e*u*e^-1, v^-1*e*v*e^-1, a^-1*s*a*(s*t*u*v*e)^-1, a^-1*t*a*(s^-1*t*u*v^-1*e^-1)^-1 ,a^-1*u*a*(s^-1*u^-1*v)^-1, a^-1*v*a*(t*u^-1*v^-1*e)^-1, a^-1*e*a*e^-1, b^-1*s*b*(s^-1*t^-1*u*v^-1)^-1, b^-1*t*b*(s^-1*v^-1*e)^-1, b^-1*u*b*(s*t^-1*u^-1*v^-1)^-1, b^-1*v*b*(t^-1*u^-1*e)^-1, b^-1*e*b*e^-1,d^-1*s*d*s, d^-1*t*d*(t^-1*e)^-1, d^-1*u*d*(u^-1*e^-1)^-1, d^-1*v*d*(v^-1*e)^-1, d^-1*e*d*e^-1,w^-1*s*w*s^-1, w^-1*t*w*(s^-1*t*v*e^-1)^-1, w^-1*u*w*(s*t*u^-1*v^-1*e^-1)^-1 ,w^-1*v*w*(s^-1*v^-1*e)^-1, w^-1*e*w*e^-1, x^-1*s*x*(s*t*u*v^-1)^-1, x^-1*t*x*t^-1, x^-1*u*x*(s^-1*v^-1)^-1, x^-1*v*x*(s^-1*t^-1*u*v*e)^-1, x^-1*e*x*e^-1, y^-1*s*y*(s*v^-1*e^-1)^-1, y^-1*t*y*(t*u*v^-1*e^-1)^-1, y^-1*u*y*(u^-1*e^-1)^-1, y^-1*v*y*(v^-1*e)^-1, y^-1*e*y*e^-1, z^-1*s*z*(s*t^-1*u^-1*v^-1*e^-1) ^-1,z^-1*t*z*(s*u*v)^-1, z^-1*u*z*(t*u^-1*v*e^-1)^-1, z^-1*v*z*(s^-1*t*u^-1)^-1, z^-1*e*z*e^-1],[[a*b,w,s],[a,b,w]]]; end, [24,243]], "A5 2^1 x ( 2^4' C 2^1 ) 3^4 C 3^1",[7,5,1],6, 1,[24,243]], # 933120.2 [[1,"abdwxyzrstuv", function(a,b,d,w,x,y,z,r,s,t,u,v) return [[a^4,b^3,(a*b)^5,a^2*b*a^2*b^-1,d^2,a^-1*d ^-1*a*d,b^-1*d^-1*b*d, 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^2, x^2,y^2,z^2,w^-1*x^-1*w*x*d, w^-1*y^-1*w*y*d,w^-1*z^-1*w*z*d, x^-1*y^-1*x*y*d,x^-1*z^-1*x*z*d, y^-1*z^-1*y*z*d,a^-1*w*a*z^-1, a^-1*x*a*x^-1,a^-1*y*a*(w*x*y*z)^-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,r^3,s^3,t^3,u^3,v^3, r^-1*s^-1*r*s,r^-1*t^-1*r*t, r^-1*u^-1*r*u,r^-1*v^-1*r*v, 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*r*a*u^-1,a^-1*s*a*s^-1, a^-1*t*a*v^-1,a^-1*u*a*r^-1, a^-1*v*a*t^-1,b^-1*r*b*s^-1, b^-1*s*b*t^-1,b^-1*t*b*r^-1, b^-1*u*b*u^-1,b^-1*v*b*v^-1, w^-1*r*w*r^-1,w^-1*s*w*s, w^-1*t*w*t,w^-1*u*w*u,w^-1*v*w*v, x^-1*r*x*r,x^-1*s*x*s^-1, x^-1*t*x*t,x^-1*u*x*u,x^-1*v*x*v, y^-1*r*y*r,y^-1*s*y*s, y^-1*t*y*t^-1,y^-1*u*y*u, y^-1*v*y*v,z^-1*r*z*r,z^-1*s*z*s, z^-1*t*z*t,z^-1*u*z*u^-1, z^-1*v*z*v], [[a*b,w,r],[a,b,r],[b,a*b*a*b^-1*a,w,r]]]; end, [24,32,15]], "A5 2^1 x ( 2^4' C 2^1 ) 3^5",[7,5,2],4, 1,[24,32,15]], # 933120.3 [[4,3840,1,14580,1,60], "A5 # 2^6 3^5 [1]",6,12, 1,[64,18]], # 933120.4 [[4,3840,2,14580,1,60], "A5 # 2^6 3^5 [2]",6,12, 1,[64,18]], # 933120.5 [[4,3840,3,14580,1,60], "A5 # 2^6 3^5 [3]",6,12, 1,[24,18]], # 933120.6 [[4,3840,4,14580,1,60], "A5 # 2^6 3^5 [4]",6,12, 1,[48,18]], # 933120.7 [[4,3840,5,14580,1,60], "A5 # 2^6 3^5 [5]",6,12, 1,[24,12,18]], # 933120.8 [[4,3840,6,14580,1,60], "A5 # 2^6 3^5 [6]",6,6, 1,[48,18]], # 933120.9 [[4,3840,7,14580,1,60], "A5 # 2^6 3^5 [7]",6,12, 1,[32,24,18]], # 933120.10 [[4,3840,5,29160,5,120,5,2], "A5 # 2^6 3^5 [8]",6,6, 1,[24,12,243]], # 933120.11 [[4,3840,6,29160,5,120,6,2], "A5 # 2^6 3^5 [9]",6,6, 1,[48,243]], # 933120.12 [[4,3840,7,29160,5,120,7,2], "A5 # 2^6 3^5 [10]",6,6, 1,[32,24,243]], # 933120.13 [[4,3840,5,29160,6,120,5,3], "A5 # 2^6 3^5 [11]",6,6, 1,[24,12,243]], # 933120.14 [[4,3840,6,29160,6,120,6,3], "A5 # 2^6 3^5 [12]",6,6, 1,[48,243]], # 933120.15 [[4,3840,7,29160,6,120,7,3], "A5 # 2^6 3^5 [13]",6,6, 1,[32,24,243]], # 933120.16 [[4,11520,1,29160,4,360,1,1], "A6 # 2^5 3^4 [1]",15,2, 3,[12,30]], # 933120.17 [[4,11520,2,29160,4,360,2,1], "A6 # 2^5 3^4 [2]",15,2, 3,[80,30]], # 933120.18 [[4,11520,3,29160,4,360,3,1], "A6 # 2^5 3^4 [3]",15,2, 3,[16,80,30]], # 933120.19 [[4,11520,4,29160,4,360,4,1], "A6 # 2^5 3^4 [4]",15,1, 3,[80,30]], # 933120.20 [[4,11520,3,58320,3,720,3,2], "A6 # 2^5 3^4 [5]",15,1, 3,[16,80,81]], # 933120.21 [[4,11520,4,58320,3,720,4,2], "A6 # 2^5 3^4 [6]",15,1, 3,[80,81]] ]; PERFGRP[319]:=[# 936000.1 [[2,60,1,15600,1], "( A5 x L2(25) ) 2^1 [1]",40,2, [1,14],[5,208]], # 936000.2 [[2,120,1,7800,1], "( A5 x L2(25) ) 2^1 [2]",40,2, [1,14],[24,26]], # 936000.3 [[3,120,1,15600,1,"d1","a2","a2"], "( A5 x L2(25) ) 2^1 [3]",40,2, [1,14],2496] ]; PERFGRP[320]:=[# 937500.1 [[1,"abxyzXYZ", function(a,b,x,y,z,X,Y,Z) return [[a^2,b^3,(a*b)^5,x^5,y^5,z^5,X^5,Y^5,Z^5,x^-1*y ^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,X^-1*Y^-1*X*Y, X^-1*Z^-1*X*Z,Y^-1*Z^-1*Y*Z, x^-1*X*x*X^-1,x^-1*Y*x*Y^-1, x^-1*Z*x*Z^-1,y^-1*X*y*X^-1, y^-1*Y*y*Y^-1,y^-1*Z*y*Z^-1, z^-1*X*z*X^-1,z^-1*Y*z*Y^-1, z^-1*Z*z*Z^-1,a^-1*X*a*Z^-1, a^-1*Y*a*Y,a^-1*Z*a*X^-1, 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, b^-1*Z*b*(X*Y^(-1*2)*Z)^-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,b*a*b*a*b^-1*a*b^-1,x,Y], [a*b,b*a*b*a*b^-1*a*b^-1,X,y]]]; end, [30,30]], "A5 5^3 x 5^3",[3,6,1],1, 1,[30,30]], # 937500.2 [[1,"abxyzXYZ", function(a,b,x,y,z,X,Y,Z) return [[a^2,b^3,(a*b)^5,x^5,y^5,z^5,X^5,Y^5,Z^5,x^-1*y ^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,X^-1*Y^-1*X*Y, X^-1*Z^-1*X*Z,Y^-1*Z^-1*Y*Z, x^-1*X*x*X^-1,x^-1*Y*x*Y^-1, x^-1*Z*x*Z^-1,y^-1*X*y*X^-1, y^-1*Y*y*Y^-1,y^-1*Z*y*Z^-1, z^-1*X*z*X^-1,z^-1*Y*z*Y^-1, z^-1*Z*z*Z^-1,a^-1*X*a*Z^-1, a^-1*Y*a*Y,a^-1*Z*a*X^-1, a^-1*x*a*(z*X^-1*Y)^-1, a^-1*y*a*(y^-1*X^2*Z^2)^-1, a^-1*z*a*(x*Y*Z)^-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, b^-1*x*b*(z*X^-1*Y^-1*Z)^-1, b^-1*y*b*(y^-1*z*X^2*Z^(-1*2))^-1, b^-1*z*b*(x*y^(-1*2)*z*Y^-1*Z)^-1], [[a*b,b*a*b*a*b^-1*a*b^-1,x]]]; end, [30]], "A5 5^3 E 5^3",[3,6,2],1, 1,30], # 937500.3 [[1,"abxyzXYZ", function(a,b,x,y,z,X,Y,Z) return [[a^2,b^3,(a*b)^5,x^5,y^5,z^5,x^-1*y^-1*x*y *X^-1,x^-1*z^-1*x*z*Y^(-1*2), y^-1*z^-1*y*z*Z^-1,X^5,Y^5,Z^5, X^-1*Y^-1*X*Y,X^-1*Z^-1*X*Z, Y^-1*Z^-1*Y*Z,x^-1*X*x*X^-1, x^-1*Y*x*Y^-1,x^-1*Z*x*Z^-1, y^-1*X*y*X^-1,y^-1*Y*y*Y^-1, y^-1*Z*y*Z^-1,z^-1*X*z*X^-1, z^-1*Y*z*Y^-1,z^-1*Z*z*Z^-1, a^-1*x*a*(z*Y*Z^-1)^-1, a^-1*y*a*(y^-1*X^2*Z^2)^-1, a^-1*z*a*(x*X*Y)^-1,a^-1*X*a*Z^-1, a^-1*Y*a*Y,a^-1*Z*a*X^-1, b^-1*x*b*(z*Y)^-1, b^-1*y*b*(y^-1*z*X^2*Y^2)^-1, b^-1*z*b*(x*y^(-1*2)*z*X*Y^2*Z^-1)^-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,b*a*b*a*b^-1*a*b^-1*x,y]]]; end, [150]], "A5 5^3 C 5^3",[3,6,3],1, 1,150], # 937500.4 [[1,"abxyzXYZ", function(a,b,x,y,z,X,Y,Z) return [[a^2,b^3,(a*b)^5*Z^-1,x^5,y^5,z^5,x^-1*y^(-1 *1)*x*y*X^-1,x^-1*z^-1*x*z *Y^(-1*2),y^-1*z^-1*y*z*Z^-1,X^5,Y^5, Z^5,X^-1*Y^-1*X*Y,X^-1*Z^-1*X*Z, Y^-1*Z^-1*Y*Z,x^-1*X*x*X^-1, x^-1*Y*x*Y^-1,x^-1*Z*x*Z^-1, y^-1*X*y*X^-1,y^-1*Y*y*Y^-1, y^-1*Z*y*Z^-1,z^-1*X*z*X^-1, z^-1*Y*z*Y^-1,z^-1*Z*z*Z^-1, a^-1*x*a*(z*Y*Z^-1)^-1, a^-1*y*a*(y^-1*X^2*Z^2)^-1, a^-1*z*a*(x*X*Y)^-1,a^-1*X*a*Z^-1, a^-1*Y*a*Y,a^-1*Z*a*X^-1, b^-1*x*b*(z*Y)^-1, b^-1*y*b*(y^-1*z*X^2*Y^2)^-1, b^-1*z*b*(x*y^(-1*2)*z*X*Y^2*Z^-1)^-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,b*a*b*a*b^-1*a*b^-1*x,y]]]; end, [150]], "A5 5^3 C N 5^3 I",[3,6,4],1, 1,150], # 937500.5 [[1,"abxyzXYZ", function(a,b,x,y,z,X,Y,Z) return [[a^2,b^3,(a*b)^5*Z^(-1*2),x^5,y^5,z^5,x^-1*y^(-1 *1)*x*y*X^-1,x^-1*z^-1*x*z *Y^(-1*2),y^-1*z^-1*y*z*Z^-1,X^5,Y^5, Z^5,X^-1*Y^-1*X*Y,X^-1*Z^-1*X*Z, Y^-1*Z^-1*Y*Z,x^-1*X*x*X^-1, x^-1*Y*x*Y^-1,x^-1*Z*x*Z^-1, y^-1*X*y*X^-1,y^-1*Y*y*Y^-1, y^-1*Z*y*Z^-1,z^-1*X*z*X^-1, z^-1*Y*z*Y^-1,z^-1*Z*z*Z^-1, a^-1*x*a*(z*Y*Z^-1)^-1, a^-1*y*a*(y^-1*X^2*Z^2)^-1, a^-1*z*a*(x*X*Y)^-1,a^-1*X*a*Z^-1, a^-1*Y*a*Y,a^-1*Z*a*X^-1, b^-1*x*b*(z*Y)^-1, b^-1*y*b*(y^-1*z*X^2*Y^2)^-1, b^-1*z*b*(x*y^(-1*2)*z*X*Y^2*Z^-1)^-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,b*a*b*a*b^-1*a*b^-1*x,y]]]; end, [150]], "A5 5^3 C N 5^3 II",[3,6,5],1, 1,150], # 937500.6 [[1,"abxyzXYZ", function(a,b,x,y,z,X,Y,Z) return [[a^2,b^3,(a*b)^5*z^-1,x^5,y^5,z^5,X^5,Y^5,Z^5, x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,X^-1*Y^-1*X*Y, X^-1*Z^-1*X*Z,Y^-1*Z^-1*Y*Z, x^-1*X*x*X^-1,x^-1*Y*x*Y^-1, x^-1*Z*x*Z^-1,y^-1*X*y*X^-1, y^-1*Y*y*Y^-1,y^-1*Z*y*Z^-1, z^-1*X*z*X^-1,z^-1*Y*z*Y^-1, z^-1*Z*z*Z^-1,a^-1*X*a*Z^-1, a^-1*Y*a*Y,a^-1*Z*a*X^-1, 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, b^-1*Z*b*(X*Y^(-1*2)*Z)^-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,b*a*b*a*b^-1*a*b^-1,x,Y], [a*b,b*a*b*a*b^-1*a*b^-1,X,y]]]; end, [30,30]], "A5 N 5^3 x 5^3",[3,6,6],1, 1,[30,30]], # 937500.7 [[1,"abxyzXYZ", function(a,b,x,y,z,X,Y,Z) return [[a^2,b^3,(a*b)^5*(z*X^(-1*2)*Y)^-1,x^5,y^5,z^5, X^5,Y^5,Z^5,x^-1*y^-1*x*y, x^-1*z^-1*x*z,y^-1*z^-1*y*z, X^-1*Y^-1*X*Y,X^-1*Z^-1*X*Z, Y^-1*Z^-1*Y*Z,x^-1*X*x*X^-1, x^-1*Y*x*Y^-1,x^-1*Z*x*Z^-1, y^-1*X*y*X^-1,y^-1*Y*y*Y^-1, y^-1*Z*y*Z^-1,z^-1*X*z*X^-1, z^-1*Y*z*Y^-1,z^-1*Z*z*Z^-1, a^-1*x*a*(z*X^-1*Y)^-1, a^-1*y*a*(y^-1*X^2*Z^2)^-1, a^-1*z*a*(x*Y*Z)^-1,a^-1*X*a*Z^-1, a^-1*Y*a*Y,a^-1*Z*a*X^-1, b^-1*x*b*(z*X^-1*Y^-1*Z)^-1, b^-1*y*b*(y^-1*z*X^2*Z^(-1*2))^-1, b^-1*z*b*(x*y^(-1*2)*z*Y^-1*Z)^-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], [[b,a*b^-1*a*b*a*b^-1*a*b*a,z,Y*Z^2]]]; end, [50]], "A5 N 5^3 E 5^3",[3,6,7],1, 1,50], # 937500.8 [[1,"abxyzXYZ", function(a,b,x,y,z,X,Y,Z) return [[a^2,b^3,(a*b)^5*z^-1,x^5*X^-1,y^5*Y^-1, z^5*Z^-1,X^5,Y^5,Z^5,x^-1*y^-1*x*y*X, x^-1*z^-1*x*z*Y^2,y^-1*z^-1*y*z*Z, X^-1*Y^-1*X*Y,X^-1*Z^-1*X*Z, Y^-1*Z^-1*Y*Z,x^-1*X*x*X^-1, x^-1*Y*x*Y^-1,x^-1*Z*x*Z^-1, y^-1*X*y*X^-1,y^-1*Y*y*Y^-1, y^-1*Z*y*Z^-1,z^-1*X*z*X^-1, z^-1*Y*z*Y^-1,z^-1*Z*z*Z^-1, a^-1*X*a*Z^-1,a^-1*Y*a*Y, a^-1*Z*a*X^-1, a^-1*x*a*(z*X^-1*Y*Z)^-1, a^-1*y*a*(y^-1*X^-1*Z^-1)^-1, a^-1*z*a*(x*X^-1*Y*Z)^-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, b^-1*x*b*(z*X^-1*Y^(-1*2)*Z^-1)^-1, b^-1*y*b*(y^-1*z*X^-1*Y^(-1*2))^-1, b^-1*z*b*(x*y^(-1*2)*z*X^-1*Y^(-1*2)*Z^2) ^-1], [[a*b,b*a*b*a*b^-1*a*b^-1*x^-1,y]]]; end, [150]], "A5 N 5^3 C 5^3",[3,6,8],1, 1,150] ]; PERFGRP[321]:=[# 943488.1 [[2,168,1,5616,1], "L3(2) x L3(3)",40,1, [2,11],[7,13]] ]; PERFGRP[322]:=[# 950400.1 [[2,720,1,1320,1], "( A6 x L2(11) ) 2^2",40,4, [3,5],[80,24]], # 950400.2 [[2,120,1,7920,1], "A5 2^1 x M11",40,2, [1,15],[24,11]] ]; PERFGRP[323]:=[# 950520.1 [[1,"abyz", function(a,b,y,z) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,y^89,z^89,y^-1 *z^-1*y*z,a^-1*y*a*z^-1, a^-1*z*a*y,b^-1*y*b*(y^(-1*37)*z^40)^-1, b^-1*z*b*(y^(-1*40)*z^36)^-1], [[a,y^5*z^(-1*8)]]]; end, [2670],[0,0,2,2,2,2]], "A5 2^1 89^2",[5,2,1],1, 1,2670] ]; PERFGRP[324]:=[# 960000.1 [[4,7680,1,7500,1,60], "A5 # 2^7 5^3 [1]",6,8, 1,[12,64,30]], # 960000.2 [[4,7680,2,7500,1,60], "A5 # 2^7 5^3 [2]",6,8, 1,[24,64,30]], # 960000.3 [[4,7680,3,7500,1,60], "A5 # 2^7 5^3 [3]",6,8, 1,[24,64,30]], # 960000.4 [[4,7680,4,7500,1,60], "A5 # 2^7 5^3 [4]",6,8, 1,[24,64,30]], # 960000.5 [[4,7680,5,7500,1,60], "A5 # 2^7 5^3 [5]",6,8, 1,[24,24,30]], # 960000.6 [[4,7680,1,7500,2,60], "A5 # 2^7 5^3 [6]",6,8, 1,[12,64,30]], # 960000.7 [[4,7680,2,7500,2,60], "A5 # 2^7 5^3 [7]",6,8, 1,[24,64,30]], # 960000.8 [[4,7680,3,7500,2,60], "A5 # 2^7 5^3 [8]",6,8, 1,[24,64,30]], # 960000.9 [[4,7680,4,7500,2,60], "A5 # 2^7 5^3 [9]",6,8, 1,[24,64,30]], # 960000.10 [[4,7680,5,7500,2,60], "A5 # 2^7 5^3 [10]",6,8, 1,[24,24,30]], # 960000.11 [[4,7680,4,15000,4,120,4,3], "A5 # 2^7 5^3 [11]",6,20, 1,[24,64,125]], # 960000.12 [[4,7680,5,15000,4,120,5,3], "A5 # 2^7 5^3 [12]",6,20, 1,[24,24,125]] ]; PERFGRP[325]:=[# 962280.1 [[1,"abuvwxyz", function(a,b,u,v,w,x,y,z) return [[a^4,b^3,(a*b)^11,Comm(a,b*a*b*a*b)^2/a^2, Comm(b,a^2), u^3,v^3,w^3,x^3,y^3,z^3, Comm(z,u), Comm(y,u), Comm(x,u), Comm(w,u), Comm(v,u), Comm(z,v), Comm(y,v), Comm(x,v), Comm(w,v), Comm(z,w), Comm(y,w), Comm(x,w), Comm(z,x), Comm(y,x), Comm(z,y), u^a/(v*w^2*y*z^2), v^a/(v^2*x*y^2), w^a/(w*x), x^a/(w*x^2), y^a/(v^2*w*x*y), z^a/(u*v*x), u^b/z, v^b/w, w^b/x, x^b/v, y^b/u, z^b/y], [[a^2,a*b,((b*a)^2*b)^2*a*b^2,u]]]; end, [36]], "L2(11) 2^1 3^6",[18,6,1],1, 5,[36]] ]; PERFGRP[326]:=[# 967680.1 [[1,"abduvwxyz", function(a,b,d,u,v,w,x,y,z) return [[a^6*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*a^2*d, a^2*d*b*(a^2*d)^-1*b^-1,d^2, a^-1*d*a*d^-1,b^-1*d*b*d^-1, u^-1*d*u*d^-1,v^-1*d*v*d^-1, w^-1*d*w*d^-1,x^-1*d*x*d^-1, y^-1*d*y*d^-1,z^-1*d*z*d^-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*u^-1,a^-1*v*a*v^-1, a^-1*w*a*y^-1,a^-1*x*a*x^-1, a^-1*y*a*w^-1, a^-1*z*a*(u*v*w*x*y*z)^-1, b^-1*u*b*w^-1,b^-1*v*b*z^-1, b^-1*w*b*v^-1,b^-1*x*b*y^-1, b^-1*y*b*x^-1,b^-1*z*b*u^-1], [[a^3,(b^-1*a)^2*(b*a)^2*b^2*a*b*a,u], [b^2*a*b^-1*(a*b*a*b*b)^2*(a*b)^2, b*(a*b^-1)^2*a*b^2*(a*b)^2,a^2*d,y*z], [a*b, b*a*b*a*b^2*a*b^-1*a*b*a*b^-1*a*b*a *b^2*d,a^2*d,u]]]; end, [45,14,240],[[1,2]]], "A7 3^1 x 2^1 x 2^6",[23,7,1],6, 8,[45,14,240]], # 967680.2 [[1,"abuvwxyze", function(a,b,u,v,w,x,y,z,e) return [[a^6,b^4,(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 *a^2,a^2*b*a^(-1*2)*b^-1,e^2, u^-1*e*u*e^-1,v^-1*e*v*e^-1, w^-1*e*w*e^-1,x^-1*e*x*e^-1, y^-1*e*y*e^-1,z^-1*e*z*e^-1, u^2*e^-1,v^2*e^-1,w^2*e^-1, x^2*e^-1,y^2*e^-1,z^2*e^-1, u^-1*v^-1*u*v*e^-1, u^-1*w^-1*u*w*e^-1, u^-1*x^-1*u*x*e^-1, u^-1*y^-1*u*y*e^-1, u^-1*z^-1*u*z*e^-1, v^-1*w^-1*v*w*e^-1, v^-1*x^-1*v*x*e^-1, v^-1*y^-1*v*y*e^-1, v^-1*z^-1*v*z*e^-1, w^-1*x^-1*w*x*e^-1, w^-1*y^-1*w*y*e^-1, w^-1*z^-1*w*z*e^-1, x^-1*y^-1*x*y*e^-1, x^-1*z^-1*x*z*e^-1, y^-1*z^-1*y*z*e^-1, a^-1*u*a*u^-1,a^-1*v*a*v^-1, a^-1*w*a*(y*e)^-1,a^-1*x*a*x^-1, a^-1*y*a*(w*e)^-1, a^-1*z*a*(u*v*w*x*y*z*e)^-1, a^-1*e*a*e^-1,b^-1*u*b*w^-1, b^-1*v*b*z^-1,b^-1*w*b*v^-1, b^-1*x*b*(y*e)^-1,b^-1*y*b*(x*e)^-1, b^-1*z*b*u^-1,b^-1*e*b*e^-1], [[a^3,(b^-1*a)^2*(b*a)^2*b^2*a*b*a,u],[a,b]]]; end, [45,128],[[1,2],[1,-2]]], "A7 3^1 x ( 2^6 C 2^1 )",[23,7,2],6, 8,[45,128]], # 967680.3 [[1,"abduvwxyz", function(a,b,d,u,v,w,x,y,z) return [[a^6*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*a^2*d, a^2*d*b*(a^2*d)^-1*b^-1,d^2, a^-1*d*a*d^-1,b^-1*d*b*d^-1, u^-1*d*u*d^-1,v^-1*d*v*d^-1, w^-1*d*w*d^-1,x^-1*d*x*d^-1, y^-1*d*y*d^-1,z^-1*d*z*d^-1, u^2*d^-1,v^2*d^-1,w^2*d^-1, x^2*d^-1,y^2*d^-1,z^2*d^-1, u^-1*v^-1*u*v*d^-1, u^-1*w^-1*u*w*d^-1, u^-1*x^-1*u*x*d^-1, u^-1*y^-1*u*y*d^-1, u^-1*z^-1*u*z*d^-1, v^-1*w^-1*v*w*d^-1, v^-1*x^-1*v*x*d^-1, v^-1*y^-1*v*y*d^-1, v^-1*z^-1*v*z*d^-1, w^-1*x^-1*w*x*d^-1, w^-1*y^-1*w*y*d^-1, w^-1*z^-1*w*z*d^-1, x^-1*y^-1*x*y*d^-1, x^-1*z^-1*x*z*d^-1, y^-1*z^-1*y*z*d^-1, a^-1*u*a*u^-1,a^-1*v*a*v^-1, a^-1*w*a*(y*d)^-1,a^-1*x*a*x^-1, a^-1*y*a*(w*d)^-1, a^-1*z*a*(u*v*w*x*y*z*d)^-1, b^-1*u*b*w^-1,b^-1*v*b*z^-1, b^-1*w*b*v^-1,b^-1*x*b*(y*d)^-1, b^-1*y*b*(x*d)^-1,b^-1*z*b*u^-1], [[a^3,(b^-1*a)^2*(b*a)^2*b^2*a*b*a,w], [a*b,b*a*b*a*b^2*a*b^-1*a*b*a*b^-1*a*b *a*b^2*d,a^2*d,x*y*z*d]]]; end, [45,1920],[[1,2],[1,-2]]], "A7 3^1 x ( 2^6 C N 2^1 )",[23,7,3],6, 8,[45,1920]], # 967680.4 [[1,"abdef", function(a,b,d,e,f) return [[a^2,b^4*(e^2*f^2)^-1,(a*b)^7*d^-1*e,(a^-1 *b^-1*a*b)^5*(e^2*f^2)^-1, (a*b^2)^5*(e*f)^-1,(a*b*a*b*a*b^3)^5 *(e^2*f^-1)^-1, (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,e^4, f^4,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*b*a,b^2*a*b^-1*a*b*a*b^2*a*b*d], [a,b*a*b*a*b^-1*a*b^2*f^-1], [a*e^2,b^-1*a*b^-1*a*b*a*b^2]]]; end, [63,224,224],[[1,2],[6,6]]], "L3(4) 3^1 x ( 2^1 A 2^1 ) x ( 2^1 A 2^1 )",[27,4,1],-48, 20,[63,224,224]], # 967680.5 [[2,1920,1,504,1], "( A5 x L2(8) ) # 2^5 [1]",[35,5,1],2, [1,4],[12,9]], # 967680.6 [[2,1920,2,504,1], "( A5 x L2(8) ) # 2^5 [2]",[35,5,2],2, [1,4],[24,9]], # 967680.7 [[2,1920,3,504,1], "( A5 x L2(8) ) # 2^5 [3]",[35,5,3],2, [1,4],[16,24,9]], # 967680.8 [[2,1920,4,504,1], "( A5 x L2(8) ) # 2^5 [4]",[35,5,4],1, [1,4],[80,9]], # 967680.9 [[2,1920,5,504,1], "( A5 x L2(8) ) # 2^5 [5]",[35,5,5],2, [1,4],[10,24,9]], # 967680.10 [[2,1920,6,504,1], "( A5 x L2(8) ) # 2^5 [6]",[35,5,6],2, [1,4],[80,9]], # 967680.11 [[2,1920,7,504,1], "( A5 x L2(8) ) # 2^5 [7]",[35,5,7],2, [1,4],[32,9]], # 967680.12 [[2,168,1,5760,1], "( L3(2) x A6 ) # 2^4 [1]",[37,4,1],1, [2,3],[7,16]], # 967680.13 [[2,2688,1,360,1], "( L3(2) x A6 ) # 2^4 [2]",[37,4,2],2, [2,3],[8,16,6]], # 967680.14 [[2,2688,2,360,1], "( L3(2) x A6 ) # 2^4 [3]",[37,4,3],2, [2,3],[16,6]], # 967680.15 [[2,2688,3,360,1], "( L3(2) x A6 ) # 2^4 [4]",[37,4,4],2, [2,3],[16,14,6]], # 967680.16 [[2,1344,1,720,1], "( L3(2) x A6 ) # 2^4 [5]",[37,4,5],2, [2,3],[8,80]], # 967680.17 [[2,1344,2,720,1], "( L3(2) x A6 ) # 2^4 [6]",[37,4,6],2, [2,3],[14,80]], # 967680.18 [[3,2688,1,720,1,"d1","d2"], "( L3(2) x A6 ) # 2^4 [7]",[37,4,7],2, [2,3],[320,640]], # 967680.19 [[3,2688,2,720,1,"e1","d2"], "( L3(2) x A6 ) # 2^4 [8]",[37,4,8],2, [2,3],640], # 967680.20 [[3,2688,3,720,1,"d1","d2"], "( L3(2) x A6 ) # 2^4 [9]",[37,4,9],2, [2,3],[640,560]] ]; PERFGRP[327]:=[# 976500.1 [[1,"abc", function(a,b,c) return [[c^62,b^5,b*c^-1*b*c*(c^-1*b*c*b)^-1,c^(-1 *3)*b*c^3 *(b^-1*c^-1*b^2*c^-1*b^-1*c^2) ^-1,a^2,c*a*c*a^-1,(b*a)^3, b^3*c*b^2*c^2*a*b^3*c*b*a*c*b^-1*c^(-1*4) *b^(-1*2)*a],[[b,c]]]; end, [126]], "L2(125)",22,-1, 55,126] ]; PERFGRP[328]:=[# 979200.1 [[1,"ab", function(a,b) return [[a^2,b^5,(a*b)^15,(a^-1*b^-1*a*b)^5,(a*b^2)^17, (a^-1*b^(-1*2)*a*b^2)^2,(a*b*a*b*a*b^(-1*2))^4, (a*b*a*b^2)^5], [[b*(b*a)^3*b^-1*a,(a*b^-1*a*b)^2*b]]]; end, [85]], "Sp4(4)",28,-1, 56,85] ]; PERFGRP[329]:=[# 979776.1 [[4,1344,1,122472,1,168], "L3(2) # 2^3 3^6 [1]",12,1, 2,[8,63]], # 979776.2 [[4,1344,2,122472,1,168], "L3(2) # 2^3 3^6 [2]",12,1, 2,[14,63]], # 979776.3 [[4,1344,1,122472,2,168], "L3(2) # 2^3 3^6 [3]",12,1, 2,[8,21]], # 979776.4 [[4,1344,2,122472,2,168], "L3(2) # 2^3 3^6 [4]",12,1, 2,[14,21]] ]; PERFGRP[330]:=fail; # 983040, A5 # 2^14 PERFGRP[331]:=[# 987840.1 [[2,60,1,16464,1], "A5 x L3(2) 2^1 # 7^2",[32,2,2],1, [1,2],[5,49]] ]; ############################################################################# ## #E perf12.grp . . . . . . . . . . . . . . . . . . . . . . . . . ends here ##