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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 perf4.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 30720-30720 ## All data is based on Holt/Plesken: Perfect Groups, OUP 1989 ## PERFGRP[71]:=[# 30720.1 [[1,"abdstuvef", function(a,b,d,s,t,u,v,e,f) return [[a^2*d,b^3,(a*b)^5,d^2,d^-1*b^-1*d*b,e^4,f^4, d^-1*a^-1*d*a,d^-1*s^-1*d*s, d^-1*t^-1*d*t,d^-1*u^-1*d*u, d^-1*v^-1*d*v,d^-1*e^-1*d*e, d^-1*f^-1*d*f,e^-1*a^-1*e*a, e^-1*b^-1*e*b,e^-1*s^-1*e*s, e^-1*t^-1*e*t,e^-1*u^-1*e*u, e^-1*v^-1*e*v,e^-1*f^-1*e*f, f^-1*a^-1*f*a,f^-1*b^-1*f*b, f^-1*s^-1*f*s,f^-1*t^-1*f*t, f^-1*u^-1*f*u,f^-1*v^-1*f*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 *f^2,t^-1*u^-1*t*u*f^2, t^-1*v^-1*t*v*e^2*f^2,u^-1*v^-1*u *v,a^-1*s*a*u^-1*f^2, a^-1*t*a*v^-1,a^-1*u*a*s^-1*f^2, a^-1*v*a*t^-1, b^-1*s*b*(t*v*e*f^-1)^-1, b^-1*t*b*(s*t*u*v*f)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1 *f^2],[[a*b,s,e,f],[a,b,e],[a,b,f]]]; end, [24,64,64]], "A5 2^1 x ( 2^4 E ( 2^1 A x 2^1 A ) ) C ( 2^1 x 2^1 )",[1,9,1],32, 1,[24,64,64]], # 30720.2 [[1,"abstuveSTUV", function(a,b,s,t,u,v,e,S,T,U,V) return [[a^2,b^3,(a*b)^5,s^2*S^-1,t^2*T^-1,u^2*U^(-1 *1),v^2*V^-1,e^2,s^-1*t^-1*s*t, u^-1*v^-1*u*v,s^-1*u^-1*s*u, s^-1*v^-1*s*v,t^-1*u^-1*t*u, t^-1*v^-1*t*v,S^2,T^2,U^2,V^2, 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^-1,a^-1*V*a*T^-1, b^-1*S*b*(T*V)^-1, b^-1*T*b*(S*T*U*V)^-1, b^-1*U*b*(U*V)^-1,b^-1*V*b*U^-1, s^-1*S*s*S^-1,s^-1*T*s*T^-1, s^-1*U*s*U^-1,s^-1*V*s*V^-1, t^-1*S*t*S^-1,t^-1*T*t*T^-1, t^-1*U*t*U^-1,t^-1*V*t*V^-1, u^-1*S*u*S^-1,u^-1*T*u*T^-1, u^-1*U*u*U^-1,u^-1*V*u*V^-1, v^-1*S*v*S^-1,v^-1*T*v*T^-1, v^-1*U*v*U^-1,v^-1*V*v*V^-1, e^-1*S*e*S^-1,e^-1*T*e*T^-1, e^-1*U*e*U^-1,e^-1*V*e*V^-1, 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*U^-1*S^-1, b^-1*t*b*(s*t*u*v)^-1, b^-1*u*b*(u*v)^-1*(U*V)^-1, b^-1*v*b*u^-1,e^-1*a^-1*e*a, e^-1*b^-1*e*b*(U*V)^-1, 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,t,u,e]]]; end, [240]], "A5 ( 2^4 E 2^1 E 2^4 ) A",[1,9,2],1, 1,240], # 30720.3 [[1,"abstuveSTUV", function(a,b,s,t,u,v,e,S,T,U,V) return [[a^2*e^-1,b^3,(a*b)^5,s^2*S^-1,t^2*T^-1, u^2*U^-1,v^2*V^-1,e^2,s^-1*t^-1*s*t ,u^-1*v^-1*u*v,s^-1*u^-1*s*u, s^-1*v^-1*s*v,t^-1*u^-1*t*u, t^-1*v^-1*t*v,S^2,T^2,U^2,V^2, 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^-1,a^-1*V*a*T^-1, b^-1*S*b*(T*V)^-1, b^-1*T*b*(S*T*U*V)^-1, b^-1*U*b*(U*V)^-1,b^-1*V*b*U^-1, s^-1*S*s*S^-1,s^-1*T*s*T^-1, s^-1*U*s*U^-1,s^-1*V*s*V^-1, t^-1*S*t*S^-1,t^-1*T*t*T^-1, t^-1*U*t*U^-1,t^-1*V*t*V^-1, u^-1*S*u*S^-1,u^-1*T*u*T^-1, u^-1*U*u*U^-1,u^-1*V*u*V^-1, v^-1*S*v*S^-1,v^-1*T*v*T^-1, v^-1*U*v*U^-1,v^-1*V*v*V^-1, e^-1*S*e*S^-1,e^-1*T*e*T^-1, e^-1*U*e*U^-1,e^-1*V*e*V^-1, 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*U^-1*S^-1, b^-1*t*b*(s*t*u*v)^-1, b^-1*u*b*(u*v)^-1*(U*V)^-1, b^-1*v*b*u^-1,e^-1*a^-1*e*a, e^-1*b^-1*e*b*(U*V)^-1, 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,t,u,e]]]; end, [240]], "A5 ( 2^4 E N 2^1 E 2^4 ) A",[1,9,3],1, 1,240], # 30720.4 [[1,"abdstuvSTUV", function(a,b,d,s,t,u,v,S,T,U,V) return [[a^2*d^-1,b^3,(a*b)^5,d^2,b^-1*d*b*d^-1, s^2*S^-1,t^2*T^-1,u^2*U^-1, v^2*V^-1,S^2,T^2,U^2,V^2,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,d^-1*s*d*s, d^-1*t*d*t,d^-1*u*d*u,d^-1*v*d*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*(t*v*T*U)^-1, b^-1*t*b*(s*t*u*v*T*U*V)^-1, b^-1*u*b*(u*v*U)^-1,b^-1*v*b*u], [[s,t,u,d]]]; end, [240]], "A5 2^1 ( 2^4 A 2^4 )",[1,9,4],1, 1,240], # 30720.5 [[1,"abstuvSTUVj", function(a,b,s,t,u,v,S,T,U,V,j) return [[a^2,b^3,(a*b)^5,j^2,j^-1*a^-1*j*a,j^-1 *b^-1*j*b,j^-1*s^-1*j*s, j^-1*t^-1*j*t,j^-1*u^-1*j*u, j^-1*v^-1*j*v,j^-1*S^-1*j*S, j^-1*T^-1*j*T,j^-1*U^-1*j*U, j^-1*V^-1*j*V,s^2,t^2,u^2,v^2,S^2,T^2,U^2, V^2,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*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*j, t^-1*S^-1*t*S,t^-1*T^-1*t*T, t^-1*U^-1*t*U*j,t^-1*V^-1*t*V*j, u^-1*S^-1*u*S,u^-1*T^-1*u*T*j, u^-1*U^-1*u*U,u^-1*V^-1*u*V, v^-1*S^-1*v*S*j,v^-1*T^-1*v*T*j, v^-1*U^-1*v*U,v^-1*V^-1*v*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, 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)^-1, b^-1*t*b*(s*t*u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*S*b*(T*V)^-1, b^-1*T*b*(S*T*U*V)^-1, b^-1*U*b*(U*V)^-1,b^-1*V*b*U^-1], [[a,b,s]]]; end, [32]], "A5 ( 2^4 x 2^4 ) C 2^1",[1,9,5],2, 1,32], # 30720.6 [[1,"abstuvSTUVd", function(a,b,s,t,u,v,S,T,U,V,d) return [[a^2*d^-1,b^3,(a*b)^5,d^2,d^-1*a^-1*d*a, d^-1*b^-1*d*b,d^-1*s^-1*d*s, d^-1*t^-1*d*t,d^-1*u^-1*d*u, d^-1*v^-1*d*v,d^-1*S^-1*d*S, d^-1*T^-1*d*T,d^-1*U^-1*d*U, d^-1*V^-1*d*V,s^2,t^2,u^2,v^2,S^2,T^2,U^2, V^2,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*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*d, t^-1*S^-1*t*S,t^-1*T^-1*t*T, t^-1*U^-1*t*U*d,t^-1*V^-1*t*V*d, u^-1*S^-1*u*S,u^-1*T^-1*u*T*d, u^-1*U^-1*u*U,u^-1*V^-1*u*V, v^-1*S^-1*v*S*d,v^-1*T^-1*v*T*d, v^-1*U^-1*v*U,v^-1*V^-1*v*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, 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)^-1, b^-1*t*b*(s*t*u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*S*b*(T*V)^-1, b^-1*T*b*(S*T*U*V)^-1, b^-1*U*b*(U*V)^-1,b^-1*V*b*U^-1], [[a*b,s]]]; end, [384]], "A5 ( 2^4 x 2^4 ) C N 2^1",[1,9,6],2, 1,384], # 30720.7 [[1,"abstuvSTUVg", function(a,b,s,t,u,v,S,T,U,V,g) return [[a^2,b^3,(a*b)^5,g^2,g^-1*a^-1*g*a,g^-1 *b^-1*g*b,g^-1*s^-1*g*s, g^-1*t^-1*g*t,g^-1*u^-1*g*u, g^-1*v^-1*g*v,g^-1*S^-1*g*S, g^-1*T^-1*g*T,g^-1*U^-1*g*U, g^-1*V^-1*g*V,s^2,t^2,u^2,v^2,S^2,T^2,U^2, V^2,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*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, t^-1*S^-1*t*S,t^-1*T^-1*t*T, t^-1*U^-1*t*U,t^-1*V^-1*t*V, u^-1*S^-1*u*S,u^-1*T^-1*u*T, u^-1*U^-1*u*U,u^-1*V^-1*u*V, v^-1*S^-1*v*S,v^-1*T^-1*v*T, v^-1*U^-1*v*U,v^-1*V^-1*v*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, 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)^-1, b^-1*t*b*(s*t*u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*S*b*(T*V*g)^-1, b^-1*T*b*(S*T*U*V)^-1, b^-1*U*b*(U*V)^-1,b^-1*V*b*U^-1], [[a,b,S],[a*b,b*a*b*a*b^-1*a*b^-1,S,s]]]; end, [16,12]], "A5 2^4 x ( 2^4 E 2^1 )",[1,9,7],2, 1,[16,12]], # 30720.8 [[1,"abstuvSTUVd", function(a,b,s,t,u,v,S,T,U,V,d) return [[a^2*d^-1,b^3,(a*b)^5,d^2,d^-1*a^-1*d*a, d^-1*b^-1*d*b,d^-1*s^-1*d*s, d^-1*t^-1*d*t,d^-1*u^-1*d*u, d^-1*v^-1*d*v,d^-1*S^-1*d*S, d^-1*T^-1*d*T,d^-1*U^-1*d*U, d^-1*V^-1*d*V,s^2,t^2,u^2,v^2,S^2,T^2,U^2, V^2,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*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, t^-1*S^-1*t*S,t^-1*T^-1*t*T, t^-1*U^-1*t*U,t^-1*V^-1*t*V, u^-1*S^-1*u*S,u^-1*T^-1*u*T, u^-1*U^-1*u*U,u^-1*V^-1*u*V, v^-1*S^-1*v*S,v^-1*T^-1*v*T, v^-1*U^-1*v*U,v^-1*V^-1*v*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, 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)^-1, b^-1*t*b*(s*t*u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*S*b*(T*V*d)^-1, b^-1*T*b*(S*T*U*V)^-1, b^-1*U*b*(U*V)^-1,b^-1*V*b*U^-1], [[a,b,S],[a*b,S,s]]]; end, [16,24]], "A5 2^4 x ( 2^4 E N 2^1 )",[1,9,8],2, 1,[16,24]], # 30720.9 [[1,"abdstuvSTUV", function(a,b,d,s,t,u,v,S,T,U,V) return [[a^2*d^-1,b^3,(a*b)^5,d^2,d^-1*b^-1*d*b, d^-1*a^-1*d*a,d^-1*s^-1*d*s, d^-1*t^-1*d*t,d^-1*u^-1*d*u, d^-1*v^-1*d*v,d^-1*S^-1*d*S, d^-1*T^-1*d*T,d^-1*U^-1*d*U, d^-1*V^-1*d*V,s^2,t^2,u^2,v^2, s^-1*t^-1*s*t,u^-1*v^-1*u*v, s^-1*u^-1*s*u,s^-1*v^-1*s*v, t^-1*u^-1*t*u,t^-1*v^-1*t*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)^-1, b^-1*t*b*(s*t*u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, S^2,T^2,U^2,V^2,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^-1, a^-1*V*a*T^-1,b^-1*S*b*(T*V)^-1, b^-1*T*b*(S*T*U*V)^-1, b^-1*U*b*(U*V)^-1,b^-1*V*b*U^-1, s^-1*S*s*S^-1,s^-1*T*s*T^-1, s^-1*U*s*U^-1,s^-1*V*s*V^-1, t^-1*S*t*S^-1,t^-1*T*t*T^-1, t^-1*U*t*U^-1,t^-1*V*t*V^-1, u^-1*S*u*S^-1,u^-1*T*u*T^-1, u^-1*U*u*U^-1,u^-1*V*u*V^-1, v^-1*S*v*S^-1,v^-1*T*v*T^-1, v^-1*U*v*U^-1,v^-1*V*v*V^-1], [[a,b,S],[a,b,s],[a*b,s,S]]]; end, [16,16,24]], "A5 2^1 x 2^4 x 2^4",[1,9,9],2, 1,[16,16,24]], # 30720.10 [[1,"abdstuvSTUV", function(a,b,d,s,t,u,v,S,T,U,V) return [[a^2*d^-1,b^3,(a*b)^5,d^2,b^-1*d*b*(d*U*V) ^-1,d^-1*a^-1*d*a,d^-1*s^-1*d *s,d^-1*t^-1*d*t,d^-1*u^-1*d*u, d^-1*v^-1*d*v,d^-1*S^-1*d*S, d^-1*T^-1*d*T,d^-1*U^-1*d*U, d^-1*V^-1*d*V,s^2,t^2,u^2,v^2, s^-1*t^-1*s*t,u^-1*v^-1*u*v, s^-1*u^-1*s*u,s^-1*v^-1*s*v, t^-1*u^-1*t*u,t^-1*v^-1*t*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)^-1, b^-1*t*b*(s*t*u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, S^2,T^2,U^2,V^2,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^-1, a^-1*V*a*T^-1,b^-1*S*b*(T*V)^-1, b^-1*T*b*(S*T*U*V)^-1, b^-1*U*b*(U*V)^-1,b^-1*V*b*U^-1, s^-1*S*s*S^-1,s^-1*T*s*T^-1, s^-1*U*s*U^-1,s^-1*V*s*V^-1, t^-1*S*t*S^-1,t^-1*T*t*T^-1, t^-1*U*t*U^-1,t^-1*V*t*V^-1, u^-1*S*u*S^-1,u^-1*T*u*T^-1, u^-1*U*u*U^-1,u^-1*V*u*V^-1, v^-1*S*v*S^-1,v^-1*T*v*T^-1, v^-1*U*v*U^-1,v^-1*V*v*V^-1], [[a,b,S],[b,d,s,u]]]; end, [16,80]], "A5 2^4 x ( 2^1 E 2^4 )",[1,9,10],1, 1,[16,80]], # 30720.11 [[1,"abdstuvSTUV", function(a,b,d,s,t,u,v,S,T,U,V) return [[a^2*d^-1,b^3,(a*b)^5,d^2,b^-1*d*b*(d*u*v*T *U)^-1,s^2*S^-1,t^2*T^-1, u^2*U^-1,v^2*V^-1,S^2,T^2,U^2,V^2, 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, d^-1*s*d*s,d^-1*t*d*t,d^-1*u*d*u, d^-1*v*d*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*(t*v*T*U)^-1, b^-1*t*b*(s*t*u*v*T*U*V)^-1, b^-1*u*b*(u*v*U)^-1,b^-1*v*b*u], [[s,t,u,d]]]; end, [240]], "A5 2^1 E 2^4 A 2^4",[1,9,11],1, 1,240], # 30720.12 [[1,"abstuvewxyz", function(a,b,s,t,u,v,e,w,x,y,z) return [[a^2,b^3,(a*b)^5,e^2,e^-1*a^-1*e*a,e^-1 *b^-1*e*b,e^-1*s^-1*e*s, e^-1*t^-1*e*t,e^-1*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,w^2,w*s^-1*w*s, w*t^-1*w*t,w*u^-1*w*u,w*v^-1*w*v, s^2*w,t^2*w,u^2*z,v^2*z,s^-1*t^-1*s*t*w, s^-1*u^-1*s*u*w*x*z, s^-1*v^-1*s*v*x*y, t^-1*u^-1*t*u*w*y*z, t^-1*v^-1*t*v*w*x*z,u^-1*v^-1*u*v *z,a^-1*s*a*u^-1,a^-1*t*a*v^-1, a^-1*u*a*s^-1,a^-1*v*a*t^-1, a^-1*w*a*z,a^-1*x*a*x,a^-1*y*a*w*x*y *z,a^-1*z*a*w,b^-1*s*b*(t*v*e)^-1, b^-1*t*b*(s*t*u*v*y*z)^-1, b^-1*u*b*(u*v*w*x*y)^-1, b^-1*v*b*u^-1,b^-1*w*b*x, b^-1*x*b*y,b^-1*y*b*w,b^-1*z*b*z], [[b,a*b*a*b^-1*a,v*w,w*x,e], [a*b,b*a*b*a*b^-1*a*b^-1,s,w]]]; end, [40,12]], "A5 2^4 ( E 2^1 x C 2^4' )",[1,9,12],2, 1,[40,12]], # 30720.13 [[1,"abstuvewxyz", function(a,b,s,t,u,v,e,w,x,y,z) return [[a^2*e^-1,b^3,(a*b)^5,e^2,e^-1*a^-1*e*a, e^-1*b^-1*e*b,e^-1*s^-1*e*s, e^-1*t^-1*e*t,e^-1*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,w^2,w*s^-1*w*s, w*t^-1*w*t,w*u^-1*w*u,w*v^-1*w*v, s^2*w,t^2*w,u^2*z,v^2*z,s^-1*t^-1*s*t*w, s^-1*u^-1*s*u*w*x*z, s^-1*v^-1*s*v*x*y, t^-1*u^-1*t*u*w*y*z, t^-1*v^-1*t*v*w*x*z,u^-1*v^-1*u*v *z,a^-1*s*a*u^-1,a^-1*t*a*v^-1, a^-1*u*a*s^-1,a^-1*v*a*t^-1, a^-1*w*a*z,a^-1*x*a*x,a^-1*y*a*w*x*y *z,a^-1*z*a*w,b^-1*s*b*(t*v*e)^-1, b^-1*t*b*(s*t*u*v*y*z)^-1, b^-1*u*b*(u*v*w*x*y)^-1, b^-1*v*b*u^-1,b^-1*w*b*x, b^-1*x*b*y,b^-1*y*b*w,b^-1*z*b*z], [[b,a*b*a*b^-1*a,v*w,w*x,e],[a*b,s]]]; end, [40,24]], "A5 2^4 ( E N 2^1 x C 2^4' )",[1,9,13],2, 1,[40,24]], # 30720.14 [[1,"abdstuvwxyz", function(a,b,d,s,t,u,v,w,x,y,z) return [[a^2*d^-1,b^3,(a*b)^5,d^2,d^-1*b^-1*d*b, d^-1*a^-1*d*a,d^-1*s^-1*d*s, d^-1*t^-1*d*t,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,w^2,w*s^-1*w*s, w*t^-1*w*t,w*u^-1*w*u,w*v^-1*w*v, s^2*w,t^2*w,u^2*z,v^2*z,s^-1*t^-1*s*t*w, s^-1*u^-1*s*u*w*x*z, s^-1*v^-1*s*v*x*y, t^-1*u^-1*t*u*w*y*z, t^-1*v^-1*t*v*w*x*z,u^-1*v^-1*u*v *z,a^-1*s*a*u^-1,a^-1*t*a*v^-1, a^-1*u*a*s^-1,a^-1*v*a*t^-1, a^-1*w*a*z,a^-1*x*a*x,a^-1*y*a*w*x*y *z,a^-1*z*a*w,b^-1*s*b*(t*v)^-1, b^-1*t*b*(s*t*u*v*y*z)^-1, b^-1*u*b*(u*v*w*x*y)^-1, b^-1*v*b*u^-1,b^-1*w*b*x, b^-1*x*b*y,b^-1*y*b*w,b^-1*z*b*z], [[b,a*b*a*b^-1*a,v*w,w*x],[a*b,s,w]]]; end, [40,24]], "A5 2^1 x ( 2^4 C 2^4' )",[1,9,14],2, 1,[40,24]], # 30720.15 [[1,"abstuvewxyz", function(a,b,s,t,u,v,e,w,x,y,z) return [[a^2,b^3,(a*b)^5,e^2,e^-1*a^-1*e*a,e^-1 *b^-1*e*b,e^-1*s^-1*e*s, e^-1*t^-1*e*t,e^-1*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,w^2,w^-1*s^-1*w*s, w^-1*t^-1*w*t,w^-1*u^-1*w*u, w^-1*v^-1*w*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,y^-1*z^-1*y*z, x^-1*z^-1*x*z,s^2,t^2,u^2,v^2, 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^-1,a^-1*v*a*t^-1, a^-1*w*a*z,a^-1*x*a*x,a^-1*y*a*w*x*y *z,a^-1*z*a*w,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, b^-1*w*b*x,b^-1*x*b*y,b^-1*y*b*w, b^-1*z*b*z], [[b,a*b*a*b^-1*a,w*x,s],[a*b,b*a*b*a*b^-1*a *b^-1,s,w]]]; end, [10,12]], "A5 ( 2^4 E 2^1 ) x 2^4'",[1,9,15],2, 1,[10,12]], # 30720.16 [[1,"abstuvewxyz", function(a,b,s,t,u,v,e,w,x,y,z) return [[a^2*e^-1,b^3,(a*b)^5,e^2,e^-1*a^-1*e*a, e^-1*b^-1*e*b,e^-1*s^-1*e*s, e^-1*t^-1*e*t,e^-1*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,w^2,w^-1*s^-1*w*s, w^-1*t^-1*w*t,w^-1*u^-1*w*u, w^-1*v^-1*w*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,y^-1*z^-1*y*z, x^-1*z^-1*x*z,s^2,t^2,u^2,v^2, 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^-1,a^-1*v*a*t^-1, a^-1*w*a*z,a^-1*x*a*x,a^-1*y*a*w*x*y *z,a^-1*z*a*w,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, b^-1*w*b*x,b^-1*x*b*y,b^-1*y*b*w, b^-1*z*b*z], [[b,a*b*a*b^-1*a,w*x,s],[a*b,s,w]]]; end, [10,24]], "A5 ( 2^4 E N 2^1 ) x 2^4'",[1,9,16],2, 1,[10,24]], # 30720.17 [[1,"abstuvewxyz", function(a,b,s,t,u,v,e,w,x,y,z) return [[a^2,b^3,(a*b)^5,e^2,e^-1*a^-1*e*a,e^-1 *b^-1*e*b,e^-1*s^-1*e*s, e^-1*t^-1*e*t,e^-1*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,w^2,w^-1*s^-1*w*s, w^-1*t^-1*w*t,w^-1*u^-1*w*u, w^-1*v^-1*w*v,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,s^2,t^2,u^2,v^2, 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^-1,a^-1*v*a*t^-1, a^-1*w*a*z,a^-1*x*a*x,a^-1*y*a*w*x*y *z,a^-1*z*a*w,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, b^-1*w*b*x,b^-1*x*b*y,b^-1*y*b*w, b^-1*z*b*z],[[a*b,s]]]; end, [384]], "A5 ( 2^4 E x 2^4' C ) 2^1",[1,9,17],2, 1,384], # 30720.18 [[1,"abdstuvwxyz", function(a,b,d,s,t,u,v,w,x,y,z) return [[a^2*d^-1,b^3,(a*b)^5,d^2,d^-1*b^-1*d*b, d^-1*a^-1*d*a,d^-1*s^-1*d*s, d^-1*t^-1*d*t,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,w^2,w^-1*s^-1*w*s, w^-1*t^-1*w*t,w^-1*u^-1*w*u, w^-1*v^-1*w*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,y^-1*z^-1*y*z, x^-1*z^-1*x*z,s^2,t^2,u^2,v^2, 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^-1,a^-1*v*a*t^-1, a^-1*w*a*z,a^-1*x*a*x,a^-1*y*a*w*x*y *z,a^-1*z*a*w,b^-1*s*b*(t*v)^-1, b^-1*t*b*(s*t*u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*w*b*x,b^-1*x*b*y,b^-1*y*b*w, b^-1*z*b*z], [[b,a*b*a*b^-1*a,w*x,s],[a,b,w],[a*b,s,w]]]; end, [10,16,24]], "A5 2^1 x 2^4 x 2^4'",[1,9,18],2, 1,[10,16,24]], # 30720.19 [[1,"abstuvewxyz", function(a,b,s,t,u,v,e,w,x,y,z) return [[a^2*e^-1,b^3,(a*b)^5,e^2,e^-1*a^-1*e*a, e^-1*b^-1*e*b,e^-1*s^-1*e*s, e^-1*t^-1*e*t,e^-1*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,w^2,w^-1*s^-1*w*s, w^-1*t^-1*w*t,w^-1*u^-1*w*u, w^-1*v^-1*w*v,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,s^2,t^2,u^2,v^2, 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^-1,a^-1*v*a*t^-1, a^-1*w*a*z,a^-1*x*a*x,a^-1*y*a*w*x*y *z,a^-1*z*a*w,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, b^-1*w*b*x,b^-1*x*b*y,b^-1*y*b*w, b^-1*z*b*z],[[a*b,s]]]; end, [384]], "A5 ( 2^4 E x 2^4' C ) N 2^1",[1,9,19],2, 1,384], # 30720.20 [[1,"abstuvwxyzg", function(a,b,s,t,u,v,w,x,y,z,g) return [[a^2*g^-1,b^3,(a*b)^5,g^2,g^-1*a^-1*g*a, g^-1*b^-1*g*b,g^-1*s^-1*g*s, g^-1*t^-1*g*t,g^-1*u^-1*g*u, g^-1*v^-1*g*v,g^-1*w^-1*g*w, g^-1*x^-1*g*x,g^-1*y^-1*g*y, g^-1*z^-1*g*z,w^2,w^-1*s^-1*w*s, w^-1*t^-1*w*t,w^-1*u^-1*w*u, w^-1*v^-1*w*v,w^-1*x^-1*w*x *g^-1,w^-1*y^-1*w*y*g^-1, w^-1*z^-1*w*z*g^-1, x^-1*y^-1*x*y*g^-1, x^-1*z^-1*x*z*g^-1, y^-1*z^-1*y*z*g^-1,s^2,t^2,u^2,v^2, 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^-1,a^-1*v*a*t^-1, a^-1*w*a*z,a^-1*x*a*x,a^-1*y*a*w*x*y *z,a^-1*z*a*w,b^-1*s*b*(t*v)^-1, b^-1*t*b*(s*t*u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*w*b*x,b^-1*x*b*y,b^-1*y*b*w, b^-1*z*b*z], [[a,b,w],[b,a*b*a*b^-1*a^-1*w*x,s]]]; end, [16,80]], "A5 2^4 x ( 2^4' C N 2^1 )",[1,9,20],2, 1,[16,80]], # 30720.21 [[1,"abstuvwxyzg", function(a,b,s,t,u,v,w,x,y,z,g) return [[a^2,b^3,(a*b)^5,g^2,g^-1*a^-1*g*a,g^-1 *b^-1*g*b,g^-1*s^-1*g*s, g^-1*t^-1*g*t,g^-1*u^-1*g*u, g^-1*v^-1*g*v,g^-1*w^-1*g*w, g^-1*x^-1*g*x,g^-1*y^-1*g*y, g^-1*z^-1*g*z,w^2,w^-1*s^-1*w*s, w^-1*t^-1*w*t,w^-1*u^-1*w*u, w^-1*v^-1*w*v,w^-1*x^-1*w*x *g^-1,w^-1*y^-1*w*y*g^-1, w^-1*z^-1*w*z*g^-1, x^-1*y^-1*x*y*g^-1, x^-1*z^-1*x*z*g^-1, y^-1*z^-1*y*z*g^-1,s^2,t^2,u^2,v^2, 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^-1,a^-1*v*a*t^-1, a^-1*w*a*z,a^-1*x*a*x,a^-1*y*a*w*x*y *z,a^-1*z*a*w,b^-1*s*b*(t*v)^-1, b^-1*t*b*(s*t*u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*w*b*x,b^-1*x*b*y,b^-1*y*b*w, b^-1*z*b*z],[[a,b,w],[a,b,s]]]; end, [16,32]], "A5 2^4 x ( 2^4' C 2^1 )",[1,9,21],2, 1,[16,32]], # 30720.22 [[1,"abdstuvwxyz", function(a,b,d,s,t,u,v,w,x,y,z) return [[a^2*d^-1,b^3,(a*b)^5,d^2*w*z,b^-1*d*b*(d*u *v*y)^-1,d^-1*a^-1*d*a, d^-1*s^-1*d*s*x*y, d^-1*t^-1*d*t*w*y*z, d^-1*u^-1*d*u*w*y*z, d^-1*v^-1*d*v*x*y,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^2,w^-1*s^-1*w*s, w^-1*t^-1*w*t,w^-1*u^-1*w*u, w^-1*v^-1*w*v,s^2*w,t^2*w,u^2*z,v^2*z, s^-1*t^-1*s*t*w,s^-1*u^-1*s*u*w*x *z,s^-1*v^-1*s*v*x*y, t^-1*u^-1*t*u*w*y*z, t^-1*v^-1*t*v*w*x*z,u^-1*v^-1*u*v *z,a^-1*s*a*(u*x)^-1, a^-1*t*a*(v*x*z)^-1, a^-1*u*a*(s*y)^-1, a^-1*v*a*(t*x*y*z)^-1,a^-1*w*a*z, a^-1*x*a*x,a^-1*y*a*w*x*y*z, a^-1*z*a*w,b^-1*s*b*(t*v*x)^-1, b^-1*t*b*(s*t*u*v*x*z)^-1, b^-1*u*b*(u*v*w*x*y)^-1, b^-1*v*b*(u*w*x*y)^-1,b^-1*w*b*x, b^-1*x*b*y,b^-1*y*b*w,b^-1*z*b*z], [[b,d*t]]]; end, [160]], "A5 2^1 E 2^4 C 2^4'",[1,9,22],1, 1,160], # 30720.23 [[1,"abdstuvwxyz", function(a,b,d,s,t,u,v,w,x,y,z) return [[a^2*d^-1,b^3,(a*b)^5,d^2,b^-1*d*b*(d*u*v) ^-1,d^-1*a^-1*d*a,d^-1*s^-1*d *s,d^-1*t^-1*d*t,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,w^2,w^-1*s^-1*w*s, w^-1*t^-1*w*t,w^-1*u^-1*w*u, w^-1*v^-1*w*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,y^-1*z^-1*y*z, x^-1*z^-1*x*z,s^2,t^2,u^2,v^2, 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^-1,a^-1*v*a*t^-1, a^-1*w*a*z,a^-1*x*a*x,a^-1*y*a*w*x*y *z,a^-1*z*a*w,b^-1*s*b*(t*v)^-1, b^-1*t*b*(s*t*u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*w*b*x,b^-1*x*b*y,b^-1*y*b*w, b^-1*z*b*z], [[b,a*b*a*b^-1*a,w*x,s],[b,d,w,z]]]; end, [10,80]], "A5 ( 2^1 E 2^4 ) x 2^4'",[1,9,23],1, 1,[10,80]], # 30720.24 [[1,"abwxyzdstuv", function(a,b,w,x,y,z,d,s,t,u,v) return [[a^2*d^-1,b^3,(a*b)^5,v^2,(v*s)^2,(y*v)^2,(z*v)^2, (x*v)^2,(w*v)^2,a*d*a^-1*d,a*s*a^-1*u, a*v*a^-1*t,a*u*a^-1*s,a*v*a^-1*t, b^-1*d*b*d*u*v,b^-1*s*b*t*v, b^-1*t*b*s*t*u*v,b^-1*u*b*u*v, b^-1*v*b*u,z^2,y^2,x^2,w^2,(z*y)^2*d*u, (z*x)^2*d*u*v,(x*y)^2*d*s*v,(z*w)^2*d, (y*w)^2*d*t,(x*w)^2*d*s*t,b^-1*z*b*z*t*u, b^-1*y*b*w,b^-1*x*b*y,b^-1*w*b*x, a^-1*z*a*w,a^-1*y*a*(w*x*y*z*s)^-1, a^-1*w*a*z,a^-1*x*a*x],[[b,w]]]; end, [160]], "A5 2^4' C N 2^1 E 2^4",[1,9,24],1, 1,160], # 30720.25 [[1,"abwxyzdstuv", function(a,b,w,x,y,z,d,s,t,u,v) return [[a^2,b^3,(a*b)^5,v^2,(v*s)^2,(y*v)^2,(z*v)^2,(x*v)^2, (w*v)^2,a*d*a^-1*d,a*s*a^-1*u, a*v*a^-1*t,a*u*a^-1*s,a*v*a^-1*t, b^-1*d*b*d*u*v,b^-1*s*b*t*v, b^-1*t*b*s*t*u*v,b^-1*u*b*u*v, b^-1*v*b*u,z^2,y^2,x^2,w^2,(z*y)^2*d*u, (z*x)^2*d*u*v,(x*y)^2*d*s*v,(z*w)^2*d, (y*w)^2*d*t,(x*w)^2*d*s*t,b^-1*z*b*z*t*u, b^-1*y*b*w,b^-1*x*b*y,b^-1*w*b*x, a^-1*z*a*w,a^-1*y*a*(w*x*y*z*s)^-1, a^-1*w*a*z,a^-1*x*a*x],[[b,w]]]; end, [160]], "A5 2^4' C 2^1 E 2^4",[1,9,25],1, 1,160], # 30720.26 [[1,"abdwxyzWXYZ", function(a,b,d,w,x,y,z,W,X,Y,Z) return [[a^2*d^-1,b^3,(a*b)^5,d^2,d^-1*b^-1*d*b, d^-1*a^-1*d*a,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*W^-1*d*W, d^-1*X^-1*d*X,d^-1*Y^-1*d*Y, d^-1*Z^-1*d*Z,w^2,x^2,y^2,z^2, 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*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,W^2, X^2,Y^2,Z^2,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*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,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], [[a*b*a*b^-1*a,b,w*x,W], [a*b*a*b^-1*a,b,W*X,w],[a*b,w,W]]]; end, [10,10,24]], "A5 2^1 x 2^4' x 2^4'",[1,9,26],2, 1,[10,10,24]], # 30720.27 [[1,"abdwxyzWXYZ", function(a,b,d,w,x,y,z,W,X,Y,Z) return [[a^2*d^-1,b^3,(a*b)^5,d^2,d^-1*a^-1*d*a, d^-1*b^-1*d*b,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*W^-1*d*W, d^-1*X^-1*d*X,d^-1*Y^-1*d*Y, d^-1*Z^-1*d*Z,w^2,x^2,y^2,z^2, 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*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,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,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], [[a*b*a*b^-1*a,b,w*x,W], [b,a*b*a*b^-1*a^-1*W*X,w]]]; end, [10,80]], "A5 2^4' x ( 2^4' C N 2^1 )",[1,9,27],2, 1,[10,80]], # 30720.28 [[1,"abfwxyzWXYZ", function(a,b,f,w,x,y,z,W,X,Y,Z) return [[a^2,b^3,(a*b)^5,f^2,f^-1*a^-1*f*a,f^-1 *b^-1*f*b,f^-1*w^-1*f*w, f^-1*x^-1*f*x,f^-1*y^-1*f*y, f^-1*z^-1*f*z,f^-1*W^-1*f*W, f^-1*X^-1*f*X,f^-1*Y^-1*f*Y, f^-1*Z^-1*f*Z,w^2,x^2,y^2,z^2, 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*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,W^2, X^2,Y^2,Z^2,W^-1*X^-1*W*X*f, W^-1*Y^-1*W*Y*f,W^-1*Z^-1*W*Z*f, X^-1*Y^-1*X*Y*f,X^-1*Z^-1*X*Z*f, Y^-1*Z^-1*Y*Z*f,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,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], [[a*b*a*b^-1*a,b,w*x,W],[a,b,w]]]; end, [10,32]], "A5 2^4' x ( 2^4' C 2^1 )",[1,9,28],2, 1,[10,32]], # 30720.29 [[1,"abewxyzWXYZ", function(a,b,e,w,x,y,z,W,X,Y,Z) return [[a^2,b^3,(a*b)^5,e^2,e^-1*a^-1*e*a,e^-1 *b^-1*e*b,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*W^-1*e*W, e^-1*X^-1*e*X,e^-1*Y^-1*e*Y, e^-1*Z^-1*e*Z,w^2,x^2,y^2,z^2, w^-1*x^-1*w*x*e,w^-1*y^-1*w*y*e, w^-1*z^-1*w*z*e,x^-1*y^-1*x*y*e, x^-1*z^-1*x*z*e,y^-1*z^-1*y*z*e, 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,W^2, X^2,Y^2,Z^2,W^-1*X^-1*W*X*e, W^-1*Y^-1*W*Y*e,W^-1*Z^-1*W*Z*e, X^-1*Y^-1*X*Y*e,X^-1*Z^-1*X*Z*e, Y^-1*Z^-1*Y*Z*e,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,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],[[a,b,w*W]]]; end, [32]], "A5 ( 2^4' C x 2^4' C ) 2^1",[1,9,29],2, 1,32], # 30720.30 [[1,"abewxyzWXYZ", function(a,b,e,w,x,y,z,W,X,Y,Z) return [[a^2*e^-1,b^3,(a*b)^5,e^2,e^-1*a^-1*e*a, e^-1*b^-1*e*b,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*W^-1*e*W, e^-1*X^-1*e*X,e^-1*Y^-1*e*Y, e^-1*Z^-1*e*Z,w^2,x^2,y^2,z^2, w^-1*x^-1*w*x*e,w^-1*y^-1*w*y*e, w^-1*z^-1*w*z*e,x^-1*y^-1*x*y*e, x^-1*z^-1*x*z*e,y^-1*z^-1*y*z*e, 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,W^2, X^2,Y^2,Z^2,W^-1*X^-1*W*X*e, W^-1*Y^-1*W*Y*e,W^-1*Z^-1*W*Z*e, X^-1*Y^-1*X*Y*e,X^-1*Z^-1*X*Z*e, Y^-1*Z^-1*Y*Z*e,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,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],[[a*b,w*W]]]; end, [384]], "A5 ( 2^4' C x 2^4' C ) N 2^1",[1,9,30],2, 1,384], # 30720.31 [[1,"abgwxyzWXYZ", function(a,b,g,w,x,y,z,W,X,Y,Z) return [[a^2,b^3,(a*b)^5,g^2,g^-1*a^-1*g*a,g^-1 *b^-1*g*b,g^-1*w^-1*g*w, g^-1*x^-1*g*x,g^-1*y^-1*g*y, g^-1*z^-1*g*z,g^-1*W^-1*g*W, g^-1*X^-1*g*X,g^-1*Y^-1*g*Y, g^-1*Z^-1*g*Z,w^2,x^2,y^2,z^2, 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*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,W^2, X^2,Y^2,Z^2,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*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,w^-1*W*w*W^-1, w^-1*X*w*X^-1*g,w^-1*Y*w*Y^-1*g, w^-1*Z*w*Z^-1*g,x^-1*W*x*W^-1*g, x^-1*X*x*X^-1,x^-1*Y*x*Y^-1*g, x^-1*Z*x*Z^-1*g,y^-1*W*y*W^-1*g, y^-1*X*y*X^-1*g,y^-1*Y*y*Y^-1, y^-1*Z*y*Z^-1*g,z^-1*W*z*W^-1*g, z^-1*X*z*X^-1*g,z^-1*Y*z*Y^-1*g, z^-1*Z*z*Z^-1],[[a,b,w]]]; end, [32]], "A5 ( 2^4' x 2^4' ) C 2^1",[1,9,31],2, 1,32], # 30720.32 [[1,"abgwxyzWXYZ", function(a,b,g,w,x,y,z,W,X,Y,Z) return [[a^2*g^-1,b^3,(a*b)^5,g^2,g^-1*a^-1*g*a, g^-1*b^-1*g*b,g^-1*w^-1*g*w, g^-1*x^-1*g*x,g^-1*y^-1*g*y, g^-1*z^-1*g*z,g^-1*W^-1*g*W, g^-1*X^-1*g*X,g^-1*Y^-1*g*Y, g^-1*Z^-1*g*Z,w^2,x^2,y^2,z^2, 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*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,W^2, X^2,Y^2,Z^2,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*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,w^-1*W*w*W^-1, w^-1*X*w*X^-1*g,w^-1*Y*w*Y^-1*g, w^-1*Z*w*Z^-1*g,x^-1*W*x*W^-1*g, x^-1*X*x*X^-1,x^-1*Y*x*Y^-1*g, x^-1*Z*x*Z^-1*g,y^-1*W*y*W^-1*g, y^-1*X*y*X^-1*g,y^-1*Y*y*Y^-1, y^-1*Z*y*Z^-1*g,z^-1*W*z*W^-1*g, z^-1*X*z*X^-1*g,z^-1*Y*z*Y^-1*g, z^-1*Z*z*Z^-1],[[a*b,w]]]; end, [384]], "A5 ( 2^4' x 2^4' ) C N 2^1",[1,9,32],2, 1,384], # 30720.33 [[1,"abdwxyzWXYZ", function(a,b,d,w,x,y,z,W,X,Y,Z) return [[a^2*d^-1,b^3,(a*b)^5,d^2,d^-1*b^-1*d*b, d^-1*a^-1*d*a,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^2*W^-1,x^2*X^-1, y^2*Y^-1,z^2*Z^-1,W^2,X^2,Y^2,Z^2, w*x*w^-1*x^-1,w*y*w^-1*y^-1, w*z*w^-1*z^-1,x*y*x^-1*y^-1, x*z*x^-1*z^-1,y*z*y^-1*z^-1, a^-1*w*a*z^-1,a^-1*x*a*x^-1, a^-1*y*a*(w*x*y*z*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], [[a*b,w],[a*b*a*b^-1*a,b,w*x^-1]]]; end, [24,20]], "A5 2^1 x ( 2^4' A 2^4' )",[1,9,33],2, 1,[24,20]], # 30720.34 [[1,"abdwxyzWXYZ", function(a,b,d,w,x,y,z,W,X,Y,Z) return [[a^2*d,b^3,(a*b)^5,d^2,d^-1*a^-1*d*a,d^-1 *b^-1*d*b,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^2*W^-1,x^2*X^-1, y^2*Y^-1,z^2*Z^-1,W^2,X^2,Y^2,Z^2, w*x*w^-1*x^-1*d,w*y*w^-1*y^-1*d, w*z*w^-1*z^-1*d,x*y*x^-1*y^-1*d, x*z*x^-1*z^-1*d,y*z*y^-1*z^-1*d, a^-1*w*a*z^-1,a^-1*x*a*x^-1, a^-1*y*a*(w*x*y*z*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], [[b,a*b*a*b^-1*a^-1*w*x], [a*b*a*b^-1*a,b,w*x^-1]]]; end, [80,20]], "A5 ( 2^4' C N 2^1 ) A 2^4'",[1,9,34],2, 1,[80,20]], # 30720.35 [[1,"abdwxyzWXYZ", function(a,b,d,w,x,y,z,W,X,Y,Z) return [[a^2,b^3,(a*b)^5,d^2,d^-1*a^-1*d*a,d^-1 *b^-1*d*b,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^2*W^-1,x^2*X^-1, y^2*Y^-1,z^2*Z^-1,W^2,X^2,Y^2,Z^2, w*x*w^-1*x^-1*d,w*y*w^-1*y^-1*d, w*z*w^-1*z^-1*d,x*y*x^-1*y^-1*d, x*z*x^-1*z^-1*d,y*z*y^-1*z^-1*d, a^-1*w*a*z^-1,a^-1*x*a*x^-1, a^-1*y*a*(w*x*y*z*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], [[a,b,W],[a*b*a*b^-1*a,b,w*x^-1]]]; end, [32,20]], "A5 ( 2^4' C 2^1 ) A 2^4'",[1,9,35],2, 1,[32,20]], # 30720.36 [[1,"abdwxyzWXYZ", function(a,b,d,w,x,y,z,W,X,Y,Z) return [[a^2*d,b^3,(a*b)^5,d^2,b^-1*d^-1*b*d,w^2*W ^-1,x^2*X^-1,y^2*Y^-1,z^2*Z^-1, w*x*w^-1*x^-1,w*y*w^-1*y^-1, w*z*w^-1*z^-1,x*y*x^-1*y^-1, x*z*x^-1*z^-1,y*z*y^-1*z^-1, a^-1*w*a*(z*Z)^-1, a^-1*x*a*(x*W*X*Y)^-1, a^-1*y*a*(w*x*y*z*W*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*d*w, d^-1*x*d*x,d^-1*y*d*y,d^-1*z*d*z], [[b,d,w]]]; end, [80]], "A5 2^1 ( 2^4' A 2^4' )",[1,9,36],1, 1,80], # 30720.37 [[1,"abdwxyzWXYZ", function(a,b,d,w,x,y,z,W,X,Y,Z) return [[a^2*d^-1,b^3,(a*b)^5,d^2,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,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,w*W*w*W,w*X*w*X,w*Y*w*Y,w*Z*w*Z, a^-1*w*a*z*Z,a^-1*x*a*x*W*X*Y, a^-1*y*a*w*x*y*z*X*Y,a^-1*z*a*w, b^-1*w*b*x,b^-1*x*b*y,b^-1*y*b*w, b^-1*z*b*z,a^-1*W*a*Z,a^-1*X*a*X, a^-1*Y*a*W*X*Y*Z,a^-1*Z*a*W, b^-1*W*b*X,b^-1*X*b*Y,b^-1*Y*b*W, b^-1*Z*b*Z],[[b,d,w]]]; end, [80]], "A5 2^1 ( 2^4' E 2^4' )",[1,9,37],1, 1,80] ]; ############################################################################# ## #E perf4.grp . . . . . . . . . . . . . . . . . . . . . . . . . ends here ##