Real-time collaboration for Jupyter Notebooks, Linux Terminals, LaTeX, VS Code, R IDE, and more,
all in one place.
Real-time collaboration for Jupyter Notebooks, Linux Terminals, LaTeX, VS Code, R IDE, and more,
all in one place.
| Download
GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it
Project: cocalc-sagemath-dev-slelievre
Views: 418346############################################################################# ## #W perf2.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 7800-20160 ## All data is based on Holt/Plesken: Perfect Groups, OUP 1989 ## PERFGRP[39]:=[# 7800.1 [[1,"bca", function(b,c,a) return [[b^5,c^12,c^(-1*2)*b*c^2*(b*c^-1*b^2*c)^-1, c^-1*b^2*c*b*(b*c^-1*b^2*c)^-1,a^2, c*a*c*a^-1,(b*a)^3,(c^4*b*c*b*a)^3],[[b,c]]]; end, [26]], "L2(25)",22,-1, 14,26] ]; PERFGRP[40]:=[# 7920.1 [[1,"ab", function(a,b) return [[a^2,b^4,(a*b)^11,(a*b^2)^6,a*b^-1*a*b^-1*a*b *a*b*a*b^-1*a*b*a*b^2*a *b^-1*a*b], [[a*b^-1*a*b^-1*a*b*a*b*a,b]]]; end, [11]], "M11",28,-1, 15,11] ]; PERFGRP[41]:=[# 9720.1 [[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^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], [[a*b,w],[b,a*b*a*b^-1*a,w*x^-1]]]; end, [24,15]], "A5 2^1 x 3^4'",[2,4,1],2, 1,[24,15]], # 9720.2 [[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^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], [[a*b,w],[a^2,b,w*x^-1]]]; end, [24,60]], "A5 2^1 x N 3^4'",[2,4,2],2, 1,[24,60]], # 9720.3 [[1,"abstuv", function(a,b,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^-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], [[b,a*b*a*b^-1*a,u]]]; end, [45]], "A5 2^1 3^4",[2,4,3],1, 1,45], # 9720.4 (otherpres.) [[1,"abdstuv", function(a,b,d,s,t,u,v) return [[a^2*d^-1,b^3,(a*b)^5,d^2,d^-1*b^-1*d*b, 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], [[b,a*b*a*b^-1*a,u]]]; end, [45]]] ]; PERFGRP[42]:=[# 9828.1 [[1,"abc", function(a,b,c) return [[c^13,b^3,(c*b)^3*c^(-1*3)*b^-1,c^(-1*4)*b*c^2*b *c*b*c*b^-1,a^2,c*a*c*a^-1,(b*a)^3], [[b,c]]]; end, [28]], "L2(27)",22,-1, 16,28] ]; PERFGRP[43]:=[# 10080.1 [[1,"abcd", function(a,b,c,d) return [[a^2,b^3,(a*b)^5,c^2,d^3,(c*d)^7,(c^-1*d^-1*c *d)^4,a^-1*c^-1*a*c,a^-1*d^-1*a*d ,b^-1*c^-1*b*c,b^-1*d^-1*b*d], [[b,a*b*a*b^-1*a,c,d],[a,b,d,c*d*c*d^-1*c]]] ; end, [5,7]], "A5 x L3(2)",[31,0,1,32],1, [1,2],[5,7]] ]; PERFGRP[44]:=[# 10752.1 [[1,"abxyzXYZ", function(a,b,x,y,z,X,Y,Z) return [[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4,x^2,y^2, z^2,x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,X^2,Y^2,Z^2, 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*(x*y*z)^-1,a^-1*z*a*x^-1, b^-1*x*b*y^-1,b^-1*y*b*(x*y)^-1, b^-1*z*b*z^-1,a^-1*X*a*Z^-1, a^-1*Y*a*(X*Y*Z)^-1,a^-1*Z*a*X^-1, b^-1*X*b*Y^-1,b^-1*Y*b*(X*Y)^-1, b^-1*Z*b*Z^-1,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,b,X],[a,b,x]]]; end, [8,8]], "L3(2) 2^3 x 2^3",[8,6,1],1, 2,[8,8]], # 10752.2 [[1,"abxyzXYZ", function(a,b,x,y,z,X,Y,Z) return [[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4*(Y*Z)^-1 ,x^2,y^2,z^2,x^-1*y^-1*x*y, x^-1*z^-1*x*z,y^-1*z^-1*y*z,X^2, Y^2,Z^2,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*(x*y*z)^-1,a^-1*z*a*x^-1, b^-1*x*b*y^-1,b^-1*y*b*(x*y)^-1, b^-1*z*b*z^-1,a^-1*X*a*Z^-1, a^-1*Y*a*(X*Y*Z)^-1,a^-1*Z*a*X^-1, b^-1*X*b*Y^-1,b^-1*Y*b*(X*Y)^-1, b^-1*Z*b*Z^-1,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,b,X],[b,a*b*a*b^-1*a,x,z,X]]]; end, [8,14]], "L3(2) 2^3 x N 2^3",[8,6,2],1, 2,[8,14]], # 10752.3 [[1,"abxyzXYZ", function(a,b,x,y,z,X,Y,Z) return [[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4,x^2*X^(-1 *1),y^2*Y^-1,z^2*Z^-1, x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,a^-1*x*a*(z*Y)^-1, a^-1*y*a*(x*y*z)^-1, a^-1*z*a*(x*X*Y*Z)^-1, b^-1*x*b*(y*X)^-1, b^-1*y*b*(x*y*Z)^-1, b^-1*z*b*(z*X*Y)^-1,a^-1*X*a*Z^-1, a^-1*Y*a*(X*Y*Z)^-1,a^-1*Z*a*X^-1, b^-1*X*b*Y^-1,b^-1*Y*b*(X*Y)^-1, b^-1*Z*b*Z^-1],[[b,a*b*a*b^-1*a,x*Z]] ]; end, [28]], "L3(2) 2^3 A 2^3",[8,6,3],1, 2,28], # 10752.4 [[1,"abxyzXYZ", function(a,b,x,y,z,X,Y,Z) return [[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4*(y*z*X*Z) ^-1,x^2*X^-1,y^2*Y^-1,z^2*Z^-1, x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,a^-1*x*a*(z*Y)^-1, a^-1*y*a*(x*y*z)^-1, a^-1*z*a*(x*X*Y*Z)^-1, b^-1*x*b*(y*X)^-1, b^-1*y*b*(x*y*Z)^-1, b^-1*z*b*(z*X*Y)^-1,a^-1*X*a*Z^-1, a^-1*Y*a*(X*Y*Z)^-1,a^-1*Z*a*X^-1, b^-1*X*b*Y^-1,b^-1*Y*b*(X*Y)^-1, b^-1*Z*b*Z^-1], [[b,a*b*a*b*a*b^-1*a*b*a*b*a,x*Z]]]; end, [112]], "L3(2) N 2^3 A 2^3",[8,6,4],1, 2,112], # 10752.5 [[1,"abxyzuvw", function(a,b,x,y,z,u,v,w) return [[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4,u^2,v^2, w^2,u^-1*v^-1*u*v,u^-1*w^-1*u*w, v^-1*w^-1*v*w,x^2,y^2,z^2, x^-1*y^-1*x*y,x^-1*z^-1*x*z, y^-1*z^-1*y*z,a^-1*u*a*(v*w)^-1, a^-1*v*a*v^-1,a^-1*w*a*(u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*w*b*w^-1,a^-1*x*a*z^-1, a^-1*y*a*(x*y*z)^-1,a^-1*z*a*x^-1, b^-1*x*b*y^-1,b^-1*y*b*(x*y)^-1, b^-1*z*b*z^-1,u^-1*x*u*x^-1, u^-1*y*u*y^-1,u^-1*z*u*z^-1, v^-1*x*v*x^-1,v^-1*y*v*y^-1, v^-1*z*v*z^-1,w^-1*x*w*x^-1, w^-1*y*w*y^-1,w^-1*z*w*z^-1], [[a,b,u],[a,b,x]]]; end, [8,8]], "L3(2) 2^3 x 2^3'",[8,6,5],1, 2,[8,8]], # 10752.6 [[1,"abxyzuvw", function(a,b,x,y,z,u,v,w) return [[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4*(u*v*w)^(-1 *1),u^2,v^2,w^2,u^-1*v^-1*u*v, u^-1*w^-1*u*w,v^-1*w^-1*v*w,x^2, y^2,z^2,x^-1*y^-1*x*y,x^-1*z^-1*x*z ,y^-1*z^-1*y*z,a^-1*u*a*(v*w)^-1, a^-1*v*a*v^-1,a^-1*w*a*(u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*w*b*w^-1,a^-1*x*a*z^-1, a^-1*y*a*(x*y*z)^-1,a^-1*z*a*x^-1, b^-1*x*b*y^-1,b^-1*y*b*(x*y)^-1, b^-1*z*b*z^-1,u^-1*x*u*x^-1, u^-1*y*u*y^-1,u^-1*z*u*z^-1, v^-1*x*v*x^-1,v^-1*y*v*y^-1, v^-1*z*v*z^-1,w^-1*x*w*x^-1, w^-1*y*w*y^-1,w^-1*z*w*z^-1], [[a,b,u],[b,a*b^-1*a*b*a,x,z,u]]]; end, [8,14]], "L3(2) 2^3 x N 2^3'",[8,6,6],1, 2,[8,14]], # 10752.7 [[1,"abxyzuvw", function(a,b,x,y,z,u,v,w) return [[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4*(y*z*u*v *w)^-1,u^2,v^2,w^2,u^-1*v^-1*u*v, u^-1*w^-1*u*w,v^-1*w^-1*v*w,x^2, y^2,z^2,x^-1*y^-1*x*y,x^-1*z^-1*x*z ,y^-1*z^-1*y*z,a^-1*u*a*(v*w)^-1, a^-1*v*a*v^-1,a^-1*w*a*(u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*w*b*w^-1,a^-1*x*a*z^-1, a^-1*y*a*(x*y*z)^-1,a^-1*z*a*x^-1, b^-1*x*b*y^-1,b^-1*y*b*(x*y)^-1, b^-1*z*b*z^-1,u^-1*x*u*x^-1, u^-1*y*u*y^-1,u^-1*z*u*z^-1, v^-1*x*v*x^-1,v^-1*y*v*y^-1, v^-1*z*v*z^-1,w^-1*x*w*x^-1, w^-1*y*w*y^-1,w^-1*z*w*z^-1], [[b,a*b*a*b^-1*a,x,u,w], [b,a*b^-1*a*b*a,x,z,u]]]; end, [14,14]], "L3(2) N 2^3 x N 2^3'",[8,6,7],1, 2,[14,14]], # 10752.8 [[1,"abxyzuvw", function(a,b,x,y,z,u,v,w) return [[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4,u^2,v^2, w^2,u^-1*v^-1*u*v,u^-1*w^-1*u*w, v^-1*w^-1*v*w,x^2,y^2,z^2, 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*(x*y*z)^-1,a^-1*z*a*x^-1, b^-1*x*b*(y*w)^-1,b^-1*y*b*(x*y)^-1, b^-1*z*b*(z*u)^-1,a^-1*u*a*(v*w)^-1, a^-1*v*a*v^-1,a^-1*w*a*(u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*w*b*w^-1,u^-1*x*u*x^-1, u^-1*y*u*y^-1,u^-1*z*u*z^-1, v^-1*x*v*x^-1,v^-1*y*v*y^-1, v^-1*z*v*z^-1,w^-1*x*w*x^-1, w^-1*y*w*y^-1,w^-1*z*w*z^-1], [[b,a*b*a*b^-1*a,x,w]]]; end, [56]], "L3(2) 2^3 E 2^3'",[8,6,8],1, 2,56], # 10752.9 [[1,"abxyzuvw", function(a,b,x,y,z,u,v,w) return [[a^2*(u*w)^-1,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4 *(y*z*v)^-1,u^2,v^2,w^2,u^-1*v^-1*u*v, u^-1*w^-1*u*w,v^-1*w^-1*v*w,x^2, y^2,z^2,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*(x*y*z)^-1,a^-1*z*a*x^-1, b^-1*x*b*(y*w)^-1,b^-1*y*b*(x*y)^-1, b^-1*z*b*(z*u)^-1,a^-1*u*a*(v*w)^-1, a^-1*v*a*v^-1,a^-1*w*a*(u*v)^-1, b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1, b^-1*w*b*w^-1,u^-1*x*u*x^-1, u^-1*y*u*y^-1,u^-1*z*u*z^-1, v^-1*x*v*x^-1,v^-1*y*v*y^-1, v^-1*z*v*z^-1,w^-1*x*w*x^-1, w^-1*y*w*y^-1,w^-1*z*w*z^-1], [[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1*x*y*u, x*u*w]]]; end, [64]], "L3(2) N 2^3 E 2^3'",[8,6,9],1, 2,64] ]; PERFGRP[45]:=[# 11520.1 [[1,"abcstuve", function(a,b,c,s,t,u,v,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,e^2, 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,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*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)^-1],[[a,c,v]]]; end, [12]], "A6 2^4 E 2^1",[13,5,1],2, 3,12], # 11520.2 [[1,"abcstuve", function(a,b,c,s,t,u,v,e) return [[a^2*e^-1,b^3,c^3,(b*c)^4*e^-1,(b*c^-1)^5, a^-1*b^-1*c*b*c*b^-1*c*b*c^-1,e^2, 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,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*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)^-1],[[c*b*a*e,b,s]]]; end, [80]], "A6 2^4 E N 2^1",[13,5,2],2, 3,80], # 11520.3 [[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^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, c^-1*s*c*(t*u)^-1,c^-1*t*c*t^-1, c^-1*u*c*(s*u)^-1, c^-1*v*c*(s*t*u*v)^-1], [[b,c],[c*b*a*d,b,s]]]; end, [16,80]], "A6 2^1 x 2^4",[13,5,3],2, 3,[16,80]], # 11520.4 [[1,"abcdstuv", function(a,b,c,d,s,t,u,v) return [[a^2*d^-1,b^3,c^3*(s*v)^-1,(b*c)^4*(d*s)^-1 ,(b*c^-1)^5, a^-1*b^-1*c*b*c*b^-1*c*b*c^-1,d^2, b^-1*d*b*(d*u*v)^-1, c^-1*d*c*(d*t*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, c^-1*s*c*(t*u)^-1,c^-1*t*c*t^-1, c^-1*u*c*(s*u)^-1, c^-1*v*c*(s*t*u*v)^-1], [[c*b*a*u,b,c^-1*a*c*u,t]]]; end, [80]], "A6 2^1 E 2^4",[13,5,4],1, 3,80] ]; PERFGRP[46]:=[# 12144.1 [[1,"abc", function(a,b,c) return [[c^11*a^2,c*b^3*c^-1*b^-1,b^23,a^2*b^-1 *a^2*b,a^2*c^-1*a^2*c,a^4,c*a*c*a^-1, (b*a)^3],[[b,c^2]]]; end, [48]], "L2(23) 2^1 = SL(2,23)",22,-2, 13,48] ]; PERFGRP[47]:=[# 12180.1 [[1,"abc", function(a,b,c) return [[c^14,c*b^4*c^-1*b^-1,b^29,a^2,c*a*c*a^-1, (b*a)^3,c^(-1*5)*b*c^2*b*c^3*a*b^2*a*c*b^2*a], [[b,c]]]; end, [30]], "L2(29)",22,-1, 17,30] ]; PERFGRP[48]:=[# 14400.1 [[1,"abcd", function(a,b,c,d) return [[a^4,b^3,(a*b)^5,a^2*b*a^2*b^-1,c^4,d^3,(c*d)^5, c^2*d*c^2*d^-1,a^-1*c^-1*a*c, a^-1*d^-1*a*d,b^-1*c^-1*b*c, b^-1*d^-1*b*d],[[a*b,c,d],[a,b,c*d]]]; end, [24,24]], "A5 2^1 x A5 2^1",[29,2,1,30],4, [1,1],[24,24]] ]; PERFGRP[49]:=[# 14520.1 [[1,"abyz", function(a,b,y,z) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,y^11,z^11,y^-1 *z^-1*y*z,a^-1*y*a*z^-1, a^-1*z*a*y, b^-1*y*b*(y^-1*z^(-1*3))^-1, b^-1*z*b*y^(-1*4)],[[a,b]]]; end, [121]], "A5 2^1 11^2",[5,2,1],1, 1,121], # 14520.2 (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^11,z^11,y^-1*z^-1*y*z, a^-1*y*a*z^-1,a^-1*z*a*y, b^-1*y*b*(y^-1*z^(-1*3))^-1, b^-1*z*b*y^(-1*4)],[[a,b]]]; end, [121]]] ]; PERFGRP[50]:=[# 14580.1 [[1,"abwxyzd", function(a,b,w,x,y,z,d) return [[a^2,b^3,(a*b)^5,w^3,x^3,y^3,z^3,d^3,a^-1*d*a*d ^-1,b^-1*d*b*d^-1,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*d, b^-1*y*b*w^-1*d^-1, b^-1*z*b*z^-1*d^-1], [[a*b,b*a*b*a*b^-1*a*b^-1,w*d]]]; end, [18]], "A5 3^4' E 3^1",[2,5,1],3, 1,18] ]; PERFGRP[51]:=[# 14880.1 [[1,"abc", function(a,b,c) return [[c^15,c*b^9*c^-1*b^-1,b^31,a^2,c*a*c*a^-1, (b*a)^3],[[b,c]]]; end, [32]], "L2(31)",22,-1, 18,32] ]; PERFGRP[52]:=[# 15000.1 [[1,"abxyz", function(a,b,x,y,z) return [[a^4,b^3,(a*b)^5,a^2*b*a^2*b^-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,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], [[a*b,x],[a*b,b*a*b*a*b^-1*a*b^-1,y]]]; end, [24,30]], "A5 2^1 x 5^3",[3,3,1],2, 1,[24,30]], # 15000.2 [[1,"abxyz", function(a,b,x,y,z) return [[a^4,b^3,a^2*b*a^2*b^-1,(a*b)^5*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,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], [[a*b,x],[a*b,b*a*b*a*b^-1*a*b^-1,y]]]; end, [24,30]], "A5 2^1 x N 5^3",[3,3,2],2, 1,[24,30]], # 15000.3 [[1,"abyzd", function(a,b,y,z,d) return [[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,y^5,z^5,d^5,y ^-1*d^-1*y*d,z^-1*d^-1*z*d, y^-1*z^-1*y*z*d^-1, a^-1*y*a*z^-1*d^(-1*2),a^-1*z*a*y, a^-1*d*a*d^-1,b^-1*y*b*z, b^-1*z*b*(y*z^-1)^-1, b^-1*d*b*d^-1],[[a,b]]]; end, [125]], "A5 2^1 5^2 C 5^1",[3,3,3],5, 1,125], # 15000.4 (otherpres.) [[1,"abDyzd", function(a,b,D,y,z,d) return [[a^2*D^-1,b^3,(a*b)^5,D^2,D^-1*b^-1*D*b, y^5,z^5,d^5,y^-1*d^-1*y*d, z^-1*d^-1*z*d,y^-1*z^-1*y*z *d^-1,a^-1*y*a*z^-1*d^(-1*2), a^-1*z*a*y,a^-1*d*a*d^-1, b^-1*y*b*z,b^-1*z*b*(y*z^-1)^-1, b^-1*d*b*d^-1],[[a,b]]]; end, [125]]] ]; PERFGRP[53]:=[# 15120.1 [[1,"abd", function(a,b,d) return [[a^6*d,b^4*d,(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^(-1*2)*d*b^-1, d^2,d*a*d*a^-1,d*b*d*b^-1], [[a^3,(b^-1*a)^2*(b*a)^2*b^2*a*b*a^4,d], [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]]]; end, [45,240]], "A7 3^1 x 2^1",[23,1,1],-6, 8,[45,240]] ]; PERFGRP[54]:=[# 15360.1 [[1,"abstuvef", function(a,b,s,t,u,v,e,f) return [[a^2,b^3,(a*b)^5,e^4,f^4,e^-1*a^-1*e*a,e^(-1 *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,e],[a,b,f]]]; end, [64,64]], "A5 ( 2^4 E ( 2^1 A x 2^1 A ) ) C ( 2^1 x 2^1 )",[1,8,1],16, 1,[64,64]], # 15360.2 [[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^2, 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, 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*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], [[a*b,s,e,f],[a*b,b*a*b*a*b^-1*a*b^-1,s*f,e] ,[a,b,f]]]; end, [24,12,64]], "A5 2^1 x ( 2^4 E ( 2^1 A x 2^1 ) ) C 2^1",[1,8,2],16, 1,[24,12,64]], # 15360.3 [[1,"abstuvSTUV", function(a,b,s,t,u,v,S,T,U,V) return [[a^2,b^3,(a*b)^5,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]]]; end, [16,16]], "A5 2^4 x 2^4",[1,8,3],1, 1,[16,16]], # 15360.4 [[1,"abstuvwxyz", function(a,b,s,t,u,v,w,x,y,z) return [[a^2,b^3,(a*b)^5,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]]]; end, [40]], "A5 2^4 C 2^4'",[1,8,4],1, 1,40], # 15360.5 [[1,"abstuvwxyz", function(a,b,s,t,u,v,w,x,y,z) return [[a^2,b^3,(a*b)^5,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,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, w^-1*s*w*s^-1,w^-1*t*w*t^-1, w^-1*u*w*u^-1,w^-1*v*w*v^-1, x^-1*s*x*s^-1,x^-1*t*x*t^-1, x^-1*u*x*u^-1,x^-1*v*x*v^-1, y^-1*s*y*s^-1,y^-1*t*y*t^-1, y^-1*u*y*u^-1,y^-1*v*y*v^-1, z^-1*s*z*s^-1,z^-1*t*z*t^-1, z^-1*u*z*u^-1,z^-1*v*z*v^-1], [[a,b,w],[a*b*a*b^-1*a,b,w*x,s]]]; end, [16,10]], "A5 2^4 x 2^4'",[1,8,5],1, 1,[16,10]], # 15360.6 [[1,"abwxyzWXYZ", function(a,b,w,x,y,z,W,X,Y,Z) return [[a^2,b^3,(a*b)^5,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]]]; end, [10,10]], "A5 2^4' x 2^4'",[1,8,6],1, 1,[10,10]], # 15360.7 [[1,"abwxyzWXYZ", function(a,b,w,x,y,z,W,X,Y,Z) return [[a^2,b^3,(a*b)^5,w^2*W^-1,x^2*X^-1,y^2*Y^(-1 *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*a*b^-1*a,b,w*x^-1]]]; end, [20]], "A5 2^4' A 2^4'",[1,8,7],1, 1,20] ]; PERFGRP[55]:=[# 15600.1 [[1,"bca", function(b,c,a) return [[b^5,c^12*a^2,a^4,a^2*b^-1*a^2*b,a^2*c^-1 *a^2*c,c*a*c*a^-1,(b*a)^3,(c^4*b*c*b*a)^3, c^(-1*2)*b*c^2*(b*c^-1*b^2*c)^-1, c^-1*b^2*c*b*(b*c^-1*b^2*c)^-1], [[b,c^8]]]; end, [208]], "L2(25) 2^1 = SL(2,25)",22,-2, 14,208] ]; PERFGRP[56]:=[# 16464.1 [[1,"abyz", function(a,b,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^-1*z^-1*y*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,b]]]; end, [49]], "L3(2) 2^1 7^2",[10,2,1],1, 2,49], # 16464.2 (otherpres.) [[1,"abdyz", function(a,b,d,y,z) return [[a^2*d^-1,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4 *d^-1,d^2,d^-1*b^-1*d*b,y^7,z^7, y^-1*z^-1*y*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,b]]]; end, [49]]] ]; PERFGRP[57]:=[# 17280.1 [[1,"abcstuv", function(a,b,c,s,t,u,v) return [[b^3,c^3,(b*c)^4,(b*c^-1)^5,a^-1*b^-1*c*b *c*b^-1*c*b*c^-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, c^-1*s*c*(t*u)^-1,c^-1*t*c*t^-1, c^-1*u*c*(s*u)^-1, c^-1*v*c*(s*t*u*v)^-1], [[a^3,c*a^2,s],[b,c]]]; end, [18,16]], "A6 3^1 x 2^4",[13,4,1],3, 3,[18,16]] ]; PERFGRP[58]:=[# 19656.1 [[1,"abc", function(a,b,c) return [[c^13*a^2,b^3,(c*b)^3*c^(-1*3)*b^-1,c^(-1*4)*b*c ^2*b*c*b*c*b^-1,a^4, a^2*b^-1*a^2*b,a^2*c^-1*a^2*c, c*a*c*a^-1,(b*a)^3],[[b,c^2]]]; end, [56]], "L2(27) 2^1 = SL(2,27)",22,-2, 16,56] ]; PERFGRP[59]:=[# 20160.1 [[1,"abcd", function(a,b,c,d) return [[a^2,b^3,(a*b)^5,c^4,d^3,(c*d)^7,(c^-1*d^-1*c *d)^4*c^2,c^2*d*c^2*d^-1, a^-1*c^-1*a*c,a^-1*d^-1*a*d, b^-1*c^-1*b*c,b^-1*d^-1*b*d], [[b,a*b*a*b^-1*a,c,d], [a,b,c*d,d*c*d^-1*c*d^-1*c*d*c*d^-1]] ]; end, [5,16]], "A5 x L3(2) 2^1",[31,1,1,32],2, [1,2],[5,16]], # 20160.2 [[1,"abcd", function(a,b,c,d) return [[a^4,b^3,(a*b)^5,a^2*b*a^2*b^-1,c^2,d^3,(c*d)^7, (c^-1*d^-1*c*d)^4,a^-1*c^-1*a*c, a^-1*d^-1*a*d,b^-1*c^-1*b*c, b^-1*d^-1*b*d], [[a*b,c,d],[a,b,d,c*d*c*d^-1*c]]]; end, [24,7]], "A5 2^1 x L3(2)",[31,1,2,32],2, [1,2],[24,7]], # 20160.3 [[1,"abcd", function(a,b,c,d) return [[a^4,b^3,(a*b)^5,c^2*a^2,d^3,(c*d)^7,(c^-1*d^(-1 *1)*c*d)^4*c^2,a^-1*c^-1*a*c, a^-1*d^-1*a*d,b^-1*c^-1*b*c, b^-1*d^-1*b*d], [[a*b,c*d,d*c*d^-1*c*d^-1*c*d*c*d^-1]]] ; end, [192]], "( A5 x L3(2) ) 2^1",[31,1,3],2, [1,2],192], # 20160.4 [[1,"ab", function(a,b) return [[a^2,b^4,(a*b)^15,(a*b^2)^6,(a*b)^2*(a*b^-1*a*b^2) ^2*a*b^-1*(a*b)^2*(a*b^-1)^7, a*b*a*b^-1*a*b*a*b^2*(a*b^-1)^5*a*b^2 *(a*b^-1)^5*a*b^2], [[a,b^-1*(a*b*b)^2]]]; end, [8]], "A8",[26,0,1],-1, 19,8], # 20160.5 [[1,"ab", function(a,b) return [[a^2,b^4,(a*b)^7,(a*b^2)^5,(a^-1*b^-1*a*b)^5, (a*b*a*b*a*b^3)^5,(a*b*a*b*a*b^2*a*b^-1)^5], [[a*b*a,b^2*a*b^-1*a*b*a*b^2*a*b]]]; end, [21]], "L3(4)",[27,0,1],-1, 20,21] ]; ############################################################################# ## #E perf2.grp . . . . . . . . . . . . . . . . . . . . . . . . . ends here ##