|
#############################################################################
##
## This file is part of GAP, a system for computational discrete algebra.
## This file's authors include Volkmar Felsch, Alexander Hulpke.
##
## Copyright of GAP belongs to its developers, whose names are too numerous
## to list here. Please refer to the COPYRIGHT file for details.
##
## SPDX-License-Identifier: GPL-2.0-or-later
##
## This file contains the perfect groups of sizes 21504-30240
## All data is based on Holt/Plesken: Perfect Groups, OUP 1989
##
PERFGRP[60]:=[# 21504.1
[[1,"abdxyzXYZ",
function(a,b,d,x,y,z,X,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,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],
[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,x,X]]
];
end,
[8,8,16]],
"L3(2) 2^7",[8,7,1],2,
2,[8,8,16]],
# 21504.2
[[1,"abxyzXYZf",
function(a,b,x,y,z,X,Y,Z,f)
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,f^2,f^-1*x^-1*f*x,
f^-1*y^-1*f*y,f^-1*z^-1*f*z,
f^-1*X^-1*f*X,f^-1*Y^-1*f*Y,
f^-1*Z^-1*f*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*f)^-1,
a^-1*Y*a*(X*Y*Z)^-1,
a^-1*Z*a*(X*f)^-1,a^-1*f^-1*a*f,
b^-1*X*b*Y^-1,b^-1*Y*b*(X*Y)^-1,
b^-1*Z*b*Z^-1,b^-1*f^-1*b*f,
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,
[16,8]],
"L3(2) 2^7",[8,7,2],2,
2,[16,8]],
# 21504.3
[[1,"abdxyzXYZ",
function(a,b,d,x,y,z,X,Y,Z)
return
[[a^2*d^-1,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4
*(d*Y*Z)^-1,d^2,d^-1*b^-1*d*b,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],
[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,x,X]]
];
end,
[8,14,16]],
"L3(2) 2^7",[8,7,3],2,
2,[8,14,16]],
# 21504.4
[[1,"abxyzXYZe",
function(a,b,x,y,z,X,Y,Z,e)
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,e^2,e^-1*x^-1*e*x,
e^-1*y^-1*e*y,e^-1*z^-1*e*z,
e^-1*X^-1*e*X,e^-1*Y^-1*e*Y,
e^-1*Z^-1*e*Z,a^-1*x*a*(z*e)^-1,
a^-1*y*a*(x*y*z)^-1,
a^-1*z*a*(x*e)^-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,a^-1*e^-1*a*e,
b^-1*X*b*Y^-1,b^-1*Y*b*(X*Y)^-1,
b^-1*Z*b*Z^-1,b^-1*e^-1*b*e,
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],
[[b,a*b*a*b^-1*a,x,z,X],[a,b,X]]];
end,
[14,16]],
"L3(2) 2^7",[8,7,4],2,
2,[14,16]],
# 21504.5
[[1,"abdxyzXYZ",
function(a,b,d,x,y,z,X,Y,Z)
return
[[a^2*d^-1,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4
*d^-1,d^2,b^-1*d^-1*b*d,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],
[[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,x],
[b,a*b*a*b^-1*a,x*Z]]];
end,
[16,28]],
"L3(2) 2^7",[8,7,5],2,
2,[16,28]],
# 21504.6
[[1,"abxyzeXYZ",
function(a,b,x,y,z,e,X,Y,Z)
return
[[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4,e^2,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,e^2,e^-1*x^-1*e*x,
e^-1*y^-1*e*y,e^-1*z^-1*e*z,
a^-1*x*a*(z*e*Y)^-1,
a^-1*y*a*(x*y*z)^-1,
a^-1*z*a*(x*e*X*Y*Z)^-1,
a^-1*e^-1*a*e,b^-1*x*b*(y*X)^-1,
b^-1*y*b*(x*y*Z)^-1,
b^-1*z*b*(z*X*Y)^-1,b^-1*e^-1*b*e,
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,b,X],[b,a*b*a*b^-1*a,x*Z]]];
end,
[16,28]],
"L3(2) 2^7",[8,7,6],2,
2,[16,28]],
# 21504.7
[[1,"abdxyzXYZ",
function(a,b,d,x,y,z,X,Y,Z)
return
[[a^2*d^-1,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4
*d^-1,d^2,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,d^2,
d^-1*x^-1*d*x,d^-1*y^-1*d*y,
d^-1*z^-1*d*z,a^-1*x*a*(z*d*Y)^-1,
a^-1*y*a*(x*y*z)^-1,
a^-1*z*a*(x*d*X*Y*Z)^-1,
a^-1*d^-1*a*d,b^-1*x*b*(y*X)^-1,
b^-1*y*b*(x*y*Z)^-1,
b^-1*z*b*(z*X*Y)^-1,b^-1*d^-1*b*d,
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*y*z,b,X],[b,a*b*a*b^-1*a,x*Z]]];
end,
[16,28]],
"L3(2) 2^7",[8,7,7],2,
2,[16,28]],
# 21504.8
[[1,"abdxyzXYZ",
function(a,b,d,x,y,z,X,Y,Z)
return
[[a^2*d^-1,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4
*(d*y*z*X*Z)^-1,d^2,d^-1*b^-1*d*b,
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],
[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,x,
a^2*d^-1]]];
end,
[112,16]],
"L3(2) 2^7",[8,7,8],2,
2,[112,16]],
# 21504.9
[[1,"abxyzuvwg",
function(a,b,x,y,z,u,v,w,g)
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,g^2,g^-1*x^-1*g*x,
g^-1*y^-1*g*y,g^-1*z^-1*g*z,
g^-1*u^-1*g*u,g^-1*v^-1*g*v,
g^-1*w^-1*g*w,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,
a^-1*g*a*g^-1,b^-1*x*b*y^-1,
b^-1*y*b*(x*y)^-1,b^-1*z*b*z^-1,
b^-1*g*b*g^-1,u^-1*x*u*x^-1
*g^-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*g^-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
*g^-1],[[a,b,x]]];
end,
[16]],
"L3(2) ( 2^3 x 2^3' ) C 2^1",[8,7,9],2,
2,16],
# 21504.10
[[1,"abxyzuvwf",
function(a,b,x,y,z,u,v,w,f)
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,f^2,f^-1*x^-1*f*x,
f^-1*y^-1*f*y,f^-1*z^-1*f*z,
f^-1*u^-1*f*u,f^-1*v^-1*f*v,
f^-1*w^-1*f*w,a^-1*u*a*(v*w)^-1,
a^-1*v*a*(v*f)^-1,
a^-1*w*a*(u*v*f)^-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,
a^-1*f*a*f^-1,b^-1*x*b*y^-1,
b^-1*y*b*(x*y)^-1,b^-1*z*b*z^-1,
b^-1*f*b*f^-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,x],[a,b,u]]];
end,
[16,8]],
"L3(2) 2^3 x ( 2^3' E 2^1 )",[8,7,10],2,
2,[16,8]],
# 21504.11
[[1,"abdxyzuvw",
function(a,b,d,x,y,z,u,v,w)
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,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],
[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,u,x]]
];
end,
[8,8,16]],
"L3(2) 2^7",[8,7,11],2,
2,[8,8,16]],
# 21504.12
[[1,"abxyzeuvw",
function(a,b,x,y,z,e,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,e^2,e^-1*x^-1*e*x,
e^-1*y^-1*e*y,e^-1*z^-1*e*z,
e^-1*u^-1*e*u,e^-1*v^-1*e*v,
e^-1*w^-1*e*w,a^-1*u*a*(v*w)^-1,
a^-1*v*a*(v*e)^-1,
a^-1*w*a*(u*v*e)^-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*e)^-1,
a^-1*y*a*(x*y*z)^-1,
a^-1*z*a*(x*e)^-1,a^-1*e*a*e^-1,
b^-1*x*b*y^-1,b^-1*y*b*(x*y)^-1,
b^-1*z*b*z^-1,b^-1*e*b*e^-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,z,w]]];
end,
[16]],
"L3(2) 2^7",[8,7,12],2,
2,16],
# 21504.13
[[1,"abdxyzuvw",
function(a,b,d,x,y,z,u,v,w)
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,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
*d^-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*d^-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
*d^-1],
[[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,u]]];
end,
[128]],
"L3(2) 2^7",[8,7,13],2,
2,128],
# 21504.14
[[1,"abdxyzuvw",
function(a,b,d,x,y,z,u,v,w)
return
[[a^2*d^-1,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4
*(d*u*v*w)^-1,d^2,d^-1*b^-1*d*b,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],
[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,u,x]]
];
end,
[8,14,16]],
"L3(2) 2^7",[8,7,14],2,
2,[8,14,16]],
# 21504.15
[[1,"abxyzeuvw",
function(a,b,x,y,z,e,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,e^2,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,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*e)^-1,
a^-1*y*a*(x*y*z)^-1,
a^-1*z*a*(x*e)^-1,a^-1*e*a*e^-1,
b^-1*x*b*y^-1,b^-1*y*b*(x*y)^-1,
b^-1*z*b*z^-1,b^-1*e*b*e^-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,
[16,14]],
"L3(2) 2^7",[8,7,15],2,
2,[16,14]],
# 21504.16
[[1,"abdxyzuvw",
function(a,b,d,x,y,z,u,v,w)
return
[[a^2*d^-1,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4
*(d*y*z*u*v*w)^-1,d^2,d^-1*b^-1*d*b,
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],
[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,x,u]]
];
end,
[14,14,16]],
"L3(2) 2^7",[8,7,16],2,
2,[14,14,16]],
# 21504.17
[[1,"abdxyzuvw",
function(a,b,d,x,y,z,u,v,w)
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,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],
[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,x,u]]
];
end,
[56,16]],
"L3(2) 2^7",[8,7,17],2,
2,[56,16]],
# 21504.18
[[1,"abxyzeuvw",
function(a,b,x,y,z,e,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,e^2,e^-1*x^-1*e*x,
e^-1*y^-1*e*y,e^-1*z^-1*e*z,
e^-1*u^-1*e*u,e^-1*v^-1*e*v,
e^-1*w^-1*e*w,a^-1*x*a*(z*e)^-1,
a^-1*y*a*(x*y*z)^-1,
a^-1*z*a*(x*e)^-1,a^-1*e*a*e^-1,
b^-1*x*b*(y*w)^-1,b^-1*y*b*(x*y)^-1,
b^-1*z*b*(z*u)^-1,b^-1*e*b*e^-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],[a,b,u]]];
end,
[56,16]],
"L3(2) 2^7",[8,7,18],2,
2,[56,16]],
# 21504.19
[[1,"abdxyzuvw",
function(a,b,d,x,y,z,u,v,w)
return
[[a^2*d^-1,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4
*d^-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,d^2,d^-1*x^-1*d*x,
d^-1*y^-1*d*y,d^-1*z^-1*d*z,
d^-1*u^-1*d*u,d^-1*v^-1*d*v,
d^-1*w^-1*d*w,a^-1*x*a*(z*d)^-1,
a^-1*y*a*(x*y*z)^-1,
a^-1*z*a*(x*d)^-1,a^-1*d*a*d^-1,
b^-1*x*b*(y*w)^-1,b^-1*y*b*(x*y)^-1,
b^-1*z*b*(z*u)^-1,b^-1*d*b*d^-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],[a*y*z,b,u]]];
end,
[56,16]],
"L3(2) 2^7",[8,7,19],2,
2,[56,16]],
# 21504.20
[[1,"abxyzuvwf",
function(a,b,x,y,z,u,v,w,f)
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*f^-1,y^2*f^-1,
z^2*f^-1,x^-1*y^-1*x*y*f^-1,
x^-1*z^-1*x*z*f^-1,y^-1*z^-1*y
*z,f^2,f^-1*x^-1*f*x,f^-1*y^-1*f*y
,f^-1*z^-1*f*z,f^-1*u^-1*f*u,
f^-1*v^-1*f*v,f^-1*w^-1*f*w,
a^-1*x*a*z^-1,a^-1*y*a*(x*y*z)^-1,
a^-1*z*a*x^-1,a^-1*f*a*f^-1,
b^-1*x*b*(y*w)^-1,b^-1*y*b*(x*y)^-1,
b^-1*z*b*(z*u)^-1,b^-1*f*b*f^-1,
a^-1*u*a*(v*w)^-1,a^-1*v*a*(v*f)^-1,
a^-1*w*a*(u*v*f)^-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
*f^-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*f^-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
*f^-1],
[[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,u]]];
end,
[128]],
"L3(2) 2^7",[8,7,20],2,
2,128],
# 21504.21
[[1,"abxyzuvwe",
function(a,b,x,y,z,u,v,w,e)
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*e^-1,y^2*e^-1,
z^2*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^2,e^-1*x^-1*e*x,e^-1*y^-1*e*y
,e^-1*z^-1*e*z,e^-1*u^-1*e*u,
e^-1*v^-1*e*v,e^-1*w^-1*e*w,
a^-1*x*a*(z*e)^-1,
a^-1*y*a*(x*y*z)^-1,
a^-1*z*a*(x*e)^-1,a^-1*e*a*e^-1,
b^-1*x*b*(y*w)^-1,b^-1*y*b*(x*y)^-1,
b^-1*z*b*(z*u)^-1,b^-1*e*b*e^-1,
a^-1*u*a*(v*w)^-1,a^-1*v*a*(v*e)^-1,
a^-1*w*a*(u*v*e)^-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
*e^-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*e^-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
*e^-1],[[a*y*z,b,u]]];
end,
[16]],
"L3(2) 2^7",[8,7,21],2,
2,16],
# 21504.22
[[1,"abdxyzuvw",
function(a,b,d,x,y,z,u,v,w)
return
[[a^2*(d*u*w)^-1,b^3,(a*b)^7,d^2,d^-1*b^-1
*d*b,(a^-1*b^-1*a*b)^4*(d*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,d],
[a*b,b*a*b^-1*a*b^-1*a*b*a*b^-1,x,u]]
];
end,
[64,16]],
"L3(2) 2^1 x ( N 2^3 E 2^3' )",[8,7,22],2,
2,[64,16]]
];
PERFGRP[61]:=[# 21600.1
[[1,"abcde",
function(a,b,c,d,e)
return
[[a^2,b^3,(a*b)^5,c^2,d^3,e^3,(d*e)^4,(d*e^-1)^5,
c^-1*d^-1*e*d*e*d^-1*e*d*e^-1,
a^-1*d^-1*a*d,a^-1*e^-1*a*e,
b^-1*d^-1*b*d,b^-1*e^-1*b*e],
[[b,a*b*a*b^-1*a,d,e],[a,b,c,d]]];
end,
[5,6]],
"A5 x A6",[33,0,1],1,
[1,3],[5,6]]
];
PERFGRP[62]:=[# 23040.1
[[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^4,
e^-1*s^-1*e*s,e^-1*t^-1*e*t,
e^-1*u^-1*e*u,e^-1*v^-1*e*v,s^2,
t^2,u^2,v^2,s^-1*t^-1*s*t,
s^-1*u^-1*s*u*e^2,s^-1*v^-1*s*v,
t^-1*u^-1*t*u,t^-1*v^-1*t*v*e^2,
u^-1*v^-1*u*v,a^-1*s*a*u^-1,
a^-1*t*a*v^-1,a^-1*u*a*s^-1,
a^-1*v*a*t^-1,b^-1*s*b*(t*v*e)^-1,
b^-1*t*b*(s*t*u*v)^-1,
b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1,
c^-1*s*c*(t*u)^-1,c^-1*t*c*t^-1,
c^-1*u*c*(s*u*e)^-1,
c^-1*v*c*(s*t*u*v*e^2)^-1],[[b,c]]];
end,
[64]],
"A6 ( 2^4 E 2^1 A ) C 2^1",[13,6,1],4,
3,64],
# 23040.2
[[1,"abcstuve",
function(a,b,c,s,t,u,v,e)
return
[[a^2*e^2,b^3,c^3,(b*c)^4*e^2,(b*c^-1)^5,a^-1
*b^-1*c*b*c*b^-1*c*b*c^-1,
e^4,e^-1*s^-1*e*s,e^-1*t^-1*e*t,
e^-1*u^-1*e*u,e^-1*v^-1*e*v,s^2,
t^2,u^2,v^2,s^-1*t^-1*s*t,
s^-1*u^-1*s*u*e^2,s^-1*v^-1*s*v,
t^-1*u^-1*t*u,t^-1*v^-1*t*v*e^2,
u^-1*v^-1*u*v,a^-1*s*a*u^-1,
a^-1*t*a*v^-1,a^-1*u*a*s^-1,
a^-1*v*a*t^-1,b^-1*s*b*(t*v*e)^-1,
b^-1*t*b*(s*t*u*v)^-1,
b^-1*u*b*(u*v)^-1,b^-1*v*b*u^-1,
c^-1*s*c*(t*u)^-1,c^-1*t*c*t^-1,
c^-1*u*c*(s*u*e)^-1,
c^-1*v*c*(s*t*u*v*e^2)^-1],
[[a*e^-1,b*u]]];
end,
[384]],
"A6 ( 2^4 E 2^1 A ) C N 2^1",[13,6,2],4,
3,384],
# 23040.3
[[1,"abcdstuve",
function(a,b,c,d,s,t,u,v,e)
return
[[a^2*d^-1,b^3,c^3,(b*c)^4*d^-1,(b*c^-1)^5,
a^-1*b^-1*c*b*c*b^-1*c*b*c^-1,d^2,
d^-1*b^-1*d*b,d^-1*c^-1*d*c,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],[c*b*a*d,b,s,e]]];
end,
[12,80]],
"A6 2^1 x ( 2^4 E 2^1 )",[13,6,3],4,
3,[12,80]]
];
PERFGRP[63]:=[# 24360.1
[[1,"abc",
function(a,b,c)
return
[[c^14*a^2,c*b^4*c^-1*b^-1,b^29,a^4,a^2*b^(-1
*1)*a^2*b,a^2*c^-1*a^2*c,
c*a*c*a^-1,(b*a)^3,
c^(-1*5)*b*c^2*b*c^3*a*b^2*a*c*b^2*a],
[[b,c^4]]];
end,
[120]],
"L2(29) 2^1 = SL(2,29)",22,-2,
17,120]
];
PERFGRP[64]:=[# 25308.1
[[1,"abc",
function(a,b,c)
return
[[c^18,c*b^4*c^-1*b^-1,b^37,a^2,c*a*c*a^-1,
(b*a)^3,c^(-1*2)*b*c^2*b^3*a*b^2*a*c*b^2*a],
[[b,c]]];
end,
[38]],
"L2(37)",22,-1,
21,38]
];
PERFGRP[65]:=[# 25920.1
[[1,"ab",
function(a,b)
return
[[a^2,b^5,(a*b)^9,(a^-1*b^-1*a*b)^3,(b*a*b*a
*b^-1*a*b^-1*a)^2],
[[a*b*a*b^-1*a*b^-1*a,b]]];
end,
[27]],
"U4(2)",28,-1,
22,27]
];
PERFGRP[66]:=[# 28224.1
[[1,"abcd",
function(a,b,c,d)
return
[[a^2,b^3,(a*b)^7,(a^-1*b^-1*a*b)^4,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,c*d*c*d^-1*c,d]]]
;
end,
[7,7]],
"L3(2) x L3(2)",[34,0,1],1,
[2,2],[7,7]]
];
PERFGRP[67]:=[# 29120.1
[[1,"ab",
function(a,b)
return
[[a^2,b^4,(a*b)^5,(a^-1*b^-1*a*b)^7,(a*b^2)^13,
a*b^-1*a*b^2*a*b^2*(a*b^-1*a*b*a*b^2)^2
*a*b^2*a*b*(a*b^2)^4],
[[b^-1*a*b*a*b,b*a*b*a*b^2*a*b^2*a]]];
end,
[65]],
"Sz(8)",28,-1,
23,65]
];
PERFGRP[68]:=[# 29160.1
[[1,"abwxyzd",
function(a,b,w,x,y,z,d)
return
[[a^4,b^3,(a*b)^5,a^2*b*a^2*b^-1,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,w],[a*b,b*a*b*a*b^-1*a*b^-1,w*d]]];
end,
[24,18]],
"A5 2^1 x 3^4' E 3^1",[2,5,1],6,
1,[24,18]],
# 29160.2
[[1,"abstuvd",
function(a,b,s,t,u,v,d)
return
[[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,d^3,d^-1*a
^-1*d*a,d^-1*b^-1*d*b,
d^-1*s^-1*d*s,s^3,t^3,u^3,v^3,
s^-1*t^-1*s*t,s^-1*u^-1*s*u
*d^-1,s^-1*v^-1*s*v,
t^-1*u^-1*t*u,t^-1*v^-1*t*v
*d^-1,u^-1*v^-1*u*v,
a^-1*s*a*u^-1,a^-1*t*a*v^-1,
a^-1*u*a*(s^-1*d)^-1,
a^-1*v*a*(t^-1*d)^-1,
b^-1*s*b*(s*v^-1*d^-1)^-1,
b^-1*t*b*(t*u^-1*v*d)^-1,
b^-1*u*b*u^-1,b^-1*v*b*v^-1],
[[a,b]]];
end,
[243]],
"A5 2^1 3^4 C 3^1 I",[2,5,2],3,
1,243],
# 29160.3
[[1,"abstuve",
function(a,b,s,t,u,v,e)
return
[[a^4,b^3,(a*b)^5,a^2*b^-1*a^2*b,e^3,e^-1*a
^-1*e*a,e^-1*b^-1*e*b,
e^-1*s^-1*e*s,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*e^-1,
t^-1*u^-1*t*u*e^-1,
t^-1*v^-1*t*v*e,u^-1*v^-1*u*v,
a^-1*s*a*(u*e^-1)^-1,
a^-1*t*a*(v*e)^-1,a^-1*u*a*s,
a^-1*v*a*t,b^-1*s*b*(s*v^-1)^-1,
b^-1*t*b*(t*u^-1*v*e^-1)^-1,
b^-1*u*b*u^-1,b^-1*v*b*v^-1],
[[a,b]]];
end,
[243]],
"A5 2^1 3^4 C 3^1 II",[2,5,3],3,
1,243],
# 29160.4
[[1,"abcwxyz",
function(a,b,c,w,x,y,z)
return
[[a^2,b^3,c^3,(b*c)^4,(b*c^-1)^5,a^-1*b^-1*c
*b*c*b^-1*c*b*c^-1,w^3,x^3,y^3,
z^3,w^-1*x^-1*w*x,w^-1*y^-1*w*y,
w^-1*z^-1*w*z,x^-1*y^-1*x*y,
x^-1*z^-1*x*z,y^-1*z^-1*y*z,
a^-1*w*a*z^-1,a^-1*x*a*x^-1,
a^-1*y*a*(w^-1*x^-1*y^-1*z^-1)
^-1,a^-1*z*a*w^-1,
b^-1*w*b*x^-1,b^-1*x*b*y^-1,
b^-1*y*b*w^-1,b^-1*z*b*z^-1,
c^-1*w*c*(w^-1*x*y^-1*z^-1)^-1,
c^-1*x*c*(x^-1*z)^-1,
c^-1*y*c*(w*x^-1)^-1,
c^-1*z*c*x],[[b,c*a*b*c,z]]];
end,
[30]],
"A6 3^4'",[14,4,1],1,
3,30],
# 29160.5 (otherpres.)
[[1,"abDstuvd",
function(a,b,D,s,t,u,v,d)
return
[[a^2*D^-1,b^3,(a*b)^5,D^2,D^-1*b^-1*D*b,
d^3,d^-1*a^-1*d*a,d^-1*b^-1*d*b,
d^-1*s^-1*d*s,s^3,t^3,u^3,v^3,
s^-1*t^-1*s*t,s^-1*u^-1*s*u
*d^-1,s^-1*v^-1*s*v,
t^-1*u^-1*t*u,t^-1*v^-1*t*v
*d^-1,u^-1*v^-1*u*v,
a^-1*s*a*u^-1,a^-1*t*a*v^-1,
a^-1*u*a*(s^-1*d)^-1,
a^-1*v*a*(t^-1*d)^-1,
b^-1*s*b*(s*v^-1*d^-1)^-1,
b^-1*t*b*(t*u^-1*v*d)^-1,
b^-1*u*b*u^-1,b^-1*v*b*v^-1],
[[a,b]]];
end,
[243]]],
# 29160.6 (otherpres.)
[[1,"abdstuve",
function(a,b,d,s,t,u,v,e)
return
[[a^2*d^-1,b^3,(a*b)^5,d^2,d^-1*b^-1*d*b,
e^3,e^-1*a^-1*e*a,e^-1*b^-1*e*b,
e^-1*s^-1*e*s,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*e^-1,
t^-1*u^-1*t*u*e^-1,
t^-1*v^-1*t*v*e,u^-1*v^-1*u*v,
a^-1*s*a*(u*e^-1)^-1,
a^-1*t*a*(v*e)^-1,a^-1*u*a*s,
a^-1*v*a*t,b^-1*s*b*(s*v^-1)^-1,
b^-1*t*b*(t*u^-1*v*e^-1)^-1,
b^-1*u*b*u^-1,b^-1*v*b*v^-1],
[[a,b]]];
end,
[243]]]
];
PERFGRP[69]:=[# 29760.1
[[1,"abc",
function(a,b,c)
return
[[c^15*a^2,c*b^9*c^-1*b^-1,b^31,a^4,a^2*b^(-1
*1)*a^2*b,a^2*c^-1*a^2*c,
c*a*c*a^-1,(b*a)^3],[[b,c^2]]];
end,
[64]],
"L2(31) 2^1 = SL(2,31)",22,-2,
18,64]
];
PERFGRP[70]:=[# 30240.1
[[1,"abcde",
function(a,b,c,d,e)
return
[[a^2,b^3,(a*b)^5,c^2,d^3,(c*d)^7,e^-1*d^-1*
(c*d)^3,
(e*d^-1*e*d)^-1*c^-1*e*d^-1*e*d*c,
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,e]]];
end,
[5,9]],
"A5 x L2(8)",[35,0,1],1,
[1,4],[5,9]]
];
[ Dauer der Verarbeitung: 0.18 Sekunden
(vorverarbeitet)
]
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