gap> f:=[1];
[ 1 ]
gap> 
gap> f[1]:=(1,4,3,2);
(1,4,3,2)
gap> f[2]:=(1,2,6,5);
(1,2,6,5)
gap> f[3]:=(2,3,7,6);
(2,3,7,6)
gap> f[4]:=(3,4,8,7);
(3,4,8,7)
gap> f[5]:=(4,1,5,8);
(1,5,8,4)
gap> f[6]:=(5,6,7,8);
(5,6,7,8)
gap> 
gap> c:=[1];
[ 1 ]
gap> 
gap> for i in [1..6]  do
>   for j in [1..6] do
>     c[6*(i-1)+j]:=f[i]*f[j]^-1;
>   od;
> od;
gap> 
gap> C:=Group(c,[1]);
Error, sorry, the elements of <arg> lie in no common ring domain in
Domain( Concatenation( gens, [ id ] ) ) called from
Group( c, [ 1 ] ) called from
main loop
brk> C:=Group(c,c[1]);
Syntax error: warning, undefined global variable in *errin* line 1
C:=Group(c,c[1]);
  ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/permgr\
p.g line 219
if not IsBound( InfoPermGroup1 )  then InfoPermGroup1 := Ignore;  fi;
                               ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/permgr\
p.g line 219
if not IsBound( InfoPermGroup1 )  then InfoPermGroup1 := Ignore;  fi;
                                                       ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/permgr\
p.g line 220
if not IsBound( InfoPermGroup2 )  then InfoPermGroup2 := Ignore;  fi;
                               ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/permgr\
p.g line 220
if not IsBound( InfoPermGroup2 )  then InfoPermGroup2 := Ignore;  fi;
                                                       ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/ratcla\
ss.g line 57
if not IsBound( InfoClasses1 )  then InfoClasses1 := Ignore; fi;
                             ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/ratcla\
ss.g line 57
if not IsBound( InfoClasses1 )  then InfoClasses1 := Ignore; fi;
                                                   ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/ratcla\
ss.g line 58
if not IsBound( InfoClasses2 )  then InfoClasses2 := Ignore; fi;
                             ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/ratcla\
ss.g line 58
if not IsBound( InfoClasses2 )  then InfoClasses2 := Ignore; fi;
                                                   ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/aggrou\
p.g line 103
if not IsBound( InfoAgGroup1 )  then InfoAgGroup1 := Ignore;  fi;
                             ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/aggrou\
p.g line 103
if not IsBound( InfoAgGroup1 )  then InfoAgGroup1 := Ignore;  fi;
                                                   ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/aggrou\
p.g line 104
if not IsBound( InfoAgGroup2 )  then InfoAgGroup2 := Ignore;  fi;
                             ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/aggrou\
p.g line 104
if not IsBound( InfoAgGroup2 )  then InfoAgGroup2 := Ignore;  fi;
                                                   ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/agnorm\
.g line 59
if not IsBound( InfoAgNorm1 )  then InfoAgNorm1 := Ignore;  fi;
                            ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/agnorm\
.g line 59
if not IsBound( InfoAgNorm1 )  then InfoAgNorm1 := Ignore;  fi;
                                                 ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/agnorm\
.g line 60
if not IsBound( InfoAgNorm2 )  then InfoAgNorm2 := Ignore;  fi;
                            ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/agnorm\
.g line 60
if not IsBound( InfoAgNorm2 )  then InfoAgNorm2 := Ignore;  fi;
                                                 ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/agcomp\
le.g line 47
if not IsBound( InfoAgCo1 )  then InfoAgCo1 := Ignore;  fi;
                          ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/agcomp\
le.g line 47
if not IsBound( InfoAgCo1 )  then InfoAgCo1 := Ignore;  fi;
                                             ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/agcomp\
le.g line 48
if not IsBound( InfoAgCo2 )  then InfoAgCo2 := Ignore;  fi;
                          ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/agcomp\
le.g line 48
if not IsBound( InfoAgCo2 )  then InfoAgCo2 := Ignore;  fi;
                                             ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/agclas\
s.g line 72
if not IsBound( InfoAgClass1 )  then  InfoAgClass1 := Ignore;  fi;
                             ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/agclas\
s.g line 72
if not IsBound( InfoAgClass1 )  then  InfoAgClass1 := Ignore;  fi;
                                                    ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/agclas\
s.g line 73
if not IsBound( InfoAgClass2 )  then  InfoAgClass2 := Ignore;  fi;
                             ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/agclas\
s.g line 73
if not IsBound( InfoAgClass2 )  then  InfoAgClass2 := Ignore;  fi;
                                                    ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/agcent\
.g line 71
if not IsBound( InfoAgCent1 )  then  InfoAgCent1 := Ignore;  fi;
                            ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/agcent\
.g line 71
if not IsBound( InfoAgCent1 )  then  InfoAgCent1 := Ignore;  fi;
                                                  ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/agcent\
.g line 72
if not IsBound( InfoAgCent2 )  then  InfoAgCent2 := Ignore;  fi;
                            ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/agcent\
.g line 72
if not IsBound( InfoAgCent2 )  then  InfoAgCent2 := Ignore;  fi;
                                                  ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/onecoh\
om.g line 47
if not IsBound( Info1Coh1 )  then Info1Coh1 := Ignore;  fi;
                          ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/onecoh\
om.g line 47
if not IsBound( Info1Coh1 )  then Info1Coh1 := Ignore;  fi;
                                             ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/onecoh\
om.g line 48
if not IsBound( Info1Coh2 )  then Info1Coh2 := Ignore;  fi;
                          ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/onecoh\
om.g line 48
if not IsBound( Info1Coh2 )  then Info1Coh2 := Ignore;  fi;
                                             ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/onecoh\
om.g line 49
if not IsBound( Info1Coh3 )  then Info1Coh3 := Ignore;  fi;
                          ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/onecoh\
om.g line 49
if not IsBound( Info1Coh3 )  then Info1Coh3 := Ignore;  fi;
                                             ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/saggro\
up.g line 47
if not IsBound(InfoSagGroup1)  then InfoSagGroup1 := Ignore;  fi;
                            ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/saggro\
up.g line 47
if not IsBound(InfoSagGroup1)  then InfoSagGroup1 := Ignore;  fi;
                                                   ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/saggro\
up.g line 48
if not IsBound(InfoSagGroup2)  then InfoSagGroup2 := Ignore;  fi;
                            ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/saggro\
up.g line 48
if not IsBound(InfoSagGroup2)  then InfoSagGroup2 := Ignore;  fi;
                                                   ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/saggro\
up.g line 49
if not IsBound(InfoSagGroup3)  then InfoSagGroup3 := Ignore;  fi;
                            ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/saggro\
up.g line 49
if not IsBound(InfoSagGroup3)  then InfoSagGroup3 := Ignore;  fi;
                                                   ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/sagsbg\
rp.g line 69
if not IsBound(InfoMaxSubgp2)      then InfoMaxSubgp2 := Ignore;      fi;
                            ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/sagsbg\
rp.g line 69
if not IsBound(InfoMaxSubgp2)      then InfoMaxSubgp2 := Ignore;      fi;
                                                       ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/sagsbg\
rp.g line 70
if not IsBound(InfoEulerFct2)      then InfoEulerFct2 := Ignore;      fi;
                            ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/sagsbg\
rp.g line 70
if not IsBound(InfoEulerFct2)      then InfoEulerFct2 := Ignore;      fi;
                                                       ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/sagsbg\
rp.g line 71
if not IsBound(InfoSagCent2)       then InfoSagCent2  := Ignore;      fi;
                           ^
Syntax error: warning, undefined global variable in C:\gap\gap3r4p2/lib/sagsbg\
rp.g line 71
if not IsBound(InfoSagCent2)       then InfoSagCent2  := Ignore;      fi;
                                                       ^
Group( (1,4,3)(2,5,6), (1,4,2)(3,6,7), (1,3,2)(4,7,8), (1,8,5)(2,4,3), 
(1,4,3,2)(5,8,7,6), (1,3,4)(2,6,5), (1,6,5)(2,7,3), (1,2,6,5)(3,7,8,4), 
(1,2,6)(4,8,5), (1,2,5)(6,8,7), (1,2,4)(3,7,6), (1,5,6)(2,3,7), (2,7,6)
(3,8,4), (1,4,8,5)(2,3,7,6), (2,3,6)(5,8,7), (1,2,3)(4,8,7), (1,5,6,2)
(3,4,8,7), (2,6,7)(3,4,8), (1,4,5)(3,8,7), (3,4,7)(5,8,6), (1,5,8)(2,3,4), 
(1,6,2)(4,5,8), (1,5,8,4)(2,6,7,3), (1,5,4)(3,7,8), (1,8,4)(5,7,6), (1,2,3,4)
(5,6,7,8), (1,5,2)(6,7,8), (2,6,3)(5,7,8), (3,7,4)(5,6,8), (1,4,8)(5,6,7) )
brk> quit;
gap> Size(C);
168
gap> (4,8,1,3,6,2) in C;
false
gap> Elements(C);
[ (), (3,4,7)(5,8,6), (3,7,4)(5,6,8), (2,3,4,5,7,6,8), (2,3,5)(4,6,7), 
  (2,3,6)(5,8,7), (2,4,7,8,3,5,6), (2,4,8)(3,7,5), (2,4,5)(3,8,6), 
  (2,5,3)(4,7,6), (2,5,4)(3,6,8), (2,5,8,4,6,3,7), (2,6,3)(5,7,8), 
  (2,6,7)(3,4,8), (2,6,5,3,8,7,4), (2,7,8)(4,6,5), (2,7,3,6,4,8,5), 
  (2,7,6)(3,8,4), (2,8,6,7,5,4,3), (2,8,7)(4,5,6), (2,8,4)(3,5,7), 
  (1,2)(3,5)(4,6)(7,8), (1,2)(3,6)(4,8)(5,7), (1,2)(3,8)(4,5)(6,7), 
  (1,2,3)(4,8,7), (1,2,3,4)(5,6,7,8), (1,2,3,8,6,5,7), (1,2,4,6,5,8,3), 
  (1,2,4,7)(3,6,8,5), (1,2,4)(3,7,6), (1,2,5)(6,8,7), (1,2,5,7,3,4,6), 
  (1,2,5,8)(3,6,7,4), (1,2,6)(4,8,5), (1,2,6,5)(3,7,8,4), (1,2,6,4,7,3,8), 
  (1,2,7,3)(4,5,6,8), (1,2,7,5,8,6,4), (1,2,7)(3,5,4), (1,2,8,3,4,7,5), 
  (1,2,8)(3,5,6), (1,2,8,6)(3,7,4,5), (1,3,2)(4,7,8), (1,3,7,2)(4,8,6,5), 
  (1,3,8,5,6,4,2), (1,3,5)(4,6,8), (1,3,6)(4,7,5), (1,3,7,6,4,5,8), 
  (1,3)(2,4)(5,7)(6,8), (1,3,2,4,5,6,7), (1,3,5,8,7,2,4), 
  (1,3)(2,5)(4,8)(6,7), (1,3,6,4)(2,5,7,8), (1,3,8,7)(2,5,4,6), 
  (1,3)(2,6)(4,7)(5,8), (1,3,4)(2,6,5), (1,3,7)(2,6,8), (1,3,4,5)(2,7,8,6), 
  (1,3,5,6)(2,7,4,8), (1,3,8)(2,7,5), (1,3,2,8)(4,6,5,7), (1,3,4,2,8,7,6), 
  (1,3,6,7,2,8,5), (1,4,3,2)(5,8,7,6), (1,4,6,8,5,7,2), (1,4,2)(3,6,7), 
  (1,4,8)(5,6,7), (1,4,3,5,7,8,6), (1,4,5)(3,8,7), (1,4,7,8)(2,3,6,5), 
  (1,4,8,5)(2,3,7,6), (1,4,6)(2,3,8), (1,4,3)(2,5,6), (1,4,7)(2,5,8), 
  (1,4)(2,5)(3,7)(6,8), (1,4,5,3,2,6,8), (1,4,7,2,6,3,5), (1,4,2,6)(3,7,5,8), 
  (1,4,2,7,8,5,3), (1,4,8,6,3,2,7), (1,4)(2,7)(3,8)(5,6), (1,4,6,3)(2,8,7,5), 
  (1,4)(2,8)(3,5)(6,7), (1,4,5,7)(2,8,3,6), (1,5,2)(6,7,8), 
  (1,5,6,2)(3,4,8,7), (1,5,7,4,3,8,2), (1,5,3)(4,8,6), (1,5,4)(3,7,8), 
  (1,5,6,3,8,4,7), (1,5)(2,3)(4,7)(6,8), (1,5,8)(2,3,4), (1,5,6)(2,3,7), 
  (1,5,7,6)(2,4,8,3), (1,5)(2,4)(3,6)(7,8), (1,5,3,8)(2,4,6,7), 
  (1,5,4,3)(2,6,8,7), (1,5,8,4)(2,6,7,3), (1,5,7)(2,6,4), (1,5,8,2,7,6,3), 
  (1,5,2,7)(3,4,6,8), (1,5,3,6,2,7,4), (1,5,4,7,6,2,8), (1,5,2,8,4,3,6), 
  (1,5)(2,8)(3,7)(4,6), (1,6,2)(4,5,8), (1,6,8,2)(3,5,4,7), (1,6,4,3,7,5,2), 
  (1,6,3)(4,5,7), (1,6,8,7,5,3,4), (1,6,7)(3,5,8), (1,6)(2,3)(4,5)(7,8), 
  (1,6,4,8)(2,3,5,7), (1,6,7,5)(2,3,8,4), (1,6,7,8,2,4,3), (1,6,5,2,4,8,7), 
  (1,6,2,4)(3,8,5,7), (1,6,3,4,8,2,5), (1,6,2,5,3,7,8), (1,6)(2,5)(3,8)(4,7), 
  (1,6,5)(2,7,3), (1,6,8)(2,7,4), (1,6)(2,7)(3,4)(5,8), (1,6,5,3)(2,8,4,7), 
  (1,6,4)(2,8,3), (1,6,3,7)(2,8,5,4), (1,7,5,6,8,3,2), (1,7,2)(3,4,5), 
  (1,7,4,2)(3,5,8,6), (1,7,8)(3,4,6), (1,7,4,8,3,6,5), (1,7,6)(3,8,5), 
  (1,7,6,5,4,2,3), (1,7)(2,3)(4,6)(5,8), (1,7,2,3,6,8,4), (1,7,5)(2,4,6), 
  (1,7,6,8)(2,4,3,5), (1,7,3,6)(2,4,5,8), (1,7,3,2,5,4,8), (1,7,8,4,2,5,6), 
  (1,7,2,5)(3,8,6,4), (1,7,8,3)(2,6,4,5), (1,7)(2,6)(3,5)(4,8), 
  (1,7,5,4)(2,6,3,8), (1,7,3)(2,8,6), (1,7,4)(2,8,5), (1,7)(2,8)(3,4)(5,6), 
  (1,8,5,2)(3,4,7,6), (1,8,2)(3,6,5), (1,8,3,7,4,6,2), (1,8,5,4,6,7,3), 
  (1,8,4)(5,7,6), (1,8,7)(3,6,4), (1,8,2,3)(4,7,5,6), (1,8,6,2,3,5,4), 
  (1,8,4,5,2,3,7), (1,8,5)(2,4,3), (1,8,6)(2,4,7), (1,8)(2,4)(3,7)(5,6), 
  (1,8,3)(2,5,7), (1,8,7,4)(2,5,6,3), (1,8,6,7)(2,5,3,4), (1,8,2,6,7,4,5), 
  (1,8)(2,6)(3,4)(5,7), (1,8,7,3,5,2,6), (1,8,4,6)(2,7,5,3), 
  (1,8,3,5)(2,7,6,4), (1,8)(2,7)(3,6)(4,5) ]
gap> (6,4,1)(2,8,3) in C;
true
gap> Read("c:/gap/gap3r4p3/lib/abstab.g");
Error, the file 'c:/gap/gap3r4p3/lib/abstab.g' must exist and be readable in
Read( "c:/gap/gap3r4p3/lib/abstab.g" ) called from
main loop
brk> quit;
gap> Read("c:/gap/Abstab.g");
The record 'descriptions' contains brief descriptions of the functions
in this file.
Functions of importance: MakeAbStabChain, FactorPermGroupElement, Shrink
gap> h1:=(6,4,1)(2,8,3);
(1,6,4)(2,8,3)
gap> h2:=FactorPermGroupElement(C,h1);
g11*g13^-1
gap> FactorPermGroupElement(C,g11);
Error, Variable: 'g11' must have a value
gap> FactorPermGroupElement(C,c[2]);
g1
gap> FactorPermGroupElement(C,c[3]);
g11^-1
gap> FactorPermGroupElement(C,c[4]);
g11^-1*g13
gap> c[4];
(1,3,2)(4,7,8)
gap> FactorPermGroupElement(C,c[5]);
g4
gap> FactorPermGroupElement(C,c[6]);
g11*g13^-1*g11*g4^-1
gap> FactorPermGroupElement(C,c[7]);
g1^-1
gap> FactorPermGroupElement(C,c[8]);
IdWord
gap> FactorPermGroupElement(C,c[9]);
g13*g11^-2*g13^-1*g4
gap> FactorPermGroupElement(C,c[10]);
g11*g13^-2*g11^-1*g4
gap> FactorPermGroupElement(C,c[11]);
g9
gap> FactorPermGroupElement(C,c[12]);
g11*g13^-1*g11*g4
gap> FactorPermGroupElement(C,c[13]);
g11
gap> FactorPermGroupElement(C,c[14]);
g11*g1
gap> FactorPermGroupElement(C,c[15]);
IdWord
gap> FactorPermGroupElement(C,c[16]);
g13
gap> quit;