gap> x:=(24,21,20,13,19,5,23,3,18,16,6,9,22,14,4,2,17,8,15,12,7,11,10);;
gap> y:=(4,8,9,12,10)(7,6,3,5,11)(15,19,20,23,21)(18,17,14,16,22);;
gap> m23 := Group( h1,h2);
Error, Variable: 'h1' must have a value
gap> m23 := Group( x,y);
Group( ( 2,17, 8,15,12, 7,11,10,24,21,20,13,19, 5,23, 3,18,16, 6, 9,22,14, 4
 ), ( 3, 5,11, 7, 6)( 4, 8, 9,12,10)(14,16,22,18,17)(15,19,20,23,21) )
gap> Size(m23);
10200960
gap> H := Subgroup(m23, [ x*y, x^6*y^2 ] );;
gap> Size( H );
10200960
gap> H := Subgroup(m23, [ x^3*y, x^2*y^2 ] );;
gap> Size( H );
10200960
gap> H := Subgroup(m23, [ x*y^4, x^3*y^2 ] );;
gap> Size( H );
10200960
gap> H := Subgroup(m23, [ x*y, x^2*y^6 ] );;
gap> Size( H );
10200960
gap> H := Subgroup(m23, [ x*y*x*y, x^2*y^6 ] );;
gap> Size( H );
443520
gap> Index(G,H);
Error, Variable: 'G' must have a value
gap> Index(m23,H);
23
gap> H := Subgroup(m23, [ x*y*x*y, x^2*y^2 ] );;
gap> Size( H );
10200960
gap> H := Subgroup(m23, [ x*y*x^2*y, x^2*y^6 ] );;
gap> Size( H );
10200960
gap> H := Subgroup(m23, [ x*y*x*y*x*y, x^2*y^6 ] );;
gap> Size( H );
443520
gap> H := Subgroup(m23, [ x*y*x*y*x*y, x^6*y^6 ] );;
gap> Size( H );
443520
gap> H := Subgroup(m23, [ x*y*x*y*x*y, x^6*y^6*x^6 ] );;
gap> Size( H );
10200960
gap> H := Subgroup(m23, [ x*y*x*y*x*y, x^6*y^6*x^6*y^6 ] );;
gap> Size( H );
443520
gap> IsSimple(H);
true
gap> Print("M22!\n");
M22!
gap> H := Subgroup(m23, [ x*y, x^4*y^5] );;
gap> Size( H );
10200960
gap> H := Subgroup(m23, [ x*y*x*y, x^4*y^5] );;
gap> Size( H );
10200960
gap> H := Subgroup(m23, [ x*y*x*y, x^5*y^5] );;
gap> Size( H );
10200960
gap> H := Subgroup(m23, [ x*y*x*y*x*y, x^5*y^7] );;
gap> Size( H );
8
gap> GroupId(H);
rec(
  catalogue := [ 8, 2 ],
  size := 8,
  names := [ "2x4" ],
  abelianInvariants := [ 2, 4 ],
  pGroupId := 2 )
gap> Elements(H);
[ (), ( 2, 3,17, 6)( 7,21,15,24)( 9,16)(10,23)(11,13,14,20)(12,19,18,22), 
  ( 2, 6,17, 3)( 7,24,15,21)( 9,16)(10,23)(11,20,14,13)(12,22,18,19), 
  ( 2,12,17,18)( 3,19, 6,22)( 4, 8)( 7,24,15,21)(10,23)(11,13,14,20), 
  ( 2,17)( 3, 6)( 7,15)(11,14)(12,18)(13,20)(19,22)(21,24), 
  ( 2,18,17,12)( 3,22, 6,19)( 4, 8)( 7,21,15,24)(10,23)(11,20,14,13), 
  ( 2,19)( 3,18)( 4, 8)( 6,12)( 9,16)(11,14)(13,20)(17,22), 
  ( 2,22)( 3,12)( 4, 8)( 6,18)( 7,15)( 9,16)(17,19)(21,24) ]
gap> (x*y)^3;
( 2,19)( 3,18)( 4, 8)( 6,12)( 9,16)(11,14)(13,20)(17,22)
gap> x^5*y^7;
( 2, 3,17, 6)( 7,21,15,24)( 9,16)(10,23)(11,13,14,20)(12,19,18,22)
gap> a:=(x*y)^3;
( 2,19)( 3,18)( 4, 8)( 6,12)( 9,16)(11,14)(13,20)(17,22)
gap> b:=x^5*y^7;
( 2, 3,17, 6)( 7,21,15,24)( 9,16)(10,23)(11,13,14,20)(12,19,18,22)
gap> 
gap> Oder(a);
Error, Variable: 'Oder' must have a value
gap> Order(a);
Error, Function: number of args must be 2
gap> Order(H,a);
2
gap> Order(H,b);
4
gap> a;a^2;
( 2,19)( 3,18)( 4, 8)( 6,12)( 9,16)(11,14)(13,20)(17,22)
()
gap> b;b^2;b^3;b^4;
( 2, 3,17, 6)( 7,21,15,24)( 9,16)(10,23)(11,13,14,20)(12,19,18,22)
( 2,17)( 3, 6)( 7,15)(11,14)(12,18)(13,20)(19,22)(21,24)
( 2, 6,17, 3)( 7,24,15,21)( 9,16)(10,23)(11,20,14,13)(12,22,18,19)
()
gap> a*b;b*a;
( 2,18,17,12)( 3,22, 6,19)( 4, 8)( 7,21,15,24)(10,23)(11,20,14,13)
( 2,18,17,12)( 3,22, 6,19)( 4, 8)( 7,21,15,24)(10,23)(11,20,14,13)
gap> F2 := FreeGroup("x1","x2");
Group( x1, x2 )
gap> x1 := F2.1; x2 := F2.2;
x1
x2
gap> G := F2 / [(x1*x2)^2,(x1^5*x2^7)^4];
Group( x1, x2 )
gap> PG := PresentationFpGroup( G );
<< presentation with 2 gens and 2 rels of total length 52 >>
gap> Size(G);
Error, the coset enumeration has defined more than 64000 cosets:
type 'return;' if you want to continue with a new limit of 128000 cosets,
type 'quit;' if you want to quit the coset enumeration,
type 'maxlimit := 0; return;' in order to continue without a limit,
 in
AugmentedCosetTableMtc( G, H, -1, "_x" ) called from
D.operations.Size( D ) called from
Size( G ) called from
main loop
brk> maxlimit:=0;return;
0