gap> f1:=(2,4,6,8,10)(14,23,20,17,11)(24,21,18,15,13)(25,22,19,16,12);
( 2, 4, 6, 8,10)(11,14,23,20,17)(12,25,22,19,16)(13,24,21,18,15)
gap> 
gap> rf2:=(2,1,10,13,25)(17,29,20,19,18)(9,12,14,24,3)
> (6,16,28,30,21)(23,4,7,15,27)(26,22,5,8,11);
( 1,10,13,25, 2)( 3, 9,12,14,24)( 4, 7,15,27,23)( 5, 8,11,26,22)
( 6,16,28,30,21)(17,29,20,19,18)
gap> 
gap> f2:=(9,12,14,24,3)(6,16,28,30,21)(23,4,7,15,27)(26,22,5,8,11);
( 3, 9,12,14,24)( 4, 7,15,27,23)( 5, 8,11,26,22)( 6,16,28,30,21)
gap> f3:=rf2*f1*rf2^-1;
( 1,25,23,21, 5)( 6, 9,13,26,20)( 7,10,14,30,19)( 8,12,27,29,18)
gap> f8:=rf2^2*f1*rf2^-2;
( 1,12,28,20, 4)( 2,13,27,30,22)( 3,10,11,29,21)( 5, 9,15,17,19)
gap> f7:=rf2^3*f1*rf2^-3;
( 1, 8,17,30,24)( 2, 9,16,29,23)( 3, 7,18,20,22)(10,15,28,26,25)
gap> f6:=rf2^4*f1*rf2^-4;
( 1, 7,16,11,13)( 2, 5,18,28,14)( 3, 6,17,27,25)( 4,19,29,26,24)
gap> 
gap> g:=[];
[  ]
gap> g[1]:=f1;
( 2, 4, 6, 8,10)(11,14,23,20,17)(12,25,22,19,16)(13,24,21,18,15)
gap> g[2]:=f2;
( 3, 9,12,14,24)( 4, 7,15,27,23)( 5, 8,11,26,22)( 6,16,28,30,21)
gap> g[3]:=f3;
( 1,25,23,21, 5)( 6, 9,13,26,20)( 7,10,14,30,19)( 8,12,27,29,18)
gap> g[4]:=f6;
( 1, 7,16,11,13)( 2, 5,18,28,14)( 3, 6,17,27,25)( 4,19,29,26,24)
gap> g[5]:=f7;
( 1, 8,17,30,24)( 2, 9,16,29,23)( 3, 7,18,20,22)(10,15,28,26,25)
gap> g[6]:=f8;
( 1,12,28,20, 4)( 2,13,27,30,22)( 3,10,11,29,21)( 5, 9,15,17,19)
gap> 
gap> c:=[1];
[ 1 ]
gap> 
gap> for i in [1..6]  do
>   for j in [1..6] do
>     c[6*(i-1)+j]:=g[i]*g[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> quit;
gap> C:=Group(c,c[1]);
Group( ( 2,23,20,17, 8,10)( 3,24,30,28,16, 9)( 4,21,18, 7)( 5,22,19, 6)
(11,12,25,26)(13,14,27,15), ( 1, 5,21,29,27,12)( 2, 4,20,17,11,10)
( 6,18,15, 9)( 7,19,16, 8)(13,24,23,26)(14,25,22,30), ( 1,13,26,29,19, 7)
( 2,24,21, 5)( 3,25,22, 4)( 6, 8,10,14,23,20)(11,28,18,15)(12,27,17,16), 
( 1,24,21, 7, 3,22,19, 9, 2, 4, 6)( 8,25,20)(10,23,18)(11,14,29,16,12,26,28,
 15,13,30,17), ( 1, 4, 6, 8, 3,21,18, 9, 5,19,16)( 2,20,15)(10,22,17)
(11,14,23,28,12,25,30,27,13,24,29), ( 2,10, 8,17,20,23)( 3, 9,16,28,30,24)
( 4, 7,18,21)( 5, 6,19,22)(11,26,25,12)(13,15,27,14), ( 1, 5,18,29,27,25)
( 3, 6,16,28,14,24)( 4,19,30,23)( 7,15,12,10)( 8,11,13, 9)(20,26,22,21), 
( 1,13,11,29,19, 4)( 2,14,26,22)( 3, 9,12,28,30,21)( 5, 8,16,18)( 6, 7,15,17)
(23,24,25,27), ( 1,24,22, 5)( 2,23, 4, 3)( 6, 9,12,14,30,21)( 7,10,25,26,20,18
 )( 8,11,28,17)(15,27,29,16), ( 1, 4, 7, 9)( 2,22,19,17,15,13)( 3, 5, 8,10)
( 6,16,12,14,24,21)(11,26,30,29)(20,28,27,23), ( 1,12,27,29,21, 5)
( 2,10,11,17,20, 4)( 6, 9,15,18)( 7, 8,16,19)(13,26,23,24)(14,30,22,25), 
( 1,25,27,29,18, 5)( 3,24,14,28,16, 6)( 4,23,30,19)( 7,10,12,15)( 8, 9,13,11)
(20,21,22,26), ( 1,27,19)( 2,14,30, 4,24,26,20, 3,25,23,21)( 5,13,29)
( 6, 9,11,16, 7,10,28,18, 8,12,17), ( 1,26,18)( 2,23,21, 5,24,30,19, 3,22,20,
  6)( 7,25,29)( 8,12,27,16, 9,13,28,15,10,14,17), ( 1,25,23,29,18, 8)
( 2,22,30,17,15, 9)( 3,21,19, 7)( 4,20, 6, 5)(10,14,27,11)(12,13,26,28), 
( 1, 7,19,29,26,13)( 2, 5,21,24)( 3, 4,22,25)( 6,20,23,14,10, 8)(11,15,18,28)
(12,16,17,27), ( 1, 4,19,29,11,13)( 2,22,26,14)( 3,21,30,28,12, 9)
( 5,18,16, 8)( 6,17,15, 7)(23,27,25,24), ( 1,19,27)( 2,21,23,25, 3,20,26,24,
  4,30,14)( 5,29,13)( 6,17,12, 8,18,28,10, 7,16,11, 9), ( 1, 3, 6, 8)
( 2, 5, 7, 9)( 4,19,16,11,13,24)(10,25,22,20,18,15)(14,23,29,28)
(17,27,26,30), ( 1, 7,16,10, 3, 6,15, 9, 5,18,12)( 2,19,11)( 4,17,13)
(14,22,30,27,25,21,29,26,24,20,28), ( 1, 6, 4, 2, 9,19,22, 3, 7,21,24)
( 8,20,25)(10,18,23)(11,17,30,13,15,28,26,12,16,29,14), ( 1, 5,22,24)
( 2, 3, 4,23)( 6,21,30,14,12, 9)( 7,18,20,26,25,10)( 8,17,28,11)
(15,16,29,27), ( 1,18,26)( 2, 6,20,22, 3,19,30,24, 5,21,23)( 7,29,25)
( 8,17,14,10,15,28,13, 9,16,27,12), ( 1, 8, 6, 3)( 2, 9, 7, 5)( 4,24,13,11,16,
 19)(10,15,18,20,22,25)(14,28,29,23)(17,30,26,27), ( 1, 8,15,12)
( 2, 5,19,17,27,13)( 3, 7,18,28,26,25)( 4,20,30,24)( 9,16,11,10)
(21,29,23,22), ( 1,16,19, 5, 9,18,21, 3, 8, 6, 4)( 2,15,20)(10,17,22)
(11,29,24,13,27,30,25,12,28,23,14), ( 1, 9, 7, 4)( 2,13,15,17,19,22)
( 3,10, 8, 5)( 6,21,24,14,12,16)(11,29,30,26)(20,23,27,28), ( 1, 8,18,29,23,25
 )( 2, 9,15,17,30,22)( 3, 7,19,21)( 4, 5, 6,20)(10,11,27,14)(12,28,26,13), 
( 1,12,18, 5, 9,15, 6, 3,10,16, 7)( 2,11,19)( 4,13,17)(14,28,20,24,26,29,21,
 25,27,30,22), ( 1,12,15, 8)( 2,13,27,17,19, 5)( 3,25,26,28,18, 7)
( 4,24,30,20)( 9,10,11,16)(21,22,23,29) )
gap> IsSimple(C);
false
gap> N:=Size(C);
10712468422656000
gap> Factors(N);
[ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 
  3, 3, 3, 3, 3, 5, 5, 5, 7, 7, 11, 13 ]
gap> Factorial(15);
1307674368000
gap> Factorial(16);
20922789888000
gap> Factors(Factorial(16));
[ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 5, 5, 5, 7, 
  7, 11, 13 ]
gap> N1:=2^9*Factorial(16);
10712468422656000
gap> N1:=2^10*(Factorial(16)/2);
10712468422656000
gap> #A_16 semidirect C_2^10?
gap> quit;