gap> f:=[1];
[ 1 ]
gap> f[1]:=(1,2,3,4,5);
(1,2,3,4,5)
gap> f[2]:=(1,6,7,8,2);
(1,6,7,8,2)
gap> f[3]:=(2,8,9,10,3);
( 2, 8, 9,10, 3)
gap> f[4]:=(3,10,11,12,4);
( 3,10,11,12, 4)
gap> f[5]:=(5,4,12,13,14);
( 4,12,13,14, 5)
gap> f[6]:=(1,5,14,15,6);
( 1, 5,14,15, 6)
gap> f[7]:=(16,20,7,6,15);
( 6,15,16,20, 7)
gap> f[8]:=(7,20,19,9,8);
( 7,20,19, 9, 8)
gap> f[9]:=(11,10,9,17,18);
( 9,17,18,11,10)
gap> f[10]:=(12,11,18,17,13);
(11,18,17,13,12)
gap> f[11]:=(15,14,13,17,16);
(13,17,16,15,14)
gap> f[12]:=(16,17,18,19,20);
(16,17,18,19,20)
gap> c:=[1];
[ 1 ]
gap> for i in [1..12]  do
>   for j in [1..12] do
>     c[12*(i-1)+j]:=f[i]*f[j]^-1;
>   od;
> od;
gap> c[1];
()
gap> G:=Group(c,c[1]);
Group( (1,8,7,6)(2,3,4,5), ( 1, 3, 4, 5)( 2,10, 9, 8), ( 1, 2, 4, 5)
( 3,12,11,10), ( 1, 2, 3, 5)( 4,14,13,12), ( 1, 2, 3, 4)( 5, 6,15,14), 
( 1, 2, 3, 4, 5)( 6, 7,20,16,15), ( 1, 2, 3, 4, 5)( 7, 8, 9,19,20), 
( 1, 2, 3, 4, 5)( 9,10,11,18,17), ( 1, 2, 3, 4, 5)(11,12,13,17,18), 
( 1, 2, 3, 4, 5)(13,14,15,16,17), ( 1, 2, 3, 4, 5)(16,20,19,18,17), (1,6,7,8)
(2,5,4,3), ( 1, 6, 7, 2)( 3,10, 9, 8), ( 1, 6, 7, 8, 2)( 3, 4,12,11,10), 
( 1, 6, 7, 8, 2)( 4, 5,14,13,12), ( 1,15,14, 5)( 2, 6, 7, 8), ( 1, 7, 8, 2)
( 6,20,16,15), ( 1, 6, 8, 2)( 7, 9,19,20), ( 1, 6, 7, 8, 2)( 9,10,11,18,17), 
( 1, 6, 7, 8, 2)(11,12,13,17,18), ( 1, 6, 7, 8, 2)(13,14,15,16,17), 
( 1, 6, 7, 8, 2)(16,20,19,18,17), ( 1, 5, 4, 3)( 2, 8, 9,10), ( 1, 2, 7, 6)
( 3, 8, 9,10), ( 2, 8, 9, 3)( 4,12,11,10), ( 2, 8, 9,10, 3)( 4, 5,14,13,12), 
( 1, 6,15,14, 5)( 2, 8, 9,10, 3), ( 2, 8, 9,10, 3)( 6, 7,20,16,15), 
( 2, 9,10, 3)( 7, 8,19,20), ( 2, 8,10, 3)( 9,11,18,17), ( 2, 8, 9,10, 3)
(11,12,13,17,18), ( 2, 8, 9,10, 3)(13,14,15,16,17), ( 2, 8, 9,10, 3)
(16,20,19,18,17), ( 1, 5, 4, 2)( 3,10,11,12), ( 1, 2, 8, 7, 6)
( 3,10,11,12, 4), ( 2, 3, 9, 8)( 4,10,11,12), ( 3,10,11, 4)( 5,14,13,12), 
( 1, 6,15,14, 5)( 3,10,11,12, 4), ( 3,10,11,12, 4)( 6, 7,20,16,15), 
( 3,10,11,12, 4)( 7, 8, 9,19,20), ( 3,11,12, 4)( 9,10,18,17), ( 3,10,12, 4)
(11,13,17,18), ( 3,10,11,12, 4)(13,14,15,16,17), ( 3,10,11,12, 4)
(16,20,19,18,17), ( 1, 5, 3, 2)( 4,12,13,14), ( 1, 2, 8, 7, 6)
( 4,12,13,14, 5), ( 2, 3,10, 9, 8)( 4,12,13,14, 5), ( 3, 4,11,10)
( 5,12,13,14), ( 1, 6,15,14)( 4,12,13, 5), ( 4,12,13,14, 5)( 6, 7,20,16,15), 
( 4,12,13,14, 5)( 7, 8, 9,19,20), ( 4,12,13,14, 5)( 9,10,11,18,17), 
( 4,13,14, 5)(11,12,17,18), ( 4,12,14, 5)(13,15,16,17), ( 4,12,13,14, 5)
(16,20,19,18,17), ( 1, 4, 3, 2)( 5,14,15, 6), ( 1, 5,14,15)( 2, 8, 7, 6), 
( 1, 5,14,15, 6)( 2, 3,10, 9, 8), ( 1, 5,14,15, 6)( 3, 4,12,11,10), 
( 1,14,15, 6)( 4, 5,13,12), ( 1, 5,14, 6)( 7,20,16,15), ( 1, 5,14,15, 6)
( 7, 8, 9,19,20), ( 1, 5,14,15, 6)( 9,10,11,18,17), ( 1, 5,14,15, 6)
(11,12,13,17,18), ( 1, 5,15, 6)(13,14,16,17), ( 1, 5,14,15, 6)
(16,20,19,18,17), ( 1, 5, 4, 3, 2)( 6,15,16,20, 7), ( 1, 2, 8, 7)
( 6,15,16,20), ( 2, 3,10, 9, 8)( 6,15,16,20, 7), ( 3, 4,12,11,10)
( 6,15,16,20, 7), ( 4, 5,14,13,12)( 6,15,16,20, 7), ( 1, 6,14, 5)
( 7,15,16,20), ( 6,15,16, 7)( 8, 9,19,20), ( 6,15,16,20, 7)( 9,10,11,18,17), 
( 6,15,16,20, 7)(11,12,13,17,18), ( 6,16,20, 7)(13,14,15,17), ( 6,15,20, 7)
(16,19,18,17), ( 1, 5, 4, 3, 2)( 7,20,19, 9, 8), ( 1, 2, 8, 6)( 7,20,19, 9), 
( 2, 3,10, 9)( 7,20,19, 8), ( 3, 4,12,11,10)( 7,20,19, 9, 8), ( 4, 5,14,13,12)
( 7,20,19, 9, 8), ( 1, 6,15,14, 5)( 7,20,19, 9, 8), ( 6, 7,16,15)
( 8,20,19, 9), ( 7,20,19,10,11,18,17, 9, 8), ( 7,20,19, 9, 8)
(11,12,13,17,18), ( 7,20,19, 9, 8)(13,14,15,16,17), ( 7,19, 9, 8)
(16,20,18,17), ( 1, 5, 4, 3, 2)( 9,17,18,11,10), ( 1, 2, 8, 7, 6)
( 9,17,18,11,10), ( 2, 3,10, 8)( 9,17,18,11), ( 3, 4,12,11)( 9,17,18,10), 
( 4, 5,14,13,12)( 9,17,18,11,10), ( 1, 6,15,14, 5)( 9,17,18,11,10), 
( 6, 7,20,16,15)( 9,17,18,11,10), ( 7, 8, 9,17,18,11,10,19,20), 
( 9,18,12,13,17,11,10), ( 9,13,14,15,16,17,18,11,10), ( 9,16,20,19,18,11,10), 
( 1, 5, 4, 3, 2)(11,18,17,13,12), ( 1, 2, 8, 7, 6)(11,18,17,13,12), 
( 2, 3,10, 9, 8)(11,18,17,13,12), ( 3, 4,12,10)(11,18,17,13), ( 4, 5,14,13)
(11,18,17,12), ( 1, 6,15,14, 5)(11,18,17,13,12), ( 6, 7,20,16,15)
(11,18,17,13,12), ( 7, 8, 9,19,20)(11,18,17,13,12), ( 9,10,11,17,13,12,18), 
(11,18,13,12)(14,15,16,17), (11,17,13,12)(16,20,19,18), ( 1, 5, 4, 3, 2)
(13,17,16,15,14), ( 1, 2, 8, 7, 6)(13,17,16,15,14), ( 2, 3,10, 9, 8)
(13,17,16,15,14), ( 3, 4,12,11,10)(13,17,16,15,14), ( 4, 5,14,12)
(13,17,16,15), ( 1, 6,15, 5)(13,17,16,14), ( 6, 7,20,16)(13,17,15,14), 
( 7, 8, 9,19,20)(13,17,16,15,14), ( 9,10,11,18,17,16,15,14,13), (11,12,13,18)
(14,17,16,15), (13,16,15,14)(17,20,19,18), ( 1, 5, 4, 3, 2)(16,17,18,19,20), 
( 1, 2, 8, 7, 6)(16,17,18,19,20), ( 2, 3,10, 9, 8)(16,17,18,19,20), 
( 3, 4,12,11,10)(16,17,18,19,20), ( 4, 5,14,13,12)(16,17,18,19,20), 
( 1, 6,15,14, 5)(16,17,18,19,20), ( 6, 7,20,15)(16,17,18,19), ( 7, 8, 9,19)
(16,17,18,20), ( 9,10,11,18,19,20,16), (11,12,13,17)(16,18,19,20), 
(13,14,15,16)(17,18,19,20) )
gap> Size(G);
1216451004088320000
gap> IsSimple(G);
true
gap> N:=Size(G);
1216451004088320000
gap> Factor(N);
Error, Variable: 'Factor' must have a value
gap> factor(N);
Error, Variable: 'factor' must have a value
gap> FactorsInt(N);
[ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 
  5, 5, 5, 5, 7, 7, 11, 13, 17, 19 ]
gap> Centre(G);
Subgroup( Group( (1,8,7,6)(2,3,4,5), ( 1, 3, 4, 5)( 2,10, 9, 8), ( 1, 2, 4, 5)
( 3,12,11,10), ( 1, 2, 3, 5)( 4,14,13,12), ( 1, 2, 3, 4)( 5, 6,15,14), 
( 1, 2, 3, 4, 5)( 6, 7,20,16,15), ( 1, 2, 3, 4, 5)( 7, 8, 9,19,20), 
( 1, 2, 3, 4, 5)( 9,10,11,18,17), ( 1, 2, 3, 4, 5)(11,12,13,17,18), 
( 1, 2, 3, 4, 5)(13,14,15,16,17), ( 1, 2, 3, 4, 5)(16,20,19,18,17), (1,6,7,8)
(2,5,4,3), ( 1, 6, 7, 2)( 3,10, 9, 8), ( 1, 6, 7, 8, 2)( 3, 4,12,11,10), 
( 1, 6, 7, 8, 2)( 4, 5,14,13,12), ( 1,15,14, 5)( 2, 6, 7, 8), ( 1, 7, 8, 2)
( 6,20,16,15), ( 1, 6, 8, 2)( 7, 9,19,20), ( 1, 6, 7, 8, 2)( 9,10,11,18,17), 
( 1, 6, 7, 8, 2)(11,12,13,17,18), ( 1, 6, 7, 8, 2)(13,14,15,16,17), 
( 1, 6, 7, 8, 2)(16,20,19,18,17), ( 1, 5, 4, 3)( 2, 8, 9,10), ( 1, 2, 7, 6)
( 3, 8, 9,10), ( 2, 8, 9, 3)( 4,12,11,10), ( 2, 8, 9,10, 3)( 4, 5,14,13,12), 
( 1, 6,15,14, 5)( 2, 8, 9,10, 3), ( 2, 8, 9,10, 3)( 6, 7,20,16,15), 
( 2, 9,10, 3)( 7, 8,19,20), ( 2, 8,10, 3)( 9,11,18,17), ( 2, 8, 9,10, 3)
(11,12,13,17,18), ( 2, 8, 9,10, 3)(13,14,15,16,17), ( 2, 8, 9,10, 3)
(16,20,19,18,17), ( 1, 5, 4, 2)( 3,10,11,12), ( 1, 2, 8, 7, 6)
( 3,10,11,12, 4), ( 2, 3, 9, 8)( 4,10,11,12), ( 3,10,11, 4)( 5,14,13,12), 
( 1, 6,15,14, 5)( 3,10,11,12, 4), ( 3,10,11,12, 4)( 6, 7,20,16,15), 
( 3,10,11,12, 4)( 7, 8, 9,19,20), ( 3,11,12, 4)( 9,10,18,17), ( 3,10,12, 4)
(11,13,17,18), ( 3,10,11,12, 4)(13,14,15,16,17), ( 3,10,11,12, 4)
(16,20,19,18,17), ( 1, 5, 3, 2)( 4,12,13,14), ( 1, 2, 8, 7, 6)
( 4,12,13,14, 5), ( 2, 3,10, 9, 8)( 4,12,13,14, 5), ( 3, 4,11,10)
( 5,12,13,14), ( 1, 6,15,14)( 4,12,13, 5), ( 4,12,13,14, 5)( 6, 7,20,16,15), 
( 4,12,13,14, 5)( 7, 8, 9,19,20), ( 4,12,13,14, 5)( 9,10,11,18,17), 
( 4,13,14, 5)(11,12,17,18), ( 4,12,14, 5)(13,15,16,17), ( 4,12,13,14, 5)
(16,20,19,18,17), ( 1, 4, 3, 2)( 5,14,15, 6), ( 1, 5,14,15)( 2, 8, 7, 6), 
( 1, 5,14,15, 6)( 2, 3,10, 9, 8), ( 1, 5,14,15, 6)( 3, 4,12,11,10), 
( 1,14,15, 6)( 4, 5,13,12), ( 1, 5,14, 6)( 7,20,16,15), ( 1, 5,14,15, 6)
( 7, 8, 9,19,20), ( 1, 5,14,15, 6)( 9,10,11,18,17), ( 1, 5,14,15, 6)
(11,12,13,17,18), ( 1, 5,15, 6)(13,14,16,17), ( 1, 5,14,15, 6)
(16,20,19,18,17), ( 1, 5, 4, 3, 2)( 6,15,16,20, 7), ( 1, 2, 8, 7)
( 6,15,16,20), ( 2, 3,10, 9, 8)( 6,15,16,20, 7), ( 3, 4,12,11,10)
( 6,15,16,20, 7), ( 4, 5,14,13,12)( 6,15,16,20, 7), ( 1, 6,14, 5)
( 7,15,16,20), ( 6,15,16, 7)( 8, 9,19,20), ( 6,15,16,20, 7)( 9,10,11,18,17), 
( 6,15,16,20, 7)(11,12,13,17,18), ( 6,16,20, 7)(13,14,15,17), ( 6,15,20, 7)
(16,19,18,17), ( 1, 5, 4, 3, 2)( 7,20,19, 9, 8), ( 1, 2, 8, 6)( 7,20,19, 9), 
( 2, 3,10, 9)( 7,20,19, 8), ( 3, 4,12,11,10)( 7,20,19, 9, 8), ( 4, 5,14,13,12)
( 7,20,19, 9, 8), ( 1, 6,15,14, 5)( 7,20,19, 9, 8), ( 6, 7,16,15)
( 8,20,19, 9), ( 7,20,19,10,11,18,17, 9, 8), ( 7,20,19, 9, 8)
(11,12,13,17,18), ( 7,20,19, 9, 8)(13,14,15,16,17), ( 7,19, 9, 8)
(16,20,18,17), ( 1, 5, 4, 3, 2)( 9,17,18,11,10), ( 1, 2, 8, 7, 6)
( 9,17,18,11,10), ( 2, 3,10, 8)( 9,17,18,11), ( 3, 4,12,11)( 9,17,18,10), 
( 4, 5,14,13,12)( 9,17,18,11,10), ( 1, 6,15,14, 5)( 9,17,18,11,10), 
( 6, 7,20,16,15)( 9,17,18,11,10), ( 7, 8, 9,17,18,11,10,19,20), 
( 9,18,12,13,17,11,10), ( 9,13,14,15,16,17,18,11,10), ( 9,16,20,19,18,11,10), 
( 1, 5, 4, 3, 2)(11,18,17,13,12), ( 1, 2, 8, 7, 6)(11,18,17,13,12), 
( 2, 3,10, 9, 8)(11,18,17,13,12), ( 3, 4,12,10)(11,18,17,13), ( 4, 5,14,13)
(11,18,17,12), ( 1, 6,15,14, 5)(11,18,17,13,12), ( 6, 7,20,16,15)
(11,18,17,13,12), ( 7, 8, 9,19,20)(11,18,17,13,12), ( 9,10,11,17,13,12,18), 
(11,18,13,12)(14,15,16,17), (11,17,13,12)(16,20,19,18), ( 1, 5, 4, 3, 2)
(13,17,16,15,14), ( 1, 2, 8, 7, 6)(13,17,16,15,14), ( 2, 3,10, 9, 8)
(13,17,16,15,14), ( 3, 4,12,11,10)(13,17,16,15,14), ( 4, 5,14,12)
(13,17,16,15), ( 1, 6,15, 5)(13,17,16,14), ( 6, 7,20,16)(13,17,15,14), 
( 7, 8, 9,19,20)(13,17,16,15,14), ( 9,10,11,18,17,16,15,14,13), (11,12,13,18)
(14,17,16,15), (13,16,15,14)(17,20,19,18), ( 1, 5, 4, 3, 2)(16,17,18,19,20), 
( 1, 2, 8, 7, 6)(16,17,18,19,20), ( 2, 3,10, 9, 8)(16,17,18,19,20), 
( 3, 4,12,11,10)(16,17,18,19,20), ( 4, 5,14,13,12)(16,17,18,19,20), 
( 1, 6,15,14, 5)(16,17,18,19,20), ( 6, 7,20,15)(16,17,18,19), ( 7, 8, 9,19)
(16,17,18,20), ( 9,10,11,18,19,20,16), (11,12,13,17)(16,18,19,20), 
(13,14,15,16)(17,18,19,20) ), [  ] )
gap> Z:=Centre(G);
Subgroup( Group( (1,8,7,6)(2,3,4,5), ( 1, 3, 4, 5)( 2,10, 9, 8), ( 1, 2, 4, 5)
( 3,12,11,10), ( 1, 2, 3, 5)( 4,14,13,12), ( 1, 2, 3, 4)( 5, 6,15,14), 
( 1, 2, 3, 4, 5)( 6, 7,20,16,15), ( 1, 2, 3, 4, 5)( 7, 8, 9,19,20), 
( 1, 2, 3, 4, 5)( 9,10,11,18,17), ( 1, 2, 3, 4, 5)(11,12,13,17,18), 
( 1, 2, 3, 4, 5)(13,14,15,16,17), ( 1, 2, 3, 4, 5)(16,20,19,18,17), (1,6,7,8)
(2,5,4,3), ( 1, 6, 7, 2)( 3,10, 9, 8), ( 1, 6, 7, 8, 2)( 3, 4,12,11,10), 
( 1, 6, 7, 8, 2)( 4, 5,14,13,12), ( 1,15,14, 5)( 2, 6, 7, 8), ( 1, 7, 8, 2)
( 6,20,16,15), ( 1, 6, 8, 2)( 7, 9,19,20), ( 1, 6, 7, 8, 2)( 9,10,11,18,17), 
( 1, 6, 7, 8, 2)(11,12,13,17,18), ( 1, 6, 7, 8, 2)(13,14,15,16,17), 
( 1, 6, 7, 8, 2)(16,20,19,18,17), ( 1, 5, 4, 3)( 2, 8, 9,10), ( 1, 2, 7, 6)
( 3, 8, 9,10), ( 2, 8, 9, 3)( 4,12,11,10), ( 2, 8, 9,10, 3)( 4, 5,14,13,12), 
( 1, 6,15,14, 5)( 2, 8, 9,10, 3), ( 2, 8, 9,10, 3)( 6, 7,20,16,15), 
( 2, 9,10, 3)( 7, 8,19,20), ( 2, 8,10, 3)( 9,11,18,17), ( 2, 8, 9,10, 3)
(11,12,13,17,18), ( 2, 8, 9,10, 3)(13,14,15,16,17), ( 2, 8, 9,10, 3)
(16,20,19,18,17), ( 1, 5, 4, 2)( 3,10,11,12), ( 1, 2, 8, 7, 6)
( 3,10,11,12, 4), ( 2, 3, 9, 8)( 4,10,11,12), ( 3,10,11, 4)( 5,14,13,12), 
( 1, 6,15,14, 5)( 3,10,11,12, 4), ( 3,10,11,12, 4)( 6, 7,20,16,15), 
( 3,10,11,12, 4)( 7, 8, 9,19,20), ( 3,11,12, 4)( 9,10,18,17), ( 3,10,12, 4)
(11,13,17,18), ( 3,10,11,12, 4)(13,14,15,16,17), ( 3,10,11,12, 4)
(16,20,19,18,17), ( 1, 5, 3, 2)( 4,12,13,14), ( 1, 2, 8, 7, 6)
( 4,12,13,14, 5), ( 2, 3,10, 9, 8)( 4,12,13,14, 5), ( 3, 4,11,10)
( 5,12,13,14), ( 1, 6,15,14)( 4,12,13, 5), ( 4,12,13,14, 5)( 6, 7,20,16,15), 
( 4,12,13,14, 5)( 7, 8, 9,19,20), ( 4,12,13,14, 5)( 9,10,11,18,17), 
( 4,13,14, 5)(11,12,17,18), ( 4,12,14, 5)(13,15,16,17), ( 4,12,13,14, 5)
(16,20,19,18,17), ( 1, 4, 3, 2)( 5,14,15, 6), ( 1, 5,14,15)( 2, 8, 7, 6), 
( 1, 5,14,15, 6)( 2, 3,10, 9, 8), ( 1, 5,14,15, 6)( 3, 4,12,11,10), 
( 1,14,15, 6)( 4, 5,13,12), ( 1, 5,14, 6)( 7,20,16,15), ( 1, 5,14,15, 6)
( 7, 8, 9,19,20), ( 1, 5,14,15, 6)( 9,10,11,18,17), ( 1, 5,14,15, 6)
(11,12,13,17,18), ( 1, 5,15, 6)(13,14,16,17), ( 1, 5,14,15, 6)
(16,20,19,18,17), ( 1, 5, 4, 3, 2)( 6,15,16,20, 7), ( 1, 2, 8, 7)
( 6,15,16,20), ( 2, 3,10, 9, 8)( 6,15,16,20, 7), ( 3, 4,12,11,10)
( 6,15,16,20, 7), ( 4, 5,14,13,12)( 6,15,16,20, 7), ( 1, 6,14, 5)
( 7,15,16,20), ( 6,15,16, 7)( 8, 9,19,20), ( 6,15,16,20, 7)( 9,10,11,18,17), 
( 6,15,16,20, 7)(11,12,13,17,18), ( 6,16,20, 7)(13,14,15,17), ( 6,15,20, 7)
(16,19,18,17), ( 1, 5, 4, 3, 2)( 7,20,19, 9, 8), ( 1, 2, 8, 6)( 7,20,19, 9), 
( 2, 3,10, 9)( 7,20,19, 8), ( 3, 4,12,11,10)( 7,20,19, 9, 8), ( 4, 5,14,13,12)
( 7,20,19, 9, 8), ( 1, 6,15,14, 5)( 7,20,19, 9, 8), ( 6, 7,16,15)
( 8,20,19, 9), ( 7,20,19,10,11,18,17, 9, 8), ( 7,20,19, 9, 8)
(11,12,13,17,18), ( 7,20,19, 9, 8)(13,14,15,16,17), ( 7,19, 9, 8)
(16,20,18,17), ( 1, 5, 4, 3, 2)( 9,17,18,11,10), ( 1, 2, 8, 7, 6)
( 9,17,18,11,10), ( 2, 3,10, 8)( 9,17,18,11), ( 3, 4,12,11)( 9,17,18,10), 
( 4, 5,14,13,12)( 9,17,18,11,10), ( 1, 6,15,14, 5)( 9,17,18,11,10), 
( 6, 7,20,16,15)( 9,17,18,11,10), ( 7, 8, 9,17,18,11,10,19,20), 
( 9,18,12,13,17,11,10), ( 9,13,14,15,16,17,18,11,10), ( 9,16,20,19,18,11,10), 
( 1, 5, 4, 3, 2)(11,18,17,13,12), ( 1, 2, 8, 7, 6)(11,18,17,13,12), 
( 2, 3,10, 9, 8)(11,18,17,13,12), ( 3, 4,12,10)(11,18,17,13), ( 4, 5,14,13)
(11,18,17,12), ( 1, 6,15,14, 5)(11,18,17,13,12), ( 6, 7,20,16,15)
(11,18,17,13,12), ( 7, 8, 9,19,20)(11,18,17,13,12), ( 9,10,11,17,13,12,18), 
(11,18,13,12)(14,15,16,17), (11,17,13,12)(16,20,19,18), ( 1, 5, 4, 3, 2)
(13,17,16,15,14), ( 1, 2, 8, 7, 6)(13,17,16,15,14), ( 2, 3,10, 9, 8)
(13,17,16,15,14), ( 3, 4,12,11,10)(13,17,16,15,14), ( 4, 5,14,12)
(13,17,16,15), ( 1, 6,15, 5)(13,17,16,14), ( 6, 7,20,16)(13,17,15,14), 
( 7, 8, 9,19,20)(13,17,16,15,14), ( 9,10,11,18,17,16,15,14,13), (11,12,13,18)
(14,17,16,15), (13,16,15,14)(17,20,19,18), ( 1, 5, 4, 3, 2)(16,17,18,19,20), 
( 1, 2, 8, 7, 6)(16,17,18,19,20), ( 2, 3,10, 9, 8)(16,17,18,19,20), 
( 3, 4,12,11,10)(16,17,18,19,20), ( 4, 5,14,13,12)(16,17,18,19,20), 
( 1, 6,15,14, 5)(16,17,18,19,20), ( 6, 7,20,15)(16,17,18,19), ( 7, 8, 9,19)
(16,17,18,20), ( 9,10,11,18,19,20,16), (11,12,13,17)(16,18,19,20), 
(13,14,15,16)(17,18,19,20) ), [  ] )
gap> Size(Z);
1
gap> CommutatorSubgroup( G,G);
Subgroup( Group( (1,8,7,6)(2,3,4,5), ( 1, 3, 4, 5)( 2,10, 9, 8), ( 1, 2, 4, 5)
( 3,12,11,10), ( 1, 2, 3, 5)( 4,14,13,12), ( 1, 2, 3, 4)( 5, 6,15,14), 
( 1, 2, 3, 4, 5)( 6, 7,20,16,15), ( 1, 2, 3, 4, 5)( 7, 8, 9,19,20), 
( 1, 2, 3, 4, 5)( 9,10,11,18,17), ( 1, 2, 3, 4, 5)(11,12,13,17,18), 
( 1, 2, 3, 4, 5)(13,14,15,16,17), ( 1, 2, 3, 4, 5)(16,20,19,18,17), (1,6,7,8)
(2,5,4,3), ( 1, 6, 7, 2)( 3,10, 9, 8), ( 1, 6, 7, 8, 2)( 3, 4,12,11,10), 
( 1, 6, 7, 8, 2)( 4, 5,14,13,12), ( 1,15,14, 5)( 2, 6, 7, 8), ( 1, 7, 8, 2)
( 6,20,16,15), ( 1, 6, 8, 2)( 7, 9,19,20), ( 1, 6, 7, 8, 2)( 9,10,11,18,17), 
( 1, 6, 7, 8, 2)(11,12,13,17,18), ( 1, 6, 7, 8, 2)(13,14,15,16,17), 
( 1, 6, 7, 8, 2)(16,20,19,18,17), ( 1, 5, 4, 3)( 2, 8, 9,10), ( 1, 2, 7, 6)
( 3, 8, 9,10), ( 2, 8, 9, 3)( 4,12,11,10), ( 2, 8, 9,10, 3)( 4, 5,14,13,12), 
( 1, 6,15,14, 5)( 2, 8, 9,10, 3), ( 2, 8, 9,10, 3)( 6, 7,20,16,15), 
( 2, 9,10, 3)( 7, 8,19,20), ( 2, 8,10, 3)( 9,11,18,17), ( 2, 8, 9,10, 3)
(11,12,13,17,18), ( 2, 8, 9,10, 3)(13,14,15,16,17), ( 2, 8, 9,10, 3)
(16,20,19,18,17), ( 1, 5, 4, 2)( 3,10,11,12), ( 1, 2, 8, 7, 6)
( 3,10,11,12, 4), ( 2, 3, 9, 8)( 4,10,11,12), ( 3,10,11, 4)( 5,14,13,12), 
( 1, 6,15,14, 5)( 3,10,11,12, 4), ( 3,10,11,12, 4)( 6, 7,20,16,15), 
( 3,10,11,12, 4)( 7, 8, 9,19,20), ( 3,11,12, 4)( 9,10,18,17), ( 3,10,12, 4)
(11,13,17,18), ( 3,10,11,12, 4)(13,14,15,16,17), ( 3,10,11,12, 4)
(16,20,19,18,17), ( 1, 5, 3, 2)( 4,12,13,14), ( 1, 2, 8, 7, 6)
( 4,12,13,14, 5), ( 2, 3,10, 9, 8)( 4,12,13,14, 5), ( 3, 4,11,10)
( 5,12,13,14), ( 1, 6,15,14)( 4,12,13, 5), ( 4,12,13,14, 5)( 6, 7,20,16,15), 
( 4,12,13,14, 5)( 7, 8, 9,19,20), ( 4,12,13,14, 5)( 9,10,11,18,17), 
( 4,13,14, 5)(11,12,17,18), ( 4,12,14, 5)(13,15,16,17), ( 4,12,13,14, 5)
(16,20,19,18,17), ( 1, 4, 3, 2)( 5,14,15, 6), ( 1, 5,14,15)( 2, 8, 7, 6), 
( 1, 5,14,15, 6)( 2, 3,10, 9, 8), ( 1, 5,14,15, 6)( 3, 4,12,11,10), 
( 1,14,15, 6)( 4, 5,13,12), ( 1, 5,14, 6)( 7,20,16,15), ( 1, 5,14,15, 6)
( 7, 8, 9,19,20), ( 1, 5,14,15, 6)( 9,10,11,18,17), ( 1, 5,14,15, 6)
(11,12,13,17,18), ( 1, 5,15, 6)(13,14,16,17), ( 1, 5,14,15, 6)
(16,20,19,18,17), ( 1, 5, 4, 3, 2)( 6,15,16,20, 7), ( 1, 2, 8, 7)
( 6,15,16,20), ( 2, 3,10, 9, 8)( 6,15,16,20, 7), ( 3, 4,12,11,10)
( 6,15,16,20, 7), ( 4, 5,14,13,12)( 6,15,16,20, 7), ( 1, 6,14, 5)
( 7,15,16,20), ( 6,15,16, 7)( 8, 9,19,20), ( 6,15,16,20, 7)( 9,10,11,18,17), 
( 6,15,16,20, 7)(11,12,13,17,18), ( 6,16,20, 7)(13,14,15,17), ( 6,15,20, 7)
(16,19,18,17), ( 1, 5, 4, 3, 2)( 7,20,19, 9, 8), ( 1, 2, 8, 6)( 7,20,19, 9), 
( 2, 3,10, 9)( 7,20,19, 8), ( 3, 4,12,11,10)( 7,20,19, 9, 8), ( 4, 5,14,13,12)
( 7,20,19, 9, 8), ( 1, 6,15,14, 5)( 7,20,19, 9, 8), ( 6, 7,16,15)
( 8,20,19, 9), ( 7,20,19,10,11,18,17, 9, 8), ( 7,20,19, 9, 8)
(11,12,13,17,18), ( 7,20,19, 9, 8)(13,14,15,16,17), ( 7,19, 9, 8)
(16,20,18,17), ( 1, 5, 4, 3, 2)( 9,17,18,11,10), ( 1, 2, 8, 7, 6)
( 9,17,18,11,10), ( 2, 3,10, 8)( 9,17,18,11), ( 3, 4,12,11)( 9,17,18,10), 
( 4, 5,14,13,12)( 9,17,18,11,10), ( 1, 6,15,14, 5)( 9,17,18,11,10), 
( 6, 7,20,16,15)( 9,17,18,11,10), ( 7, 8, 9,17,18,11,10,19,20), 
( 9,18,12,13,17,11,10), ( 9,13,14,15,16,17,18,11,10), ( 9,16,20,19,18,11,10), 
( 1, 5, 4, 3, 2)(11,18,17,13,12), ( 1, 2, 8, 7, 6)(11,18,17,13,12), 
( 2, 3,10, 9, 8)(11,18,17,13,12), ( 3, 4,12,10)(11,18,17,13), ( 4, 5,14,13)
(11,18,17,12), ( 1, 6,15,14, 5)(11,18,17,13,12), ( 6, 7,20,16,15)
(11,18,17,13,12), ( 7, 8, 9,19,20)(11,18,17,13,12), ( 9,10,11,17,13,12,18), 
(11,18,13,12)(14,15,16,17), (11,17,13,12)(16,20,19,18), ( 1, 5, 4, 3, 2)
(13,17,16,15,14), ( 1, 2, 8, 7, 6)(13,17,16,15,14), ( 2, 3,10, 9, 8)
(13,17,16,15,14), ( 3, 4,12,11,10)(13,17,16,15,14), ( 4, 5,14,12)
(13,17,16,15), ( 1, 6,15, 5)(13,17,16,14), ( 6, 7,20,16)(13,17,15,14), 
( 7, 8, 9,19,20)(13,17,16,15,14), ( 9,10,11,18,17,16,15,14,13), (11,12,13,18)
(14,17,16,15), (13,16,15,14)(17,20,19,18), ( 1, 5, 4, 3, 2)(16,17,18,19,20), 
( 1, 2, 8, 7, 6)(16,17,18,19,20), ( 2, 3,10, 9, 8)(16,17,18,19,20), 
( 3, 4,12,11,10)(16,17,18,19,20), ( 4, 5,14,13,12)(16,17,18,19,20), 
( 1, 6,15,14, 5)(16,17,18,19,20), ( 6, 7,20,15)(16,17,18,19), ( 7, 8, 9,19)
(16,17,18,20), ( 9,10,11,18,19,20,16), (11,12,13,17)(16,18,19,20), 
(13,14,15,16)(17,18,19,20) ), 
[ ( 1, 4,11,18,20,13, 2, 8,15,17, 6, 7,12,16, 3,19)( 5, 9,14,10), 
  ( 1, 4,17, 5,11,18, 3,15, 8, 7, 9,12,14, 6,10)( 2,16)(19,20) ] )
gap> G1:=CommutatorSubgroup( G,G);
Subgroup( Group( (1,8,7,6)(2,3,4,5), ( 1, 3, 4, 5)( 2,10, 9, 8), ( 1, 2, 4, 5)
( 3,12,11,10), ( 1, 2, 3, 5)( 4,14,13,12), ( 1, 2, 3, 4)( 5, 6,15,14), 
( 1, 2, 3, 4, 5)( 6, 7,20,16,15), ( 1, 2, 3, 4, 5)( 7, 8, 9,19,20), 
( 1, 2, 3, 4, 5)( 9,10,11,18,17), ( 1, 2, 3, 4, 5)(11,12,13,17,18), 
( 1, 2, 3, 4, 5)(13,14,15,16,17), ( 1, 2, 3, 4, 5)(16,20,19,18,17), (1,6,7,8)
(2,5,4,3), ( 1, 6, 7, 2)( 3,10, 9, 8), ( 1, 6, 7, 8, 2)( 3, 4,12,11,10), 
( 1, 6, 7, 8, 2)( 4, 5,14,13,12), ( 1,15,14, 5)( 2, 6, 7, 8), ( 1, 7, 8, 2)
( 6,20,16,15), ( 1, 6, 8, 2)( 7, 9,19,20), ( 1, 6, 7, 8, 2)( 9,10,11,18,17), 
( 1, 6, 7, 8, 2)(11,12,13,17,18), ( 1, 6, 7, 8, 2)(13,14,15,16,17), 
( 1, 6, 7, 8, 2)(16,20,19,18,17), ( 1, 5, 4, 3)( 2, 8, 9,10), ( 1, 2, 7, 6)
( 3, 8, 9,10), ( 2, 8, 9, 3)( 4,12,11,10), ( 2, 8, 9,10, 3)( 4, 5,14,13,12), 
( 1, 6,15,14, 5)( 2, 8, 9,10, 3), ( 2, 8, 9,10, 3)( 6, 7,20,16,15), 
( 2, 9,10, 3)( 7, 8,19,20), ( 2, 8,10, 3)( 9,11,18,17), ( 2, 8, 9,10, 3)
(11,12,13,17,18), ( 2, 8, 9,10, 3)(13,14,15,16,17), ( 2, 8, 9,10, 3)
(16,20,19,18,17), ( 1, 5, 4, 2)( 3,10,11,12), ( 1, 2, 8, 7, 6)
( 3,10,11,12, 4), ( 2, 3, 9, 8)( 4,10,11,12), ( 3,10,11, 4)( 5,14,13,12), 
( 1, 6,15,14, 5)( 3,10,11,12, 4), ( 3,10,11,12, 4)( 6, 7,20,16,15), 
( 3,10,11,12, 4)( 7, 8, 9,19,20), ( 3,11,12, 4)( 9,10,18,17), ( 3,10,12, 4)
(11,13,17,18), ( 3,10,11,12, 4)(13,14,15,16,17), ( 3,10,11,12, 4)
(16,20,19,18,17), ( 1, 5, 3, 2)( 4,12,13,14), ( 1, 2, 8, 7, 6)
( 4,12,13,14, 5), ( 2, 3,10, 9, 8)( 4,12,13,14, 5), ( 3, 4,11,10)
( 5,12,13,14), ( 1, 6,15,14)( 4,12,13, 5), ( 4,12,13,14, 5)( 6, 7,20,16,15), 
( 4,12,13,14, 5)( 7, 8, 9,19,20), ( 4,12,13,14, 5)( 9,10,11,18,17), 
( 4,13,14, 5)(11,12,17,18), ( 4,12,14, 5)(13,15,16,17), ( 4,12,13,14, 5)
(16,20,19,18,17), ( 1, 4, 3, 2)( 5,14,15, 6), ( 1, 5,14,15)( 2, 8, 7, 6), 
( 1, 5,14,15, 6)( 2, 3,10, 9, 8), ( 1, 5,14,15, 6)( 3, 4,12,11,10), 
( 1,14,15, 6)( 4, 5,13,12), ( 1, 5,14, 6)( 7,20,16,15), ( 1, 5,14,15, 6)
( 7, 8, 9,19,20), ( 1, 5,14,15, 6)( 9,10,11,18,17), ( 1, 5,14,15, 6)
(11,12,13,17,18), ( 1, 5,15, 6)(13,14,16,17), ( 1, 5,14,15, 6)
(16,20,19,18,17), ( 1, 5, 4, 3, 2)( 6,15,16,20, 7), ( 1, 2, 8, 7)
( 6,15,16,20), ( 2, 3,10, 9, 8)( 6,15,16,20, 7), ( 3, 4,12,11,10)
( 6,15,16,20, 7), ( 4, 5,14,13,12)( 6,15,16,20, 7), ( 1, 6,14, 5)
( 7,15,16,20), ( 6,15,16, 7)( 8, 9,19,20), ( 6,15,16,20, 7)( 9,10,11,18,17), 
( 6,15,16,20, 7)(11,12,13,17,18), ( 6,16,20, 7)(13,14,15,17), ( 6,15,20, 7)
(16,19,18,17), ( 1, 5, 4, 3, 2)( 7,20,19, 9, 8), ( 1, 2, 8, 6)( 7,20,19, 9), 
( 2, 3,10, 9)( 7,20,19, 8), ( 3, 4,12,11,10)( 7,20,19, 9, 8), ( 4, 5,14,13,12)
( 7,20,19, 9, 8), ( 1, 6,15,14, 5)( 7,20,19, 9, 8), ( 6, 7,16,15)
( 8,20,19, 9), ( 7,20,19,10,11,18,17, 9, 8), ( 7,20,19, 9, 8)
(11,12,13,17,18), ( 7,20,19, 9, 8)(13,14,15,16,17), ( 7,19, 9, 8)
(16,20,18,17), ( 1, 5, 4, 3, 2)( 9,17,18,11,10), ( 1, 2, 8, 7, 6)
( 9,17,18,11,10), ( 2, 3,10, 8)( 9,17,18,11), ( 3, 4,12,11)( 9,17,18,10), 
( 4, 5,14,13,12)( 9,17,18,11,10), ( 1, 6,15,14, 5)( 9,17,18,11,10), 
( 6, 7,20,16,15)( 9,17,18,11,10), ( 7, 8, 9,17,18,11,10,19,20), 
( 9,18,12,13,17,11,10), ( 9,13,14,15,16,17,18,11,10), ( 9,16,20,19,18,11,10), 
( 1, 5, 4, 3, 2)(11,18,17,13,12), ( 1, 2, 8, 7, 6)(11,18,17,13,12), 
( 2, 3,10, 9, 8)(11,18,17,13,12), ( 3, 4,12,10)(11,18,17,13), ( 4, 5,14,13)
(11,18,17,12), ( 1, 6,15,14, 5)(11,18,17,13,12), ( 6, 7,20,16,15)
(11,18,17,13,12), ( 7, 8, 9,19,20)(11,18,17,13,12), ( 9,10,11,17,13,12,18), 
(11,18,13,12)(14,15,16,17), (11,17,13,12)(16,20,19,18), ( 1, 5, 4, 3, 2)
(13,17,16,15,14), ( 1, 2, 8, 7, 6)(13,17,16,15,14), ( 2, 3,10, 9, 8)
(13,17,16,15,14), ( 3, 4,12,11,10)(13,17,16,15,14), ( 4, 5,14,12)
(13,17,16,15), ( 1, 6,15, 5)(13,17,16,14), ( 6, 7,20,16)(13,17,15,14), 
( 7, 8, 9,19,20)(13,17,16,15,14), ( 9,10,11,18,17,16,15,14,13), (11,12,13,18)
(14,17,16,15), (13,16,15,14)(17,20,19,18), ( 1, 5, 4, 3, 2)(16,17,18,19,20), 
( 1, 2, 8, 7, 6)(16,17,18,19,20), ( 2, 3,10, 9, 8)(16,17,18,19,20), 
( 3, 4,12,11,10)(16,17,18,19,20), ( 4, 5,14,13,12)(16,17,18,19,20), 
( 1, 6,15,14, 5)(16,17,18,19,20), ( 6, 7,20,15)(16,17,18,19), ( 7, 8, 9,19)
(16,17,18,20), ( 9,10,11,18,19,20,16), (11,12,13,17)(16,18,19,20), 
(13,14,15,16)(17,18,19,20) ), 
[ ( 1,11,10, 3,14,16,13,15,18,12, 5)( 4,17, 7,19, 9, 8)( 6,20), 
  ( 1, 7, 5,14, 4,20, 6,19,16, 8,13,17, 3,11,15, 9, 2,18,10) ] )
gap> Size(G1);
1216451004088320000
gap> Size(G);
1216451004088320000
gap> G2:=DerivedSubgroup(G);
Subgroup( Group( (1,8,7,6)(2,3,4,5), ( 1, 3, 4, 5)( 2,10, 9, 8), ( 1, 2, 4, 5)
( 3,12,11,10), ( 1, 2, 3, 5)( 4,14,13,12), ( 1, 2, 3, 4)( 5, 6,15,14), 
( 1, 2, 3, 4, 5)( 6, 7,20,16,15), ( 1, 2, 3, 4, 5)( 7, 8, 9,19,20), 
( 1, 2, 3, 4, 5)( 9,10,11,18,17), ( 1, 2, 3, 4, 5)(11,12,13,17,18), 
( 1, 2, 3, 4, 5)(13,14,15,16,17), ( 1, 2, 3, 4, 5)(16,20,19,18,17), (1,6,7,8)
(2,5,4,3), ( 1, 6, 7, 2)( 3,10, 9, 8), ( 1, 6, 7, 8, 2)( 3, 4,12,11,10), 
( 1, 6, 7, 8, 2)( 4, 5,14,13,12), ( 1,15,14, 5)( 2, 6, 7, 8), ( 1, 7, 8, 2)
( 6,20,16,15), ( 1, 6, 8, 2)( 7, 9,19,20), ( 1, 6, 7, 8, 2)( 9,10,11,18,17), 
( 1, 6, 7, 8, 2)(11,12,13,17,18), ( 1, 6, 7, 8, 2)(13,14,15,16,17), 
( 1, 6, 7, 8, 2)(16,20,19,18,17), ( 1, 5, 4, 3)( 2, 8, 9,10), ( 1, 2, 7, 6)
( 3, 8, 9,10), ( 2, 8, 9, 3)( 4,12,11,10), ( 2, 8, 9,10, 3)( 4, 5,14,13,12), 
( 1, 6,15,14, 5)( 2, 8, 9,10, 3), ( 2, 8, 9,10, 3)( 6, 7,20,16,15), 
( 2, 9,10, 3)( 7, 8,19,20), ( 2, 8,10, 3)( 9,11,18,17), ( 2, 8, 9,10, 3)
(11,12,13,17,18), ( 2, 8, 9,10, 3)(13,14,15,16,17), ( 2, 8, 9,10, 3)
(16,20,19,18,17), ( 1, 5, 4, 2)( 3,10,11,12), ( 1, 2, 8, 7, 6)
( 3,10,11,12, 4), ( 2, 3, 9, 8)( 4,10,11,12), ( 3,10,11, 4)( 5,14,13,12), 
( 1, 6,15,14, 5)( 3,10,11,12, 4), ( 3,10,11,12, 4)( 6, 7,20,16,15), 
( 3,10,11,12, 4)( 7, 8, 9,19,20), ( 3,11,12, 4)( 9,10,18,17), ( 3,10,12, 4)
(11,13,17,18), ( 3,10,11,12, 4)(13,14,15,16,17), ( 3,10,11,12, 4)
(16,20,19,18,17), ( 1, 5, 3, 2)( 4,12,13,14), ( 1, 2, 8, 7, 6)
( 4,12,13,14, 5), ( 2, 3,10, 9, 8)( 4,12,13,14, 5), ( 3, 4,11,10)
( 5,12,13,14), ( 1, 6,15,14)( 4,12,13, 5), ( 4,12,13,14, 5)( 6, 7,20,16,15), 
( 4,12,13,14, 5)( 7, 8, 9,19,20), ( 4,12,13,14, 5)( 9,10,11,18,17), 
( 4,13,14, 5)(11,12,17,18), ( 4,12,14, 5)(13,15,16,17), ( 4,12,13,14, 5)
(16,20,19,18,17), ( 1, 4, 3, 2)( 5,14,15, 6), ( 1, 5,14,15)( 2, 8, 7, 6), 
( 1, 5,14,15, 6)( 2, 3,10, 9, 8), ( 1, 5,14,15, 6)( 3, 4,12,11,10), 
( 1,14,15, 6)( 4, 5,13,12), ( 1, 5,14, 6)( 7,20,16,15), ( 1, 5,14,15, 6)
( 7, 8, 9,19,20), ( 1, 5,14,15, 6)( 9,10,11,18,17), ( 1, 5,14,15, 6)
(11,12,13,17,18), ( 1, 5,15, 6)(13,14,16,17), ( 1, 5,14,15, 6)
(16,20,19,18,17), ( 1, 5, 4, 3, 2)( 6,15,16,20, 7), ( 1, 2, 8, 7)
( 6,15,16,20), ( 2, 3,10, 9, 8)( 6,15,16,20, 7), ( 3, 4,12,11,10)
( 6,15,16,20, 7), ( 4, 5,14,13,12)( 6,15,16,20, 7), ( 1, 6,14, 5)
( 7,15,16,20), ( 6,15,16, 7)( 8, 9,19,20), ( 6,15,16,20, 7)( 9,10,11,18,17), 
( 6,15,16,20, 7)(11,12,13,17,18), ( 6,16,20, 7)(13,14,15,17), ( 6,15,20, 7)
(16,19,18,17), ( 1, 5, 4, 3, 2)( 7,20,19, 9, 8), ( 1, 2, 8, 6)( 7,20,19, 9), 
( 2, 3,10, 9)( 7,20,19, 8), ( 3, 4,12,11,10)( 7,20,19, 9, 8), ( 4, 5,14,13,12)
( 7,20,19, 9, 8), ( 1, 6,15,14, 5)( 7,20,19, 9, 8), ( 6, 7,16,15)
( 8,20,19, 9), ( 7,20,19,10,11,18,17, 9, 8), ( 7,20,19, 9, 8)
(11,12,13,17,18), ( 7,20,19, 9, 8)(13,14,15,16,17), ( 7,19, 9, 8)
(16,20,18,17), ( 1, 5, 4, 3, 2)( 9,17,18,11,10), ( 1, 2, 8, 7, 6)
( 9,17,18,11,10), ( 2, 3,10, 8)( 9,17,18,11), ( 3, 4,12,11)( 9,17,18,10), 
( 4, 5,14,13,12)( 9,17,18,11,10), ( 1, 6,15,14, 5)( 9,17,18,11,10), 
( 6, 7,20,16,15)( 9,17,18,11,10), ( 7, 8, 9,17,18,11,10,19,20), 
( 9,18,12,13,17,11,10), ( 9,13,14,15,16,17,18,11,10), ( 9,16,20,19,18,11,10), 
( 1, 5, 4, 3, 2)(11,18,17,13,12), ( 1, 2, 8, 7, 6)(11,18,17,13,12), 
( 2, 3,10, 9, 8)(11,18,17,13,12), ( 3, 4,12,10)(11,18,17,13), ( 4, 5,14,13)
(11,18,17,12), ( 1, 6,15,14, 5)(11,18,17,13,12), ( 6, 7,20,16,15)
(11,18,17,13,12), ( 7, 8, 9,19,20)(11,18,17,13,12), ( 9,10,11,17,13,12,18), 
(11,18,13,12)(14,15,16,17), (11,17,13,12)(16,20,19,18), ( 1, 5, 4, 3, 2)
(13,17,16,15,14), ( 1, 2, 8, 7, 6)(13,17,16,15,14), ( 2, 3,10, 9, 8)
(13,17,16,15,14), ( 3, 4,12,11,10)(13,17,16,15,14), ( 4, 5,14,12)
(13,17,16,15), ( 1, 6,15, 5)(13,17,16,14), ( 6, 7,20,16)(13,17,15,14), 
( 7, 8, 9,19,20)(13,17,16,15,14), ( 9,10,11,18,17,16,15,14,13), (11,12,13,18)
(14,17,16,15), (13,16,15,14)(17,20,19,18), ( 1, 5, 4, 3, 2)(16,17,18,19,20), 
( 1, 2, 8, 7, 6)(16,17,18,19,20), ( 2, 3,10, 9, 8)(16,17,18,19,20), 
( 3, 4,12,11,10)(16,17,18,19,20), ( 4, 5,14,13,12)(16,17,18,19,20), 
( 1, 6,15,14, 5)(16,17,18,19,20), ( 6, 7,20,15)(16,17,18,19), ( 7, 8, 9,19)
(16,17,18,20), ( 9,10,11,18,19,20,16), (11,12,13,17)(16,18,19,20), 
(13,14,15,16)(17,18,19,20) ), 
[ ( 2, 5,17, 3, 7, 6, 9,19,11,13,20,14, 8,16,12)( 4,18,10), 
  ( 1,16,18, 7, 8,14, 6)( 2,15,10, 5,19, 3,12)( 4, 9,20) ] )
gap> Size(G2);
1216451004088320000
gap> FactorsInt(N);
[ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 
  5, 5, 5, 5, 7, 7, 11, 13, 17, 19 ]
gap> IsSimple(G1);
true
gap> quit;