gap> g1 := (7,9,11,13,15)(6,8,10,12,14);
( 6, 8,10,12,14)( 7, 9,11,13,15)
gap> g2 := (16,19,10,4,14)(3,5,15,20,9);
( 3, 5,15,20, 9)( 4,14,16,19,10)
gap> grp := Group(g1,g2);
Group( ( 6, 8,10,12,14)( 7, 9,11,13,15), ( 3, 5,15,20, 9)( 4,14,16,19,10) )
gap> n:=Size(grp);
20160
gap> g3:=(1,7,19,11,4)(20,18,12,5,6);
( 1, 7,19,11, 4)( 5, 6,20,18,12)
gap> grp := Group(g1,g2,g3);
Group( ( 6, 8,10,12,14)( 7, 9,11,13,15), ( 3, 5,15,20, 9)( 4,14,16,19,10), 
( 1, 7,19,11, 4)( 5, 6,20,18,12) )
gap> n:=Size(grp);
46448640
gap> g4:=(5,2,9,18,13)(19,17,14,1,8);
( 1, 8,19,17,14)( 2, 9,18,13, 5)
gap> grp := Group(g1,g2,g3,g4);
Group( ( 6, 8,10,12,14)( 7, 9,11,13,15), ( 3, 5,15,20, 9)( 4,14,16,19,10), 
( 1, 7,19,11, 4)( 5, 6,20,18,12), ( 1, 8,19,17,14)( 2, 9,18,13, 5) )
gap> n:=Size(grp);
928972800
gap> Factors(n);
[ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 5, 5, 7 ]
gap> g5:=(1,3,11,17,15)(6,2,10,17,16);
Error, Perm: cycles must be disjoint
gap> grp := Group(g1,g2,g3,g4,g5);
Error, Variable: 'g5' must have a value
gap> g5:=(1,3,11,17,15)(6,2,10,18,16);
( 1, 3,11,17,15)( 2,10,18,16, 6)
gap> grp := Group(g1,g2,g3,g4,g5);
Group( ( 6, 8,10,12,14)( 7, 9,11,13,15), ( 3, 5,15,20, 9)( 4,14,16,19,10), 
( 1, 7,19,11, 4)( 5, 6,20,18,12), ( 1, 8,19,17,14)( 2, 9,18,13, 5), 
( 1, 3,11,17,15)( 2,10,18,16, 6) )
gap> n:=Size(grp);
928972800
gap> Orbits(grp,[1..20]);
[ [ 1, 7, 8, 3, 9, 19, 10, 5, 11, 18, 17, 12, 4, 15, 6, 2, 13, 16, 14, 20 ] ]
gap> orb := last[1];
[ 1, 7, 8, 3, 9, 19, 10, 5, 11, 18, 17, 12, 4, 15, 6, 2, 13, 16, 14, 20 ]
gap> blocks := Blocks(grp,orb);
[ [ 1, 18 ], [ 7, 12 ], [ 8, 13 ], [ 3, 16 ], [ 9, 14 ], [ 5, 19 ], 
  [ 10, 15 ], [ 6, 11 ], [ 2, 17 ], [ 4, 20 ] ]
gap> op := Operation(grp,blocks,OnSets);
Group( ( 2, 5, 8, 3, 7), ( 4, 6, 7,10, 5), ( 1, 2, 6, 8,10), 
( 1, 3, 6, 9, 5), ( 1, 4, 8, 9, 7) )
gap> Size(op);
1814400
gap> Factorial(12);
479001600
gap> Factorial(10);
3628800
gap> Factorial(10)/2;
1814400
gap> m:=Factorial(10)/2;
1814400
gap> Factors(n/m);
[ 2, 2, 2, 2, 2, 2, 2, 2, 2 ]
gap> Print("test");
testgap> 
gap> Print("test/n");
test/ngap> Print("test\n");
test
gap> Print("grp=A10 semidirect C2^9\n");
grp=A10 semidirect C2^9
gap> g6:=(7,2,4,13,16)(3,12,17,20,8);
( 2, 4,13,16, 7)( 3,12,17,20, 8)
gap> grp := Group(g1,g2,g3,g4,g5,g6);
Group( ( 6, 8,10,12,14)( 7, 9,11,13,15), ( 3, 5,15,20, 9)( 4,14,16,19,10), 
( 1, 7,19,11, 4)( 5, 6,20,18,12), ( 1, 8,19,17,14)( 2, 9,18,13, 5), 
( 1, 3,11,17,15)( 2,10,18,16, 6), ( 2, 4,13,16, 7)( 3,12,17,20, 8) )
gap> n:=Size(grp);
928972800
gap> n1:=9627755206121277812101663948800000;
9627755206121277812101663948800000
gap> n2:=10712468422656000;
10712468422656000
gap> Factors(n1/(n*n2));
[ 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3 ]
gap> Print("G allows the corners to be twisted in pairs?\n");
G allows the corners to be twisted in pairs?
gap> Print("G allows the edges to be flipped in pairs?\n");
G allows the edges to be flipped in pairs?
gap> Print("G allows the edges to be flipped in pairs? (14 pairs?)\n");
G allows the edges to be flipped in pairs? (14 pairs?)
gap> oph := OperationHomomorphism(grp,op);
OperationHomomorphism( Group( ( 6, 8,10,12,14)( 7, 9,11,13,15), 
( 3, 5,15,20, 9)( 4,14,16,19,10), ( 1, 7,19,11, 4)( 5, 6,20,18,12), 
( 1, 8,19,17,14)( 2, 9,18,13, 5), ( 1, 3,11,17,15)( 2,10,18,16, 6), 
( 2, 4,13,16, 7)( 3,12,17,20, 8) ), Group( ( 2, 5, 8, 3, 7), 
( 4, 6, 7,10, 5), ( 1, 2, 6, 8,10), ( 1, 3, 6, 9, 5), ( 1, 4, 8, 9, 7) ) )
gap> ker := Kernel(oph);
Subgroup( Group( ( 6, 8,10,12,14)( 7, 9,11,13,15), ( 3, 5,15,20, 9)
( 4,14,16,19,10), ( 1, 7,19,11, 4)( 5, 6,20,18,12), ( 1, 8,19,17,14)
( 2, 9,18,13, 5), ( 1, 3,11,17,15)( 2,10,18,16, 6), ( 2, 4,13,16, 7)
( 3,12,17,20, 8) ), [ ( 2,17)( 4,20), ( 1,18)( 4,20), 
  ( 1,18)( 2,17)( 4,20)( 7,12), ( 4,20)( 8,13), ( 1,18)( 2,17)( 3,16)( 4,20), 
  ( 2,17)( 3,16)( 4,20)( 7,12)( 8,13)( 9,14), ( 1,18)( 2,17)( 5,19)( 8,13), 
  ( 2,17)( 3,16)( 7,12)(10,15), ( 1,18)( 4,20)( 6,11)( 7,12) ] )
gap> Size(ker);
512
gap> IsElementaryAbelian(ker);
true
gap> Factors(512);
[ 2, 2, 2, 2, 2, 2, 2, 2, 2 ]
gap> blocks;
[ [ 1, 18 ], [ 7, 12 ], [ 8, 13 ], [ 3, 16 ], [ 9, 14 ], [ 5, 19 ], 
  [ 10, 15 ], [ 6, 11 ], [ 2, 17 ], [ 4, 20 ] ]
gap> rep := List(blocks,x->x[1]);
[ 1, 7, 8, 3, 9, 5, 10, 6, 2, 4 ]
gap> rep := Set(List(blocks,x->x[1]));
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]
gap> stab := Stabilizer(grp,rep,OnSets);
Subgroup( Group( ( 6, 8,10,12,14)( 7, 9,11,13,15), ( 3, 5,15,20, 9)
( 4,14,16,19,10), ( 1, 7,19,11, 4)( 5, 6,20,18,12), ( 1, 8,19,17,14)
( 2, 9,18,13, 5), ( 1, 3,11,17,15)( 2,10,18,16, 6), ( 2, 4,13,16, 7)
( 3,12,17,20, 8) ), [ ( 8, 9,10)(13,14,15), ( 7, 8)( 9,10)(12,13)(14,15), 
  ( 6, 7)( 9,10)(11,12)(14,15), ( 5, 6)( 9,10)(11,19)(14,15), 
  ( 4, 5)( 9,10)(14,15)(19,20), ( 3, 4)( 9,10)(14,15)(16,20), 
  ( 2, 3)( 9,10)(14,15)(16,17), ( 1, 2)( 9,10)(14,15)(17,18) ] )
gap> Size(stab);
1814400
gap> Size(grp)/(Size(stab)*Size(ker));
1
gap> quit;