U:=( 1, 3, 8, 6)( 2, 5, 7, 4)( 9,33,25,17)(10,34,26,18)(11,35,27,19);
L:=( 9,11,16,14)(10,13,15,12)( 1,17,41,40)( 4,20,44,37)( 6,22,46,35);
F:= (17,19,24,22)(18,21,23,20)( 6,25,43,16)( 7,28,42,13)( 8,30,41,11);
R:=(25,27,32,30)(26,29,31,28)( 3,38,43,19)( 5,36,45,21)( 8,33,48,24);
B:=(33,35,40,38)(34,37,39,36)( 3, 9,46,32)( 2,12,47,29)( 1,14,48,27);
D:=(41,43,48,46)(42,45,47,44)(14,22,30,38)(15,23,31,39)(16,24,32,40);
bc:=[U*L*U^(-1)*L^(-1),U*R*U^(-1)*R^(-1),U*D*U^(-1)*D^(-1),U*F*U^(-1)*F^(-1),
U*B*U^(-1)*B^(-1),F*L*F^(-1)*L^(-1),R*L*R^(-1)*L^(-1),D*L*D^(-1)*L^(-1),
B*L*B^(-1)*L^(-1),F*R*F^(-1)*R^(-1),B*R*B^(-1)*R^(-1),D*R*D^(-1)*R^(-1),
B*F*B^(-1)*F^(-1),D*F*D^(-1)*F^(-1),B*D*B^(-1)*D^(-1)];

gens:=[U,U^(-1),D,D^(-1),F,F^(-1),B,B^(-1),L,L^(-1),R,R^(-1)];;
bcs:=List(gens,x->List(gens,y->x*y*x^(-1)*y^(-1)));;
bcs:=Flat(bcs);;
bcs:=AsSet(bcs);
bcs_cube := Group(bcs);;

bc_cube := Group(bc);;
cube := Group(U,L,F,R,B,D);;

N0:= Size( bcs_cube );
Collected( Factors(N0) );

N1:= Size( bc_cube );
Collected( Factors(N1) );

N2:=Size( cube );
Collected( Factors(N2) );