gap> U:=( 1, 3, 8, 6)( 2, 5, 7, 4)( 9,33,25,17)(10,34,26,18)(11,35,27,19);
(1,3,8,6)(2,5,7,4)(9,33,25,17)(10,34,26,18)(11,35,27,19)
gap> L:=( 9,11,16,14)(10,13,15,12)( 1,17,41,40)( 4,20,44,37)( 6,22,46,35);
(1,17,41,40)(4,20,44,37)(6,22,46,35)(9,11,16,14)(10,13,15,12)
gap> F:=(17,19,24,22)(18,21,23,20)( 6,25,43,16)( 7,28,42,13)( 8,30,41,11);
(6,25,43,16)(7,28,42,13)(8,30,41,11)(17,19,24,22)(18,21,23,20)
gap> R:=(25,27,32,30)(26,29,31,28)( 3,38,43,19)( 5,36,45,21)( 8,33,48,24);
(3,38,43,19)(5,36,45,21)(8,33,48,24)(25,27,32,30)(26,29,31,28)
gap> B:=(33,35,40,38)(34,37,39,36)( 3, 9,46,32)( 2,12,47,29)( 1,14,48,27);
(1,14,48,27)(2,12,47,29)(3,9,46,32)(33,35,40,38)(34,37,39,36)
gap> D:= (41,43,48,46)(42,45,47,44)(14,22,30,38)(15,23,31,39)(16,24,32,40);
(14,22,30,38)(15,23,31,39)(16,24,32,40)(41,43,48,46)(42,45,47,44)
gap>
gap> G:=Group(F,B,L,R,U,D);
<permutation group with 6 generators>
gap>
gap> sgs:=SmallGeneratingSet(G);
[ (1,32,41,3,6,19,35,48,22,27,11,25,9,38,16,33,17,8)(2,15,37,7,5,28,45,23,10,
    20)(4,13,34,44,12,18,26,21,31,42)(14,46,40)(29,36)(39,47),
  (1,43,27,41,11,48)(2,29,23)(3,16,6,32,9,24)(4,20,5,18,21,37,45,15,39)(7,28,
    12,31,44,47,10,13,26)(8,40)(14,25)(17,38,35,30,33,22)(19,46)(34,36,42) ]
gap>
gap> Length(sgs);
2
gap>
gap> a:=L^2*B*R*D^-1*L^-1;
(1,22,32,30,25,27,40)(2,15,12,10,39,42,20,31,28,26,29)(3,14,9,41,38,43,19)(4,
47,23,13,45,21,5,36,34,44,37)(8,33,46,35,16,48,24)
gap>
gap> b:=U*F*R*U*R^-1*U^-1*F^-1;
(3,6,27,11,33,17)(4,18,10,7)(5,26)(8,25,19)
gap>
gap> H:=Group(a,b);
<permutation group with 2 generators>
gap>
gap> G=H;
true
gap>
gap> Size(G)=Size(H);
true
gap>
gap> F:=FreeGroup("a","b");
<free group on the generators [ a, b ]>
gap>
gap> hom := GroupHomomorphismByImages( F, H, GeneratorsOfGroup(F), GeneratorsOfGroup(H) );
[ a, b ] -> [ (1,22,32,30,25,27,40)(2,15,12,10,39,42,20,31,28,26,29)(3,14,9,
    41,38,43,19)(4,47,23,13,45,21,5,36,34,44,37)(8,33,46,35,16,48,24),
  (3,6,27,11,33,17)(4,18,10,7)(5,26)(8,25,19) ]
gap>
gap> PreImagesRepresentative( hom, U );
b*a^2*b*a^-5*b*a^-1*b^-1*(a*b*a)^2*b*a^-2*b*a^-1*b^-1*a*b^-1*a^-1*b^-1*a^3*b^-
1*a^-2*(b^-1*(a*b)^2*a^4*b*a^-6*(b^-1*a^-1*b^-1*a)^2)^2*b^-1*a^3*b*(b*a)^4*a^2
*b^2*a^-3*b*a^-1*b^-1*a^-2*b*a^-5*b*a^-1*b^-1*a*b*(a*b*a^-1*b^-1*a)^2*a*(a*b)^
4*a^3*b^2*a^-3*b*a^-1*b^-1*a^-2*b*a^-5*b*a^-1*b^-1*a*b*(a*b*a^-1*b^-1*a)^2*(a*
(a*b)^4*a^3*b^2*a^-3*b*a^-1*b^-1*a^-2*b*a^-5*b*a^-1*b^-1*a*b*(a*b*a^-1*b^-1*a)
^2*a^2*b^-1*a^-2*b)^2*(a*b)^2*(b*a)^4*a^2*b^2*a^-3*b*a^-1*b^-1*a^-2*b*a^-5*b*a
^-1*b^-1*a*b*(a*b*a^-1*b^-1*a)^2*a^2*b^-1*a^-2*(b*a)^2*a^2*b^3*a^2*b*a^-1*b^-1
*a^22*b*a^-1*b^-1*a^-6*b^-2*a^2*b^-1*(b^-1*a^-1)^2*b^-6*a^4*b*(b*a^4*b*a^-7*b^
-1*a^3)^2*b*((b*a)^4*a^2*b^2*a^-3*b*a^-1*b^-1*a^-2*b*a^-5*b*a^-1*b^-1*a*b*(a*b
*a^-1*b^-1*a)^2*a^2)^2*b^-1*a^-2*b*a^2*b^-1*a^-2*(b*a)^2*b*((b*a)^4*a^2*b^2*a^
-3*b*a^-1*b^-1*a^-2*b*a^-5*b*a^-1*b^-1*a*b*(a*b*a^-1*b^-1*a)^2*a^2)^3*b^-1*a^-
2*((b*a)^2*b)^2*a*b*a^3*b^2*a^-3*b*a^-1*b^-1*a^-2*b*a^-5*b*a^-1*b^-1*a*b*(a*b*
a^-1*b^-1*a)^2*a^2*b^-5*a^-1*b^2*a^-1*b*(a*b*a^2)^2*a*b*a^-1*b*a^13*b*a^-1*b^-
1*a^-11*b*a*b^-1*a^3*(b*a^-1)^2*b^-1*a*b^-1*a^-1*b^-1*a^3*b^-1*a^-2*b^-1*a*b^2
*a*b*a^-1*((b*a)^2*a^3*b*a^-6*(b^-1*a^-1*b^-1*a)^2*b^-1*a)^2*(b*a)^2*b^2*a^4*b
*a^-7*b^-1*(a*b)^3*a^4*b*a^-7*b^-1*a^3*b*(b*a)^4*a^2*b^2*a^-3*b*a^-1*b^-1*a^-2
*b*a^-5*b*a^-1*b^-1*a*b*(a*b*a^-1*b^-1*a)^2*(a*(a*b)^4*a^3*b^2*a^-3*b*a^-1*b^-
1*a^-2*b*a^-5*b*a^-1*b^-1*a*b*(a*b*a^-1*b^-1*a)^2*a^2*b^-1*a^-2*b)^2*(a*b)^2*(
b*a)^4*a^2*b^2*a^-3*b*a^-1*b^-1*a^-2*b*a^-5*b*a^-1*b^-1*a*b*(a*b*a^-1*b^-1*a)^
2*a^2*b^-1*a^-2*b*a^4*b^3*a^2*b*a^-1*b^-1*a^22*b*a^-1*b^-1*a^-6*b^-2*a^2*b^-1*
(b^-1*a^-1)^2*b^-6*a^4*b*(b*a^4*b*a^-7*b^-1*a^3)^2*b*((b*a)^4*a^2*b^2*a^-3*b*a
^-1*b^-1*a^-2*b*a^-5*b*a^-1*b^-1*a*b*(a*b*a^-1*b^-1*a)^2*a^2)^2*b^-1*a^-2*b*a^
2*b^-1*a^-2*(b*a)^2*b*((b*a)^4*a^2*b^2*a^-3*b*a^-1*b^-1*a^-2*b*a^-5*b*a^-1*b^-
1*a*b*(a*b*a^-1*b^-1*a)^2*a^2)^3*b^-1*a^-2*((b*a)^2*b)^2*a*b*a^3*b^2*a^-3*b*a^
-1*b^-1*a^-2*b*a^-5*b*a^-1*b^-1*a*b*(a*b*a^-1*b^-1*a)^2*a^2*b^-1*a^-2*(b*a)^2*
a^3*b*a^-6*(b^-1*a^-1*b^-1*a)^2*b^-1*a*b^2*a*b*a^-1*(b*a)^2*a^3*b*a^-6*(b^-1*a
^-1*b^-1*a)^2*b^-1*(a*b)^2*a^4*b*a^-6*(b^-1*a^-1*b^-1*a)^2*b^-1*a^-1*b^-6*a*b^
6*a^2*b^5*a^-1*b*a*b^-5*a*(b*a^2*b)^2*a^-3*b^4*a^-5*b^-2*a^2*b^-1*(b^-1*a^-1)^
2*b^-6*a^4*b*(b*a^4*b*a^-7*b^-1*a^3)^2*b^2*a^-1*b*a*b^-1*a^-1*b^-1*a*b^3*a^-1*
b*(b*a^3)^2*b*a^-1*b*a^13*b*a^-1*b^-1*a^-11*b*a*b^-1*a^3*(b*a^-1)^2*b^-1*a*b^-
1*a^-1*b^-1*a^3*b^-1*a^-2*b^-1*a*b^2*a*b*a^-1*((b*a)^2*a^3*b*a^-6*(b^-1*a^-1*b
^-1*a)^2*b^-1*a)^2*(b*a)^2*b^2*a^4*b*a^-7*b^-1*(a*b)^3*a^4*b*a^-7*b^-1*a^3*b*(
b*a)^4*a^2*b^2*a^-3*b*a^-1*b^-1*a^-2*b*a^-5*b*a^-1*b^-1*a*b*(a*b*a^-1*b^-1*a)^
2*(a*(a*b)^4*a^3*b^2*a^-3*b*a^-1*b^-1*a^-2*b*a^-5*b*a^-1*b^-1*a*b*(a*b*a^-1*b^
-1*a)^2*a^2*b^-1*a^-2*b)^2*(a*b)^2*(b*a)^4*a^2*b^2*a^-3*b*a^-1*b^-1*a^-2*b*a^-
5*b*a^-1*b^-1*a*b*(a*b*a^-1*b^-1*a)^2*a^2*b^-1*a^-2*b*a^4*b^3*a^2*b*a^-1*b^-1*
a^22*b*a^-1*b^-1*a^-6*b^-2*a^2*b^-1*(b^-1*a^-1)^2*b^-6*a^4*b*(b*a^4*b*a^-7*b^-
1*a^3)^2*b*((b*a)^4*a^2*b^2*a^-3*b*a^-1*b^-1*a^-2*b*a^-5*b*a^-1*b^-1*a*b*(a*b*
a^-1*b^-1*a)^2*a^2)^2*b^-1*a^-2*b*a^2*b^-1*a^-2*(b*a)^2*b*((b*a)^4*a^2*b^2*a^-
3*b*a^-1*b^-1*a^-2*b*a^-5*b*a^-1*b^-1*a*b*(a*b*a^-1*b^-1*a)^2*a^2)^3*b^-1*a^-2
*((b*a)^2*b)^2*a*b*a^3*b^2*a^-3*b*a^-1*b^-1*a^-2*b*a^-5*b*a^-1*b^-1*a*b*(a*b*a
^-1*b^-1*a)^2*a^2*b^-1*a^-2*(b*a)^2*a^3*b*a^-6*(b^-1*a^-1*b^-1*a)^2*b^-1*a*b^2
*a*b*a^-1*(b*a)^2*a^3*b*a^-6*(b^-1*a^-1*b^-1*a)^2*b^-1*(a*b)^2*a^4*b*a^-6*(b^-
1*a^-1*b^-1*a)^2*b^-1*a^-1*b^-6*a*b^6*a^2*b^5*a^-1*b*a*b^-5*a^-1*b^-1*(a^-1*b^
-1*a*b^2)^2*b^4