[GAP Forum] AllHomomorphismClasses too slow

[Ignat Soroko]

Dear GAP community,

I am trying to work with all homomorphisms from a finitely presented
group to the symmetric groups of small degree. The following sequence
of commands

F:=FreeGroup("a","b","c","d");;
AssignGeneratorVariables(F);;
rel:=[a*b*a*b^-1*a^-1*b^-1,b*c*b*c*b^-1*c^-1*b^-1*c^-1,c*d*c*d^-1*c^-1*d^-1,
a*c*a^-1*c^-1,a*d*a^-1*d^-1,b*d*b^-1*d^-1,(a*b*c*d)^6];
G:=F/rel;S3:=SymmetricGroup(3);
AHC:=AllHomomorphismClasses(G,S3);

did not produce any result in more than 6 hours.

If I feed it into Magma calculator here:
http://magma.maths.usyd.edu.au/calc/

G<a,b,c,d>:=Group<a,b,c,d|a*b*a*b^-1*a^-1*b^-1,b*c*b*c*b^-1*c^-1*b^-1*c^-1,
c*d*c*d^-1*c^-1*d^-1,a*c*a^-1*c^-1,a*d*a^-1*d^-1,b*d*b^-1*d^-1,(a*b*c*d)^6>;
S:=SymmetricGroup(3);
homs:=Homomorphisms(G,S:Surjective:=false);
homs;

the result is instant (10 homomorphisms).

What am I doing wrong? I've always thought that GAP and Magma are
having roughly the same functionality, when it comes to dealing with
groups. How can I make GAP return a result faster?

Thank you!

Best,
Ignat