Daniel Ruberman writes in his e-mail message of 1993/04/22

Are there any plans to implement the command GroupHomomorphismByImages
for homomorphisms of Finitely Presented groups to, say, permutation groups?

Which version of GAP do you use. In GAP 3.2 you can do the following

gap> g := FreeGroup( 2, "g" );;
gap> g.relators := [ g.1^2, g.2^5, (g.1*g.2^-1)^3 ];;
gap> h := Group( (1,2)(3,4), (1,2,3,4,5) );;
gap> f := GroupHomomorphismByImages( g, h, g.generators, h.generators );;
gap> IsHomomorphism( f );
true
gap> PreImages( f, SylowSubgroup( h, 2 ) );
Subgroup( Group( g.1, g.2 ),
[ g.1^-1*g.2^-3*g.1^-1*g.2^-2*g.1^-1*g.2^-3*g.1^-1*g.2^-2*g.1^-1*\
  g.2^-1*g.1^-1*g.2^-1, g.2^-2*g.1^-1*g.2^-1*g.1^-1 ] )
gap> Index( g, last );
15

Is this not what you want?

Martin.

-- .- .-. - .. -.  .-.. --- ...- . ...  .- -. -. .. -.- .-
Martin Sch"onert,   Martin.Schoenert@Math.RWTH-Aachen.DE,  +49 241 804551
Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, D 51 Aachen, Germany