I have been having trouble using GroupHomomorphismByImages, which seems
to take a very long time in a fairly straightforward situation. Here is
an example:

g:=Group((1,2,3,4,5,6),(1,2));
R:=[];
for k in [1..2] do
   M:=NullMat(6,6,GF(3));
   for i in [1..6] do
      j:=i^g.generators[k];
      M[i][j]:=Z(3)^0;
   od;
   R[k]:=M;
od;
GroupHomomorphismByImages(g,GeneralLinearGroup(6,3),g.generators,R);

This piece of code sets up a pair of matrices R{1] and R[2] which represent
the permutation action of the two generators of the symmetric group of
degree 6 on the natural permutation representation. Everything except the
last line takes hardly any time. The final line then takes some minutes
to run.

Evidently GroupHomomorphismByImages is doing a lengthy computation, but
by looking at the manual I can't tell what it is. From looking at
interrupt messages it appears to be computing a stablizer chain. I can think
of several things it might be doing that would take rather a long time, but
am not sure which is actually taking place.
Could you please shed some light on this situation?

My main aim is to set up a record which stores some of the information
in GroupHomomorphismByImages, but I don't necessarily need all this
information. Is there any way to bypass the computation that
GroupHomomorphismByImages is doing?

I am running version 3.2 of GAP without any of the subsequent patches.

With thanks for your help,
Luis Valero
valero@math.umn.edu
School of Mathematics, University of Minnesota, Minneapolis MN 55455