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

unfortunately 'GroupHomomorphismByImages' has a lot of hidden
pitfalls, we are still trying to clean this up. The following is
going wrong: the function tries to decide if the set <R> is a subset
if the general linear group, although this should be straight forward,
this is done at the moment using a permutation representation for GL.
You can avoid this check by calling

h := g.operations.GroupHom..(g,GL(6,3),g.generators,R)

directly instead of

GroupHomomorphismByImages(g,GeneralLinearGroup(6,3),g.generators,R);

Could you please shed some light on this situation?
in GroupHomomorphismByImages, but I don't necessarily need all this
information. Is there any way to bypass the computation that
GroupHomomorphismByImages is doing?

However, this is still not good enough, because 'GroupHom..'
does not trust you. You must set

h.isMapping := true;
h.isHomomorphism := true;
h.isGroupHomomorphism := true;

in order to avoid unnecessary calculations. 'GL' and 'GroupHom...'
will be changed to be more user friendly, but I am afraid that
this will happen *after* the release of 3.3.

best wishes
Frank Celler