Again I am a bit confused and would appreciate some pointers on how best
to do the following.

Note: I have not yet done either of the upgrades and that might be my
problem. We are going to install Gap in a different place and I am
waiting on the upgrade until we move it.

I have a finitely presented group (it's M11) and a subgroup. I use
OperationCosetsFpGroup to get the permutation representation on the
cosets of the subgroup.

1. OperationHomomorphism does not produce the homomorphism I want.
I just get an error message that the permutation group is the wrong
kind of thing. Why doesn't this work? (Even if it's not designed to,
I think it should, just so one can do what I'm trying to do here.)

2. I use GroupHomomorphismByImages to produce the homomorphism I want
anyway. As recommended, I set the field isMapping to true. I then
try to compute an image: Image(f,a). Since a is one of the original
abstract generators, this should be trivial and instantaneous. It's
not. After waiting a bit, I abort this operation and use
ImagesRepresentative instead. This gives an immediate answer. Why
is Image not working here?

Generally, I would think that for efficient computations one wants to
use some small-degree permutation represenation of the group. Yet one
also must keep some connection to the original presentation of the
group in most cases. This is all I'm trying to do here. If there's a
better way, or this is the wrong idea, please let me know.

David Sibley
sibley@math.psu.edu