Dear GAP Forum members,

this is probably a stupid question, but I'm only a poor engineer
without any strong mathematical background hardly understanding
what I am doing with group theory...

I want to use GAP(4r2) with grape to to construct a CayleyGraph
for the group PGL(2,q). My generators are a set of matrices of the
form [[a*Z(q)^0, b*Z(q)^0], [c*Z(q)^0, d*Z(q)^0]] which are Elements
of PGL(2,q).

When I create the PGL by
gap> Pgl:=PGL(2,q);
it seems, that I get an isomorphic permutation group.
gap> P:=PGL(IsMatrixGroup,2,13);
seems not to work. Also, if I do something like
gap> G:=GL(2,13);
gap> c:=Center(Gl);
gap> P:=FactorGroup(Gl,c);
I get again an isomorphic permutation group.
Now my question: How can I find the proper homomorphism to convert
the generators from the form [[a*Z(q)^0, b*Z(q)^0], [c*Z(q)^0, d*Z(q)^0]]
to a form suitable for the isomorphic permutation group representation
that is used by GAP for the PGL in order to use them with the
CayleyGraph-Function from grape.

I would be very grateful if somebody could give me a hint, even if
this question seems to be very stupid.

Thanks in advance and best Regards,
Georg