[GAP Forum] subgroup of fp-group from coset table

[Derek Holt]

Dear GAP forum,

I would be grateful if someone could help me with the technicalities of the
following problem.

I have a homomorphism f: F -> G from a finitely presented group F to a
transitive permutation group G. I want to find the inverse image under f
of a point stabilizer in G. It is straightforward to do this in theory
using Schreier generators,  but I am uncertain of the most efficient way
of programming this in GAP.

I want to regard the images of the generators of f as a coset table for F,
and then define the subgroup using the coset table. Perhaps the GAP function

SubgroupOfWholeGroupByCosetTable

is the one to use, but this take a "family of a fp group" and a coset table
as arguments. I don't know what is meant by a "family of a fp group" (why
doesn't it just take F as argument?) and I would be grateful for help
in computing the coset table defined by f in GAP.

Thanks!
Derek.