[GAP Forum] FactorGroup of permutation groups

[Hulpke,Alexander]

Dear Forum, Dear Tim Kohl,

If N, H are permutation groups with H normal in N
and one computes FactorGroup(N,H) the result is expressed
in terms of generators and relations.

I suspect it is a PcGroup (which happens i factor is solvable). Otherwise it will be a permutation group.

Is there a way to
correlate the generators of FactorGroup(N,H) with a
transversal of H in N?

So you probably want the permutation action of N on the cosets of H. You can get it as `FactorCosetAction(N,H)` with the numbering of points corresponding to `RightTransversal(N,H)`.

All the best,

  Alexander Hulpke

The reason I'm asking is that N acts transitively
on a collection of groups with H as the stabilizer
and I want to study the induced action of N/H (and most
importantly subgroups thereof) as it is substantially smaller.

Thanks.

-Tim K.

– Colorado State University, Department of Mathematics, Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523–1874, USA email: hulpke at colostate.edu, http://www.math.colostate.edu/~hulpke