[GAP Forum] Canonical form for some small groups and efficient characterisation of the generalized symmetric groups

[Martin Rubey]

Dear Thomas,

Thomas Breuer <sam at Math.RWTH-Aachen.De> writes:

> When groups arise as symmetries of finite sets such as the vertices
> of graphs then it is more natural to consider *permutation isomorphism*
> (that is, conjugacy in the symmetric group on the given points).

Indeed, this might be another interesting collection, possibly even more
interesting!  That would be A000638.

Is there (some sort of) a canonical form for these?

I admit I am not completely sure right now: can we associate a conjugacy
class of subgroups of S_n, isomorphic to the Weyl group, in a sensible
way to a finite Cartan type?

> GAP's library of transitive groups provides a reasonable source of
> small groups in this sense.

Thanks for the hint, I'll have a look!

Best,

Martin