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

[Martin Rubey]

"Nicolas M. Thiery" <Nicolas.Thiery at u-psud.fr> writes:

> On Mon, Dec 18, 2017 at 01:57:04PM +0100, Martin Rubey wrote:
>> 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?
>
> The permutation action on the roots would be a rather natural choice.
> This could be extended to affine Weyl groups using affine
> permutations.

Indeed! This leaves the question whether there we can compute a
canonical form for permutation groups up to conjugacy.  I just noticed
that this is a mathoverflow question, too:

https://mathoverflow.net/q/90107/3032

Unfortunately, as of today it doesn't have a straight answer, but maybe
things have changed?

Martin