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

[Rubey Martin]

Dear Max,

>>> The permutation action on the roots would be a rather natural choice.

> Regarding Nicolas' suggestion: While it is a "natural" choice, it is not
> necessarily a "canonical" choice. At the very least, you'd have to define
> how to label the roots "canonically".

let me ask: are you saying that that there are both "bad" but also
"canonical labellings" of the roots?  (let's consider only finite type)

Or put differently: do you have an example at hand where different labellings
of the roots yield non-conjugate permutation groups?

Martin