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

[Rubey Martin]

> The bad news is that there is apparently no canonical form for permutation
> groups up to conjugacy.

> Indeed, the best thing would be what you called an "intrinsic" canonical form:
> a function f: permutation groups up to conjugacy -> strings such that

> * f(G) can be computed in sensible time
> * f(G) = f(H) if and only if G and H are conjugate

> It would be even better, if

> * f has an inverse, that is, I can reconstruct G from f(G) in reasonable time
> * f(G) is human readable

In fact, from a combinatorial point of view the most natural thing would be to
have a canonical form for "conjugacy classes of connected permutation groups"

Initially there are not all that many - until the numbers explode: https://oeis.org/A005226

Martin