[GAP Forum] ConjugacyClassesSubgroups

[Hulpke,Alexander]

Dear Forum, Dear Tim Kohl,

On December 2, 2020 at 3:48:28 PM, tkohl at math.bu.edu (tkohl at math.bu.edu<mailto:tkohl at math.bu.edu>) wrote:

Is there a way to call ConjugacyClassesSubgroups with
a fixed size for the subgroups desired, so as to avoid
having it spend time computing those of other sizes?

One can do so, with some contortions, but the interface is not to `ConjugacyClassesSubgroups` but to underlying algorithms. Also all calculations build subgroups inductively, and so some subgroups might be needed ``on the way’’, even if you do not care for them.

The four underlying algorithms are:

- Table lookup (for almost simple groups)

- Cyclic extension (for almost simple groups, not tabulated)

- A ``lifting’’ type algorithm for solvable groups (`SubgroupsSolvableGroups`)

- A liftiting type algorithm for nonsolvable groups

I will put a survey of mine (Calculating Subgroups with GAP) on arXiv that gfives more details. If you want, send me an email with a bit more detail of what you are looking for in which kinds of groups, and I might be able to give you a description of which algorithm to call how.

All the best,

  Alexander Hulpke


– 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