[GAP Forum] order of conjugacy classes?

[Russ Woodroofe]

Dear Keith, all,
Did you try using
Set(ConjugacyClassesMaximalSubgroups(G));
?

That sorts them by the < order (see 4.2 from the docs), and I believe that it should be consistent.  (I'm shocked that this isn't already applied -- you can check whether they are already sorted with IsSet.)

Do you have a concrete example where ConjugacyClassesMaximalSubgroups doesn't return the same order every time?
Best,

  --Russ

> On 17 Jun 2022, at 16:07, R. K. Dennis <gap at rkd.math.cornell.edu> wrote:
> 
> Dear Colleagues,
> 
> I have a computation where the results are stored and displayed
> in a max by conj matrix.  Here max is the number of conjugacy
> classes of maximal subgroups and conj is the number of conjugacy
> classes of elements.
> 
> The orders of the rows and columns corresponds to the classes.
> 
> But gap doesn't generate the conjugacy classes of maximal subgroups
> in the same order every time; I don't know about classes of elements
> as I haven't noticed any difference in the matrix (but I suppose
> that might depend of the type of computations I'm doing).
> 
> Ok, so my question is:
> 
> Is there a way to get gap to present the results in the same order
> every time?  I suppose I could sort the results by order of subgroup
> size.  But that wouldn't necessarily uniquely order the representatives
> of the conjugacy classes of maximal subgroups.
> 
> Is there anything reasonable to do?
> 
> For conjugacy classes of elements, gap doesn't seem to sort by
> size or order, but does seem reasonably consistent, at least for
> the small examples I've looked at.
> 
> Suggestions most welcome!
> 
> Thanks!
> 
> Keith
> 
> 
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