[GAP Forum] Conjugacy classes in projective general linear groups...

[Gordon Royle]

I am doing some Polya style counting involving sets of points in  
projective spaces ...

This involves computing the cycle-index of various projective general  
linear groups, which in turn involves computing the conjugacy classes  
of these groups.

But using ConjugacyClasses becomes slow or impossible when the group  
starts to get large... even PGL(6,5) hasn't finished after a couple  
of hours...

Of course, ProjectiveGeneralLinearGroup returns the group just as any  
old permutation group, and then ConjugacyClasses uses general  
permutation group methods, so I am throwing away a whole lot of  
information about the special nature of this situation, hence my  
question is:

Q: These groups are central to everything, so are there specialized  
methods / specialized knowledge about these particular groups that I  
can look up and use?


(There is a website http://www.uni-graz.at/~fripert/fga/k1zyklap.html  
that purports to calculate these, but it doesn't seem to work; the  
associated paper is there, but would take a long time to work through)


Thanks

Gordon

--
Associate Professor Gordon Royle
Department of Computer Science & Software Engineering
University of Western Australia
http://people.csse.uwa.edu.au/gordon