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
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