On 03.06.2009, at 15:31, Shou-Jen Hu wrote:
Dear All:
Is it possible to find all finite irreducible subgroups of SL_4(C)
in GAP?
Dear Shou-Jen Hu,
I suppose you mean the speclial linear group over the complex numbers.
Then the answer is no - if only for the reason that there are
infinitely many (imprimitive) ones, up to conjugacy in GL (or SL).
There is a (hand) classification of the finite imprimitive
irreducible subgroups of GL_4(C) by Dane Flannery and me (J. Algebra
218 (1999), 436–469 and J. Algebra 236, 419–470 (2001)), but
unfortunately the data is not available in GAP.
However, you could probably work out the subgroups of SL_4(C) from
these lists together with the (classical) results on primitive
subgroups of SL_4(C).
Regards,
Burkhard Höfling.
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