[GAP Forum] Finite irreducible subgfroups of SL_4(C)

[Burkhard Höfling]

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.