[GAP Forum] Characters of unitary groups

[Iverson, Joseph W [MATH]]

Dear GAP forum,

I would like to compute some stuff involving character tables of finite unitary groups, the smallest of which is GU(4,5). "Compute some stuff" means I need to be able to input a 4x4 matrix over GF(5^2) and get the value of any irreducible character as an output. Short of that, I would be happy with an ordered list of conjugacy class representatives for the table's columns. If I understand GAP terminology correctly, then I am asking for a character table with a stored group.
 
I have the impression that GAP's character table library should be able to help me. However:
1. I can't tell from the documentation how to ask it for the character table of GU(4,5).
2. I'm not sure if the library can give me a table with a stored group.

If what I want is computationally infeasible (e.g. since GU(4,5) has order around 177 trillion), then that would be good to know, too.

All the best,
Joey Iverson

Assistant Professor
Department of Mathematics
Iowa State University