# How do I find the irreducible representations of a group of matrices?

I have a set of permutation matrices (n x n) of a graph which form a group (the automorphisms). They are obviously a subgroup of the symmetric group S_n. Is there a way to find the irreducible representations of this group of matrices or, probably just as good, the characters of the irreducible representations?

I am new to this area of group theory (the symmetric group and subgroups) although I know about other finite groups used in the crystallographic symmetry groups along with the usual Schur's lemma, great orthogonality theorem, etc.

Any help or pointers greatly appreciated.

Thanks.

-
This has been discussed on MO a while ago. Searching with Google should unearth useful information. – Mariano Suárez-Alvarez Aug 3 '12 at 15:28
A standard strategy is to find subgroups or quotient groups whose representations you understand and induct or restrict their representations. See, for example, en.wikipedia.org/wiki/… . – Qiaochu Yuan Aug 3 '12 at 17:20
Every finite group is a subgroup of some symmetric group. Without further information, you are simply asking how to compute the irreducible representation of some given finite group. Have a look at one of the standard books on character theory, such as Serre, or Isaacs. – Alex B. Aug 3 '12 at 21:27
As Mariano said, check mathoverflow.net/questions/86019/…. For particular examples, you can use GAP function IrreducibleRepreentations. – Leandro Vendramin Aug 4 '12 at 12:27