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.

flag	asked Aug 3 at 15:15 unknown (yahoo) 1

This has been discussed on MO a while ago. Searching with Google should unearth useful information. – Mariano Suárez-Alvarez Aug 3 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/Brauer's_theorem_on_induced_characters . – Qiaochu Yuan Aug 3 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 Bartel Aug 3 at 21:27

As Mariano said, check mathoverflow.net/questions/86019/…. For particular examples, you can use GAP function IrreducibleRepreentations. – Leandro Vendramin Aug 4 at 12:27

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