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.