Frobenius Group - Representation Theory

Representation Theory

The irreducible complex representations of a Frobenius group G can be read off from those of H and K. There are two types of irreducible representations of G:

• Any irreducible representation R of H gives an irreducible representation of G using the quotient map from G to H (that is, as a restricted representation). These give the irreducible representations of G with K in their kernel.
• If S is any non-trivial irreducible representation of K, then the corresponding induced representation of G is also irreducible. These give the irreducible representations of G with K not in their kernel.