We talk about the `canonical decomposition' of a finite dimensional complex representation of a finite group.
Next, we proceed to the `Dimension theorem' (also known as the `Frobenius divisibility theorem') that says, the dimension of an irreducible finite dimensional complex representation of a finite group G divides the order of G. In this lecture, we only state the theorem and see some standard applications. We also deduce the corollary that no finite simple group can have an irreducible representation of dimension 2. The proof of the above theorem will be provided in the next lecture.
