The number of irreducible characters
We devote this chapter to the theorem which states that the number of irreducible characters of a finite group is equal to the number of conjugacy classes of the group, and to some consequences of this theorem. Together with the material from Chapter 14, the theorem provides machinery for investigating characters which is used in the remainder of the book.
Throughout, G is as usual a finite group.
A class function on G is a function ψ: G → such that ψ(x) = ψ(y) whenever x and y are conjugate elements of G (that is, ψ is constant on conjugacy classes).