# Class function

In mathematics, especially in the fields of group theory and representation theory of groups, a **class function** is a function on a group *G* that is constant on the conjugacy classes of *G*. In other words, it is invariant under the conjugation map on *G*. Such functions play a basic role in representation theory.

When *K* is the real numbers or the complex numbers, the inner product is a non-degenerate Hermitian bilinear form.