Class function
In mathematics, a class function in group theory is a function f on a group G, such that f is constant on the conjugacy classes of G. In other words, f is invariant under the conjugation map on G. Such functions play a basic role in representation theory.
In fact the character of a linear representation of G over a field K is always a class function with values in K. The class functions form the center of the group ring K[G].