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 ] . RSS class functions Categories : Group theory 