The k-characters are class functions on subsets of Gk called the k-classes of G.For a finite group G,the k-class sums form a basis for a subring of CGk,which we call the k-S-ring of G,and we think of these rings as generalized centralizer rings.We show that for a finite group G the 3-S-ring determines G.More specifically,the group characters and set products of certain 3-classes of G,which we call "uniform 3-classes",determine G.