On the Mark and Markaracter Tables of Finite Groups

Let g be a finite group and c(g) be the family of representative conjugacy classes of subgroups of g . the matrix whose h,k-entry is the number of fixed points of the set g/k under the action of h is called the table of marks of g where h,k run through all elements in c(g) . shinsaku fujita for the first time introduced the term “markaracter” to discuss marks for permutation representations and characters for linear representations in a common basis. in this paper, we compute these tables for some classes of finite groups.