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 ofý ýsubgroups of Gý. ýThe matrix whose H,K-entry is the number of ýfixed points of the set G/K under the action of H is called theý ýtable of marks of G where H,K run through all elements iný C(G)ý. 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.