On G-Character Tables For Normal Subgroups

Abstract

Let N be a normal subgroup of a finite group G. From a result due to Brauer, it can be derived that the character table of G contains square submatrices which are induced by the G-conjugacy classes of elements in N and the G-orbits of irreducible characters of N. In the present paper, we provide an  alternative approach to this fact through the structure of the group algebra. We also show that such matrices are non-singular and become a useful tool  to obtain information of N from the character table of G.