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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 .

On G -character tables for normal subgroups