Projective Character Degree Patterns of Groups of Order p 4

Abstract

In Ok (2001), the structure of the Schur multiplier was found for six of the ten non-Abelian groups of order p 4, for p an odd prime number. In this article, using elementary methods, we will establish the structure of the Schur multiplier for the remaining four groups. This subject has only received cursory attention previously and a number of small errors have been made in the existing literature. However, the main result of this article will be to find the projective character degree patterns with multiplicities and the epicentres of all p-groups of order p 4.