Non-solvable groups having five irreducible character degrees

Abstract

Let G be a finite group and let be the set of degrees of complex irreducible characters of G. An important program in character theory is to obtain the structure of G when is known. In this article, we consider a dual version of this approach. Indeed, we consider non-solvable groups with five character degrees and present a description of the set of character degrees for such groups. As an application of this result, it is shown that a finite group with five character degrees and containing no prime power must be a solvable group.