Finite groups of non-prime-power order with exactly four character codegrees

Abstract: For an irreducible complex character (\chi) of a finite group (G), the \emph{codegree} of (\chi) is defined as the ratio (|G : \ker(\chi)| / \chi(1)), where (\ker(\chi)) represents the kernel of (\chi). In this paper, we provide a detailed characterization of finite groups of non-prime power order that have exactly four irreducible character co-degrees.