Finite groups with coprime non-linear codegrees

Abstract: Given a finite group G with an irreducible character \chi \in Irr(G), the codegree of \chi is defined by cod(\chi) = |G :\ker \chi|/\chi(1). The set of non-linear irreducible character codegrees of G is denoted by cod(G|G'). In this note, we classify all finite groups G with |cod(G|G')|> 1 and for each pair of distinct elements m, n \in cod(G|G'), m and n are coprime.