Let G be a finite group and cd(G) denote the set of complex irreducible character degrees of G. Huppert conjectured that if H is a finite nonabelian simple group such that cd(G) = cd(H), then G ∼ = H × A, where A is an abelian group. In this talk, provide some examples that we cannot extend this conjecture to almost simple groups. Moreover, we show that if G is a finite group and H is an almost simple group whose socle is H 0 is a sporadic simple group or PSL(2,2 f ) with f prime such that cd(G) = cd(H), then there exists an abelian subgroup A of G such that G/A is isomorphic to H.
