Let G be a finite group and cd.G/ denote the set of complex irreducible character degrees of G. In this paper, we prove that if G is a finite group and H is an almost simple group whose socle is H0 D PSL.2; q/ with q D 2f (f prime) such that cd.G/ D cd.H /, then there exists an abelian subgroup A of G such that G=A is isomorphic to H . In view of Huppert’s conjecture (2000), the main result of this paper gives rise to some examples that G is not necessarily a direct product of A and H , and consequently, we cannot extend this conjecture to almost simple groups.
