Characterization of some almost simple groups with socle PSp4(q) by their character degrees

Let G be a finite group and cd(G) denote the set of irreducible complex character degrees of G. Suppose that. H is a projective conformal symplectic group PCSp4(q) for some prime power q. The main result of this paper is to prove that if cd(G) = cd(H), then G/Z(G) is isomorphic to H. This confirms a recent generalization of Huppert's conjecture for the almost. simple groups of Lie type.