For a finite group H, let cs(H) denote the set of non-trivial conjugacy class sizes of H and OC(H) be the set of the order components of H. In this paper, we show that if S is a finite simple group with the disconnected prime graph and G is a finite group such that cs(S)=cs(G), then ∣S∣=∣G/Z(G)∣ and OC(S)=OC(G/Z(G)). In particular, we show that for some finite simple group S, GcongStimesZ(G)