Let G be a finite group, and |G|denotes the order of G. If |G| has exactly n distinct prime factors, G is called a K n- groups. Let g∈G, and o(g)denotes the order of g. Define m(G)=∑ g∈G〖SX(〗1〖〗o(g)〖SX)〗, and let h(G) denotes the maximum order of elements in G. To generalize the quantitative characterization of finite groups, it is proposed to use the quantities h(G) and m(G)to characterize finite simple groups. First, the prime factors of |G|and the range of G are determined using h(G)and m(G), then apply the classification theorem of finite simple groups to prove that G is isomorphic to the target simple group. It is ultimately proved that if G is a K 4-group, then G PSL(2,11) if and only if m(G)=m(PSL(2,11)) and h(G)=h(PSL(2,11)). The conclusion demonstrates that the simple K 4-group PSL(2,11) can be uniquely characterized by h(G) and m(G), extending previous work on the quantitative characterization of PSL(2,11).