Characterization of the Chevalley group G2(5) by the set of numbers of the same order elements

Let G be a group and ω(G)={o(g)|g∈G} be the set of element orders of G. Let k∈ω(G) and sk=|{g∈G|o(g)=k}|. Let nse(G)={sk|k∈ω(G)}. In this paper, we prove that if G is a group and G2(5) is the Chevalley simple group of type G2 over GF(5) such that nse(G)=nse(G2(5)), then G≅G2(5).