A new characterization of A sub(12)

Purpose: It is well known that the conjugacy class sizes have an important influence on the structure of a group. This work is considering a different set of 'sizes', the number of elements of a given order. Methods: By using the set nse(G) and the order of G, We prove that G is isomorphic to A sub(12). Results: Thompson's conjecture is true for A1 sub(12). Conclusions: We proved that a finite group G is isomorphic to A sub(12), the alternating group A sub(12)of degree 12 if, and only if, |G|=|A sub(12)| and nse(G)=nse(A sub(12)).