Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2015.588.59228 by Conjugate Class Sizes]]>LiuShitian 32015153For a group, let N(G):{n| conjugate class sizes of order n in G}. The groups Ap+3, Ap+4 are characterized by N(G) only. If 5⋅p belong to the set of element orders of G, then whether are the alternating groups Ap+5 characterized by N(G). In this study, finite simple classification theorem and the properties of the set N(G) was used to characterize alternating group A28, namely, we will prove that if G is a finite group with trivial center and N(G) = N(A28), then G is isomorphic to A28.]]>Ahanjideh, N. and M. Ahanjideh,20134141164145Guiyun, C.,1996185184193Chen, G.,1999218276285Conway, J.H., R.T. Curtis, S.P. Norton, R.A. Parker and R.A. Wilson,1985Pages: 252Pages: 252Gorshkov, I.B.,201251111127James, G.D. and A. Kerber,1981Pages: 510Pages: 510Jiang, Q., C. Shao and X. Guo and W. Shi,2011A10.]]>3923492353Kondrat'ev, A.S.,1989180787797Mazurov, V.D. and E.I. Khukhro,20107th Edn.,Vasil'ev, A.V.,20096457464Williams, J.S.,198169487513Xu, M.,2013812271236Zavarnitsine, A.V.,20096112