Recognizing finite groups through order and degree pattern

The degree pattern of a finite group C is introduced in [10] and it is proved that the following simple groups are uniquely determined by their degree patterns and orders: all sporadic simple groups, alternating groups A, (p >= 5 is a twin prime) and some simple groups of Lie type. In this paper, we continue this investigation. In particular, we show that the automorphism groups of sporadic simple groups (except Aut(J(2)) and Aut(M degrees L)), all simple C-22-groups, the alternating groups A(p), A(p+1), A(p+2) and the symmetric groups S-p, Sp+1, where p is a prime, are also uniquely determined by their degree patterns and orders.