Abstract: Let G be a finite group. If G has at least one conjugacy class C  such that  |C| is divisible by at least two distinct primes, then we define ccl2(G)=max{|C||C| is a conjugacy class of G such that |C| is divisible by at least two distinct primes}. The purpose of this paper is to  discuss the influence of a given upper bound of ccl2(G) on the structure of a  nonsolvable group G when ccl2(G)≠0.

Key words: conjugacyclasslength, finite non-solvable group, structure, prime number