On The Solution Of The Equation |Aut(G)|=6r～2

In this paper, we classify the groups with automorphism groups of order 6r2, where r is a prime more than 3. That is, we have obtained the following theory: Let G be a finite group and r a prime more than 3, then |Aut(G)|= 6r2 if and only if G is one of the following groups: C73, C2 C73, C6r2+1, C2 C6r2+1.