Structure of Group of Order 2~3p~2q

In this paper,we obtain the structure of group of order 23p2q on the ground of the character of finite group and the knowledge of group extension theory and number theory,when it contains cyclic normal subgroup of order p2q.Let p,q be distinct odd prime and pq,then the groups of order 23p2q have:① 22 types when B is cyclic group;② 19 types when B is abelian group of type;③ 5 types when B is elementary abelian group;④ 5 types when B is quaternion;⑤ 10 types when B is dihedral.