关键词: 群的构造, 同构分类, 群在群上的作用, 有限群

Abstract: Let p,q be odd primes such that p>q, let G be a  group of order p³q³. By using the method of local analysis on finite groups, and by analyzing the different actions among the subgroups of G, we classified the group \%G completely, and got all the structures of the group.

Key words: actions of one group over another group, structure of group, isomorphic classification, finite group