利用矩阵的有理标准形作为工具,通过找出有限群G的Fitting子群的自同构的阶来确定群G的生成关系。给出了阶为2^4p(p=5,7)的群的构造,即2^45阶群G有52种互不同构的类型。2^47阶群G有45种互不同构的类型。且我们的证明方法比较简单。
On the base of paper[1], this paper decide the generation relation of group, by finding the order of automorphism group of Fitting subgroup of group G. And then obtain the structure of groups of order 2^4p. That is, groups of order 2^45 has 52 nonisomorphic types. Groups of order 2^47 has 45 nonisomorphic types, and the method is simple.