Finite Nilpotent Groups with Automorphism Groups of Order 16p~3(p prime)

This paper discusses the structures of nilpotent group G by using the oder of automorphism group G.In the process,first,We use the orders of automorphism group Q of some finite p-group Q to determine the structure of the Q group.We know nilpotent group G can decompose into the direct product of all its Sylow p-subgroups,then,by discussing the orders of automorphism group Pi,We can found out all the finite nilpotent groups when the order of automorphism group G equals 16p3 with p being odd primes.