On classification of groups of order p4, where p is an odd prime

The classification of p-groups is a difficult task. It is also important because these groups have certain axioms and properties of which one can have further investigation for the other finite groups. In fact, there is no complete classification for p-groups, and the only complete classification has been done for certain cases of prime numbers or for certain nilpotency classes. In this article, we give a complete description of p-groups of order p(4), where p is an odd prime. In addition, we discuss many other algebraic properties. Significantly, computer calculations were of an extensive use in this work.