On Transitive p-Groups of Degree at Most p to power 3

The problem of classifying groups is usually a difficult task. In this text we have successfully classified transitive p-groups of degree at most p to power 3 whose centre is elementary Abelian of rank 2 and also a more general case of transitive p-groups of degree at most p to power 3 whose centre is not elementary Abelian of rank 2. In our work p is an arbitrary but fixed prime number which ranges between 2 to 5. The powers of p take values 2 or 3.