  In this paper we continue the study of powerfully nilpotent groups. These are
powerful $p$-groups possessing a central series of a special kind. To each such
group one can attach a powerful nilpotency class that leads naturally to the
notion of a powerful coclass and classification in terms of an ancestry tree.
In this paper we will give a full classification of powerfully nilpotent groups
of rank $2$. The classification will then be used to arrive at a precise
formula for the number of powerfully nilpotent groups of rank $2$ and order
$p^{n}$. We will also give a detailed analysis of the ancestry tree for these
groups. The second part of the paper is then devoted to a full classification
of powerfully nilpotent groups of order up to $p^{6}$.
