  We classify finite-dimensional Nichols algebras over finite nilpotent groups
of odd order in group-theoretical terms. The main step is to show that the
conjugacy classes of such finite groups are either abelian or of type C; this
property also holds for finite conjugacy classes of finitely generated
nilpotent groups whose torsion has odd order. To extend our approach to the
setting of finite GK-dimension, we propose a new Conjecture on racks of type C.
We also prove that the bosonization a of Nichols algebra of a Yetter-Drinfeld
module over a group whose support is an infinite conjugacy class has infinite
GK-dimension. We apply this to the study of the finite GK-dimensional pointed
Hopf algebras over finitely generated torsion-free nilpotent groups.
