  We classify finite-dimensional complex Hopf algebras $A$ which are pointed,
that is, all of whose irreducible comodules are one-dimensional, and whose
group of group-like elements $G(A)$ is abelian such that all prime divisors of
the order of $G(A)$ are $>7$. Since these Hopf algebras turn out to be
deformations of a natural class of generalized small quantum groups, our result
can be read as an axiomatic description of generalized small quantum groups.
