  For each pointed abelian group $(A,c)$, there is an associated {\em Galkin
quandle} $G(A,c)$ which is an algebraic structure defined on $\Bbb Z_3\times A$
that can be used to construct knot invariants. It is known that two finite
Galkin quandles are isomorphic if and only if their associated pointed abelian
groups are isomorphic. In this paper we classify all finite pointed abelian
groups. We show that the number of nonisomorphic pointed abelian groups of
order $q^n$ ($q$ prime) is $\sum_{0\le m\le n}p(m)p(n-m)$, where $p(m)$ is the
number of partitions of integer $m$.
