I'm looking for an example of a commutative Hopf algebra $H$ such that
$H$ is a torsion free $\mathbb{Z}$ module of finite rank
$H$ is not isomorphic to the dual of a group algebra $\mathbb{Z}G$
$H \neq \mathbb{Z}$
By commutative I mean commutative in the strict sense (i.e. xy = yx) and not in the graded sense.
I have been googling a lot, but couldn't find an example.