  Let $k$ be an algebraically closed field of characteristic $p$, and let
$\mathcal{O}$ be either $k$ or its ring of Witt vectors $W(k)$. Let $G$ a
finite group and $B$ a block of $\mathcal{O}G$ with normal abelian defect group
and abelian $p'$ inertial quotient. We show that $B$ is isomorphic to its
second Frobenius twist. This is motivated by the fact that bounding Frobenius
numbers is one of the key steps towards Donovan's conjecture. For
$\mathcal{O}=k$, we give an explicit description of the basic algebra of $B$ as
a quiver with relations. It is a quantised version of the group algebra of the
semidirect product $P\rtimes L$.
