  We study the inverse problem for the versal deformation rings $R(\Gamma,V)$
of finite dimensional representations $V$ of a finite group $\Gamma$ over a
field $k$ of positive characteristic $p$. This problem is to determine which
complete local commutative Noetherian rings with residue field $k$ can arise up
to isomorphism as such $R(\Gamma,V)$. We show that for all integers $n \ge 1$
and all complete local commutative Noetherian rings $\mathcal{W}$ with residue
field $k$, the ring $\mathcal{W}[[t]]/(p^n t,t^2)$ arises in this way. This
ring is not a local complete intersection if $p^n\mathcal{W}\neq\{0\}$, so we
obtain an answer to a question of M. Flach in all characteristics.
