  Let $s$ be even and $q=p^s$. We show that the ring
$W(\mathbb{F}_{q})[\![X]\!]/(X^2-pX)$ is a quotient of the universal
deformation ring of a representation of a finite group. This amounts to giving
an example of a finite group and its $\mathbb{F}_q$-representation that lifts
to $W(\mathbb{F}_q)$ in two different ways and satisfies certain subtle extra
conditions. We achieve this by studying representations of
$\mathrm{SL}(2,\mathbb{F}_{p^2})$.
