Duncan's Sylow-subgroup criterion for versal group actions

Let $k$ be a field, let $G$ be a finite group, and let $X$ be a $k$-variety with a faithful $G$-action. For every prime $p$, let $G_p$ be a Sylow $p$-subgroup of $G$. Duncan's conjecture. The variety $X$ is $G$-versal if and only if it is $G_p$-versal for every prime $p$. The conjecture proposes that versality of a faithful finite group action can be detected on Sylow subgroups. It is refuted by a counterexample: an action of $(C_7\rtimes C_3)\times C_2$ on a degree-$2$ Del Pezzo surface.