The Polycirculant Conjecture for elusive permutation groups

Let $G$ be a finite transitive permutation group. Call $G$ elusive if it contains no derangements of prime order. The $2$-closure of $G$ on its permutation domain is the largest subgroup of the symmetric group on that domain having the same orbits on ordered pairs as $G$; $G$ is $2$-closed if it equals its $2$-closure. Polycirculant Conjecture. There are no $2$-closed elusive groups. This is a longstanding open problem in algebraic graph theory, with various partial results known.