21.28 (2026)

Let $G$ be a finite simple transitive permutation group, and let $\delta(G)$ be the proportion of derangements in $G$. Is it true that $\delta(G) \geqslant 89/325$?

Note that $\delta(G) = 89/325$ for the action of the Tits group $G = {}^2F_4(2)'$ on the cosets of a maximal parabolic subgroup of the form $2^2.[2^8].S_3$ (Forum Math. Sigma, 13 (2025), paper no. e98, 62 pp.).