Fusion Systems on a Sylow $p$-subgroup of ${\mathrm{G}}_2(p^n)$ or ${\mathrm{PSU}}_4(p^n)$

Abstract

For any prime $p$ and $S$ a $p$-group isomorphic to a Sylow $p$-subgroup of ${\mathrm{G}}_2(p^n)$ or ${\mathrm{PSU}}_4(p^n)$ with $n\in \mathbb{N}$, we determine all saturated fusion systems supported on $S$ up to isomorphism.