Primitive permutation groups with a suborbit of length 5 and vertex-primitive graphs of valency 5

Abstract

We classify finite primitive permutation groups having a suborbit of length 5. As a corollary, we obtain a classification of finite vertex-primitive graphs of valency 5. In the process, we also classify finite almost simple groups that have a maximal subgroup isomorphic to $\mathrm{Alt}(5)$ or $\mathrm{Sym}(5)$.

References in corpus (1)

• Alternating Subgroups of Exceptional Groups of Lie Type

Cited by in corpus (1)

• Tetravalent half-arc-transitive graphs with unbounded nonabelian vertex stabilizers