Inclusions of innately transitive groups into wreath products in product action with applications to $2$-arc-transitive graphs

Abstract

We study $(G,2)$-arc-transitive graphs for innately transitive permutation groups $G$ such that $G$ can be embedded into a wreath product $\symΓ\wr\sy\ell$ acting in product action on ${\Gamma }^{\ell }$. We find two such connected graphs: the first is Sylvester's double six graph with 36 vertices, while the second is a graph with $120^2$ vertices whose automorphism group is $\aut\sp 44$. We prove that under certain conditions no more such graphs exist.

References in corpus (1)

• Maximal subgroups of almost simple groups with socle $\PSL(2,q)$