A new near octagon and the Suzuki tower

Abstract

We construct and study a new near octagon of order $(2,10)$ which has its full automorphism group isomorphic to the group ${\mathrm{G}}_2(4):2$ and which contains $416$ copies of the Hall-Janko near octagon as full subgeometries. Using this near octagon and its substructures we give geometric constructions of the ${\mathrm{G}}_2(4)$-graph and the Suzuki graph, both of which are strongly regular graphs contained in the Suzuki tower. As a subgeometry of this octagon we have discovered another new near octagon, whose order is $(2,4)$.

arXiv comment24 pages, revised version with added remarks and references