The $$\mathrm {L}_3(4)$$ L 3 ( 4 ) near octagon

Abstract

In recent work we constructed two new near octagons, one related to the finite simple group $$\mathrm {G}_2(4)$$ and another one as a sub-near-octagon of the former. In the present paper, we give a direct construction of this sub-near-octagon using a split extension of the group $$\mathrm {L}_3(4)$$ . We derive several geometric properties of this $$\mathrm {L}_3(4)$$ near octagon, and determine its full automorphism group. We also prove that the $$\mathrm {L}_3(4)$$ near octagon is closely related to the second subconstituent of the distance-regular graph on 486 vertices discovered by Soicher (Eur J Combin 14:501–505, 1993).