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 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 L 3 (4). We derive several geometric properties of this L 3 (4) near octagon, and determine its full automorphism group. We also prove that the L 3 (4) near octagon is closely related to the second subconstituent of the distanceregular graph on 486 vertices discovered by Soicher in 1993.