Existence of non-abelian representations of the near hexagon Q(5,2)⊗Q(5,2)

Abstract

In [5], a new combinatorial model with four types of points and nine types of lines of the slim dense near hexagon Q(5,2)⊗Q(5,2) was provided and it was then used to construct a non-abelain representation of Q(5,2)⊗Q(5,2) in the extraspecial 2-group \(2_{-}^{1+18}\). In this paper, we give a direct proof for the existence of a non-abelian representation of Q(5,2)⊗Q(5,2) in \(2_{-}^{1+18}\).