  We prove that the near hexagon $Q(5,2) \times \mathbb{L}_3$ has a non-abelian
representation in the extra-special 2-group $2^{1+12}_+$ and that the near
hexagon $Q(5,2) \otimes Q(5,2)$ has a non-abelian representation in the
extra-special 2-group $2^{1+18}_-$. The description of the non-abelian
representation of $Q(5,2) \otimes Q(5,2)$ makes use of a new combinatorial
construction of this near hexagon.
