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

Non-abelian representations of the slim dense near hexagons on 81 and 243 points