Geodesic
Оn automorphisms of the generalized hexagon of order (3,27)
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 2, pp. 34-44
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Possible orders and fixed-point subgraphs for automorphisms of the generalized hexagon $S$ of order (3,27) are found. It is proved that, if the automorphism group of $S$ acts transitively on points, then $S$ is isomorphic to the classical generalized hexagon corresponding to the building of the Steinberg group $^3D_4(3)$. 
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I. N. Belousov; A. A. Makhnev. Оn automorphisms of the generalized hexagon of order (3,27). Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 2, pp. 34-44. http://geodesic.mathdoc.fr/item/TIMM_2009_15_2_a2/

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