The automorphism group of a class of strongly regular graphs related to

In [A. Devillers, H. Van Maldeghem, Partial linear spaces built on hexagons, European J. Combin. 28 (2007) 901–915], Devillers and Van Maldeghem determined the automorphism group of four classes of geometries that have as collinearity graph the graph Γ ( q ) of all elliptic hyperplanes of a given parabolic quadric Q ( 6 , q ) in PG ( 6 , q ) (adjacency is given by intersecting in a tangent 4-space). In their introduction they mention that at the time they were not able to determine the full automorphism group of Γ ( q ) , but that their results might be useful for proving that it is isomorphic to P Γ O ( 7 , q ) . In this note we use one of their results to prove that this is indeed the case.