On automorphisms of a strongly regular graph with parameters (117,36,15,9)

In the previous work of the authors some arrays of intersections of distance-regular graphs were found, in which the neighborhoods of the vertices are pseudogeometric graphs for pGs-3(s,t). In particular, a locally pseudo pG2(5,2)-graph is a strongly regular graph with parameters (117,36,15,9). The main result of this paper gives a description of possible orders and the structure of the subgraphs of fixed points of automorphisms of a strongly regular graph with parameters (117,36,15,9). This graph has a spectrum of 361,926,-390. The order of clicks in Γ does not exceed 1+36/3=13, the order of the cocliques in Γ does not exceed 117⋅3/39=9. Further, from this result, the following corollary is derived: if the group Γ of automorphisms of a strongly regular graph with parameters (117,36,15,9) acts transitively on the set of vertices, then the socle T of the group Γ is isomorphic to either L3(3) and Ta≅GL2(3) is a subgroup of index 117, or Ta≅GL2(3) and Ta≅U4(2).Z2 is a subgroup of index 117.