Vertex-transitive semi-triangular graphs with $\mu=7$

A semi-triangular Higman graph is a strongly regular graph with $v={m \choose 2}$, $k=2(m-2)$. The semi-triangular Higman graph with $\mu=7$ is pseudogeometric for $GQ(14,6)$. Previously, possible orders automorphisms of a pseudogeometric graph for $GQ(14,6)$ were found, and the structure subgraphs of fixed points of these automorphisms was determined. In this work we found a structure of nonsolvable group $G$ of automorphisms of a pseudogeometric graph for $GQ(14,6)$, acting transitively on the set of vertices of the graph.