On automorphisms of a distance-regular graph with intersection array {69,56,10;1,14,60}

Let $\Gamma$ be a distance-regular graph of diameter 3 with eigenvalues $\theta_0>\theta_1>\theta_2>\theta_3$. If $\theta_2=-1$, then the graph $\Gamma_3$ is strongly regular and the complementary graph $\bar\Gamma_3$ is pseudogeometric for $pG_{c_3}(k,b_1/c_2)$. If $\Gamma_3$ does not contain triangles and the number of its vertices $v$ is less than 800, then $\Gamma$ has intersection array $\{69,56,10;1,14,60\}$. In this case $\Gamma_3$ is a graph with parameters (392,46,0,6) and $\bar \Gamma_2$ is a strongly regular graph with parameters (392,115,18,40). Note that the neighborhood of any vertex in a graph with parameters $(392,115,18,40)$ is a strongly regular graph with parameters $(115,18,1,3)$, and its existence is unknown. In this paper, we find possible automorphisms of this strongly regular graph and automorphisms of a distance-regular graph with intersection array $\{69,56,10;1,14,60\}$. In particular, it is proved that the latter graph is not arc-transitive.