On automorphisms of a distance-regular graph with intersection array $\{39,36,22;1,2,18\}$

Prime divisors of orders of automorphisms and the fixed point subgraphs of automorphisms of prime orders are studied for a hypothetical distance-regular graph with intersection array $\{39,36,22;1,2,18\}$. Let $G={\rm Aut}(\Gamma)$ is nonsolvable group, $\bar G=G/S(G)$ and $\bar T$ is the socle of $\bar G$. If $\Gamma$ is vertex-symmetric then $\bar T=L\times M$ and $L, M\cong Z_5,A_5,A_6$ or $PSp(4,3)$.