Автоморфизмы дистанционно регулярного графа с массивом пересечений $\{30,27,24;1,2,10\}$

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 $\{30,27,24;1,2,10\}$. 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 $(G)$ is $\{2\}$-group, and $\bar T\cong L_2(11)$, $M_{11}$, $U_5(2)$, $M_{22}$, $A_{11}$, $HiS$.