Automorphisms of graph with intersection array $\{289,216,1;1,72,289\}$

Prime orders automorphisms and the fixed point subgraphs of automorphisms of prime orders are studied for a distance-regular graph with intersection array $\{289,216,1;1, 72,289\}$. Let nonsolvable automorphism group $G$ acts transitively on the vertex set of distance-regular graph $\Gamma$ with intersection array $\{289,216,1;1, 72,289\}$, $\bar T$ be a socle of $\bar G=G/S(G)$. Then either $\bar T\cong L_2(289)$ and $\Gamma$ is the Mathon graph or $\bar T\cong A_{29}$.