On automorphisms of a distance-regular graph with intersection array $\{35,32,1;1,4,35\}$

Prime divisors of orders of automorphisms and their fixed point subgraphs are studied for a hypothetical distance-regular graph with intersection array $\{35,32,1;1,4,35\}$. It is shown that arc-transitive distance-regular graphs with intersection array $\{35,32,1;1,4,35\}$ do not exist.