On automorphisms of strongly regular graphs with $\lambda=0$ and $\mu=3$

A strongly regular graph with $\lambda=0$ and $\mu=3$ is of degree $3$ or $21$. The automorphisms of prime order and the subgraphs of their fixed points are described for a strongly regular graph $\Gamma$ with parameters $(162,21,0,3)$. In particular, the inequality $|G/O(G)|\le 2$ holds true for $G=\operatorname{Aut}(\Gamma)$.