On the automorphism group of the Aschbacher graph

A Moore graph is a regular graph of degree $k$ and diameter $d$ with $v$ vertices such that $v\le1+k+k(k-1)+\dots+k(k-1)^{d-1}$. It is known that a Moore graph of degree $k\ge3$ has diameter 2, i.e., it is strongly regular with parameters $\lambda=0$, $\mu=1$ and $v=k^2+1$, where the degree $k$ is equal to 3, 7, or 57. It is unknown whether there exists a Moore graph of degree $k=57$. Aschbacher showed that a Moore graph with $k=57$ is not a graph of rank 3. In this connection, we call a Moore graph with $k=57$ the Aschbacher graph and investigate its automorphism group $G$ without additional assumptions (earlier, it was assumed that $G$ contains an involution).