Automorphisms of a strongly regular graph with parameters (1197, 156, 15, 21)

Let a $3$-$(V,K,\Lambda)$ scheme ${\cal E}=(X,{\cal B})$ is an extension of a symmetric $2$-scheme. Then either ${\cal E}$ is Hadamard $3$-$(4\Lambda+4,2\Lambda+2,\Lambda)$ scheme, or $V=(\Lambda+1)(\Lambda^2+5\Lambda+5)$ and $K=(\Lambda+1)(\Lambda+2)$, or $V=496$, $K=40$ and $\Lambda=3$. The complementary graph of a block graph of $3$-$(496,40,3)$ scheme is strongly regular with parameters $(6138,1197,156,252)$ and the neighborhoods of its vertices are strongly regular with parameters $(1197,156,15,21)$. In this paper automorphisms of strongly regular graph with parameters $(1197,156,15,21)$ are studied. We yet introduce the structure of automorphism groups of abovementioned graph in vetrex symmetric case.