Automorphisms of a distance-regular graph with intersection array {196, 156, 1; 1, 39, 196}

A. Makhnev and M. Samoilenko found intersection arrays of antipodal distance-regular graphs of diameter 3 and degree at most 1000 in which $\lambda=\mu$ and the neighborhoods of vertices are strongly regular. Automorphisms of distance-regular graphs in which the neighborhoods of vertices are strongly regular with second eigenvalue 3 except for graphs with intersection arrays $\{196,156,1;1,39,196\}$ and $\{205,136,1;1,68,205\}$ were found earlier. We find possible prime orders of elements in the automorphism group of a distance-regular graph with intersection array $\{196,156,1;1,39,196\}$ as well as their fixed-point subgraphs. It is proved that the automorphism group of this graph acts intransitively on the vertex set.