Automorphisms of a distance-regular graph with intersection array {176, 135, 32, 1; 1, 16, 135, 176}.

A distance-regular graph Gamma with intersection array {176, 135, 32, 1; 1, 16, 135, 176} is an AT4-graph. Its antipodal quotient Gamma is a strongly regular graph with parameters (672, 176, 40, 48). In both graphs the neighborhoods of vertices are strongly regular with parameters (176, 40, 12, 8). We study the automorphisms of these graphs. In particular, the graph Gamma is not arc-transitive. If G = Aut (contains an element of order 11, acts transitively on the vertex set of Gamma, and S(G) fixes each antipodal class, then the full preimage of the group (G/S(G))' is an extension of a group of order 3 by M-22 or U-6 (2). We describe automorphism groups of strongly regular graphs with parameters (176, 40, 12, 8) and (672, 176, 40, 48) in the vertex-symmetric case.