On automorphisms of strongly regular graphs with parameters (243, 66, 9, 21)

Orders and fixed-point subgraphs of automorphisms of strongly regular graphs with parameters (243,66,9,21) are found. These results will be useful for investigations of automorphisms of strongly regular graphs with parameters (640,243,66,108) (in such graph neighborhoods of vertices are strongly regular with parameters (243,66,9,21)).