The automorphism group of the Foster graph is a group of order 4320. It acts transitively on the vertices, on the edges and on the arcs of the graph. Therefore, the Foster graph is a
symmetric graph. It has automorphisms that take any vertex to any other vertex and any edge to any other edge. According to the
Foster census, the Foster graph, referenced as F90A, is the only cubic symmetric graph on 90 vertices. The
characteristic polynomial of the Foster graph is equal to (x-3) (x-2)^9 (x-1)^{18} x^{10} (x+1)^{18} (x+2)^9 (x+3) (x^2-6)^{12}. ==Gallery==