M22 graph

The graph is the block graph of the Steiner system S(3,6,22), where blocks are called adjacent when they are disjoint. It is strongly regular because this design is quasi-symmetric: block intersections have size 0 or 2. f) An edge . There are 616 of these, forming a single orbit. The stabilizer of one is A6.22 with vertex orbit sizes 2+30+45. The subgraph induced on the 30 is the point-line incidence graph of the generalized quadrangle GQ(2,2). The subgraph induced on the 45 is the distance-2 graph of the unique distance-regular graph with intersection array {4,2,2,2;1,1,1,2}, the generalized octagon GO(2,1), the flag graph of GQ(2,2).