Polarities of G. Higman's symmetric design and a strongly regular graph on 176 vertices

We investigate the polarities of G. Higman's symmetric 2-(176, 50, 14) design and find that there are two of them (up to conjugacy), one having 80 and the other 176 absolute points. From the latter we can derive a strongly regular graph with parameters (v, k, , )=(176, 49, 12, 14). Its group of automorphisms is Sym(8) with orbits of size 8 and 168 on the vertices. It does not carry a partial geometry or a delta space, and is not the result of mergingd=1 andd=2 in a distance regular graph with diameter 3 and girth 6 on 176 vertices.