Hemisystems and strongly regular graphs

In a recent paper, it was constructed a family of hemisystems of H(3,p2), for every prime p of the form p=1+4a2, stabilised by PSL(2,p)×C[Formula presented]. In the case p=5, the full automorphism group is 3.A7, and the hemisystem is isomorphic to a sporadic one described by A. Cossidente and T. Penttila in 2005. Here, we investigate the new family of hemisystems and the related strongly regular graphs. In this way, we find a new family of strongly regular graphs, cospectral but not isomorphic to the Cossidente–Penttila graph.