The cohomology of the Sylow 2-subgroup of the Higman–Sims group

In this paper we compute the mod 2 cohomology of the Sylow 2-subgroup of the Higman–Sims group HS, one of the 26 sporadic simple groups. We obtain its Poincaré series as well as an explicit description of it as a ring with 17 generators and 79 relations.