Symmetric Generation of the Higman-Sims Group Original Research Article

In this paper we use the ideas developed in [Curtis, 1990] and [Curtis, 1993] to give a new elementary construction of the Higman-Sims group. The 176 point geometry found by Higman emerges naturally, complete with permutations on the 176 points plus 176 quadrics which generate HS:2. In addition, the permutation action of HS:2 on 100 points, with point stabilizer M22:2, is an easy by-product of this approach.