Matches in DBpedia 2014 for { ?s ?p In the mathematical field of group theory, the Higman–Sims group HS is a sporadic simple group found by Donald G. Higman and Charles C. Sims (1968) of order 29 · 32 · 53 · 7 · 11 = 44352000. ≈ 4 · 107.It is the simple subgroup of index two in the group of automorphisms of the Higman–Sims graph. The Higman–Sims graph has 100 nodes, so the Higman–Sims group HS is a transitive group of permutations of a 100 element set.The Higman–Sims group was discovered in 1967, when Higman and Sims were attending a presentation by Marshall Hall on the Hall–Janko group. This is also a permutation group of 100 points, and the stabilizer of a point is a subgroup with two other orbits of lengths 36 and 63. Inspired by this they decided to check for other rank 3 permutation groups on 100 points. They soon focused on a possible one containing the Mathieu group M22, which has permutation representations on 22 and 77 points. (The latter representation arises because the M22 Steiner system has 77 blocks.) By putting together these two representations, they found HS, with a one-point stabilizer isomorphic to M22.Graham Higman (1969) independently discovered the group as a doubly transitive permutation group acting on a certain 'geometry' on 176 points.The Schur multiplier has order 2, the outer automorphism group has order 2, and the group 2.HS.2 appears as an involution centralizer in the Harada–Norton group.. }
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- Higman–Sims_group abstract "In the mathematical field of group theory, the Higman–Sims group HS is a sporadic simple group found by Donald G. Higman and Charles C. Sims (1968) of order 29 · 32 · 53 · 7 · 11 = 44352000. ≈ 4 · 107.It is the simple subgroup of index two in the group of automorphisms of the Higman–Sims graph. The Higman–Sims graph has 100 nodes, so the Higman–Sims group HS is a transitive group of permutations of a 100 element set.The Higman–Sims group was discovered in 1967, when Higman and Sims were attending a presentation by Marshall Hall on the Hall–Janko group. This is also a permutation group of 100 points, and the stabilizer of a point is a subgroup with two other orbits of lengths 36 and 63. Inspired by this they decided to check for other rank 3 permutation groups on 100 points. They soon focused on a possible one containing the Mathieu group M22, which has permutation representations on 22 and 77 points. (The latter representation arises because the M22 Steiner system has 77 blocks.) By putting together these two representations, they found HS, with a one-point stabilizer isomorphic to M22.Graham Higman (1969) independently discovered the group as a doubly transitive permutation group acting on a certain 'geometry' on 176 points.The Schur multiplier has order 2, the outer automorphism group has order 2, and the group 2.HS.2 appears as an involution centralizer in the Harada–Norton group.".