Databases of Groups [HB 26]

New Features:

• Portions of the online ATLAS of Finite Group Representations are now supplied with Magma. The basic access function is called ATLASGroup. This allows access to representations of various ``nearly simple'' groups as matrix and permutation groups

• All groups of order p⁴, p⁵, p⁶ for any prime p are now available as part of the SmallGroup database. These groups were contributed by Boris Girnat, Robert McKibbin, M.F. Newman, E.A. O'Brien, and M.R. Vaughan-Lee.

• The almost simple groups database now holds information on all simple groups of order less than 1.6×10⁷, plus M₂₄, HS, J₃, McL, Sz(32) and L₆(2). Maximal subgroups and automorphism groups can be computed for many more groups, including the simple groups: A_n for n$\le$999, L₂(q), L₃(q) and L₄(q) for all q, L₅(p), S₄(p) and U₃(p) for all primes p, L_d(2) for d$\le$14, U₆(2), U₃(9), S₈(2), O^±₈(2), O^±₁₀(2), S₆(3), O₇(3), G₂(4), G₂(5), ³D₄(2), ²F₄(2)', Co₂, Co₃, He, Fi₂₂. The code for the families of groups is by Derek Holt and Colva Roney-Dougal.

• A database of fundamental groups of small-volume closed hyperbolic 3-manifolds is now available. The data was prepared by Dunfield & Thurston, based on the manifolds in the Hodgson-Weeks census. The groups are infinite finitely presented groups. The basic access operations are ManifoldDatabase and Manifold.