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Data Libraries

GAP contains several data libraries. From the following list you can reach an individual page for each of them, giving information about the content of that data library, its author(s), and a pointer to the associated manual section which provides a more explicit documentation.

  • SmallGroups   by E. A. O'Brien, B. Eick, and H. U. Besche
    Small Groups Library. All groups of order up to 2000 (except 1024) and some infinite series of groups characterised by the prime number decomposition of their orders.
  • SglPPow  1.1 (21/11/2014) by M. Vaughan-Lee, B. Eick
    Database of groups of prime-power order for some prime-powers
  • Basic Groups
    Cyclic, abelian, dihedral, extraspecial, alternating, symmetric, Mathieu, Suzuki, and Ree groups.
  • Classical Groups
    Linear, unitary, symplectic, and orthogonal groups.
  • Perfect Groups   by D. Holt, W. Plesken, and V. Felsch
    Almost all perfect groups of order up to 10 6.
  • Transitive Permutation Groups   by A. Hulpke
    Transitive permutation groups of degree up to 30.
  • Primitive Permutation Groups   by C. Roney-Dougal and many other people
    All primitive permutation groups of degree <2500.
    For details see the Reference Manual Section Primitive Permutation Groups
  • Irreducible Solvable Matrix Groups   by M. Short
    Irreducible solvable subgroups of GL(n,q) for qn up to 243.
  • IRREDSOL  1.2.4 (18/02/2014) by B. Höfling
    A Library of irreducible solvable linear groups over finite fields and of finite primivite soluble groups
  • Integral Matrix Groups   by W. Plesken, B. Souvignier, G. Nebe, and V. Felsch.
    Irreducible maximal finite integral matrix groups of dimension up to 31.
  • CrystCat  1.1.6 (29/05/2012) by V. Felsch, F. Gähler
    The crystallographic groups catalog
  • AClib  1.2 (29/05/2012) by K. Dekimpe, B. Eick
    Almost Crystallographic Groups - A Library and Algorithms
  • Tables of Marks   by G. Pfeiffer and T. Merkwitz
    Tables of marks for many almost simple groups.
  • CTblLib  1.2.2 (07/03/2013) by T. Breuer
    The GAP Character Table Library
  • AtlasRep  1.5.0 (12/07/2011) by R. A. Wilson, R. A. Parker, S. Nickerson, J. N. Bray, T. Breuer
    A GAP Interface to the Atlas of Group Representations
  • Lie Algebras
    Free, Full Linear, and Simple Lie Algebras.
  • Smallsemi  0.6.10 (13/01/2015) by A. Distler, J. Mitchell
    A library of small semigroups
  • UnitLib  3.2.0 (11/11/2014) by A. Konovalov, E. Yakimenko
    Library of normalized unit groups of modular group algebras

Note that some of these data libraries are technically GAP packages and can be loaded by the 'LoadPackage' mechanism. Hence they occur in the navigator tree of the packages instead of the navigator tree of this page. These are the following:

  • AClib,
  • AtlasRep,
  • Character Table Library,
  • CrystCat,
  • Irreducible Solvable Linear Groups over Finite Fields,
  • SglPPow
  • ,
  • SmallSemi
  • , and
  • UnitLib.