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.
   
• 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   by B. Hoefling
  A Library of irreducible solvable linear groups over finite fields
   
• 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   by V. Felsch, F. Gähler
  The crystallographic groups catalog
   
• AClib   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   by T. Breuer
  The GAP Character Table Library
   
• AtlasRep   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.
   

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:

• Irreducible Solvable Linear Groups over Finite Fields,
• CrystCat,
• AClib,
• Character Tables, and
• AtlasRep.