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.
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