47 Group Libraries

When you start GAP, it already knows several groups. Currently GAP initially knows the following groups:

·
some basic groups, such as cyclic groups or symmetric groups (see Basic Groups),
·
Classical matrix groups (see Classical Groups),
·
the transitive permutation groups of degree at most 23 (see Transitive permutation groups),
·
a library of groups of small order (see Small Groups),
·
the finite perfect groups of size at most 106 (excluding 11 sizes) (see Finite perfect groups).
·
a library of primitive permutation groups of degree < 1000, complete for degrees < 256 (see Primitive permutation groups),
·
the irreducible solvable subgroups of GL(n,p) for n > 1 and pn < 256 (also in Primitive permutation groups),

There is usually no relation between the groups in the different libraries and a group may occur in different libraries in different incarnations.

Note that a system administrator may choose to install all, or only a few, or even none of the libraries. So some of the libraries mentioned below may not be available on your installation.

Sections

  1. Basic Groups
  2. Classical Groups
  3. Constructors for Basic Groups
  4. Selection Functions
  5. Transitive Permutation Groups
  6. Small Groups
  7. Finite Perfect Groups
  8. Primitive Permutation Groups
  9. Irreducible Maximal Finite Integral Matrix Groups

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GAP 4 manual
February 2000