GAP Manual: 37. 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, the primitive groups of degree at most 50, the solvable groups of size at least 100, the 2-groups of size at most 256, and the 3-groups of size at most 729.

Each of the set of groups above is called a library. The whole set of groups that GAP knows initially is called the GAP collection of group libraries. There is usually no relation between the groups in the different libraries.

Most libraries are accessed in a uniform manner. For each library there is a so called selection function that allows you to select the list of groups that satisfy given criterias from a library. The example function allows yo to select one group that satisfies given criterias from the library. The low-level extraction function allows you to extract a single group from a library, using a simple indexing scheme.

The first section in this chapter describes the library of basic groups (see The Basic Groups Library). This library is special, because it is not accessed in the same way as the other libraries. The next sections describe the general appearance of the selection, example, and extraction function (see Selection Functions, Example Functions, and Extraction Functions). The last sections in this chapter describe the group libraries currently available in GAP (see The Primitive Groups Library, The Solvable Groups Library, The 2-Groups Library, The Irreducible Solvable Linear Groups Library).

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

This chapter contains the following sections:

• 37.1. The Basic Groups Library
• 37.2. Selection Functions
• 37.3. Example Functions
• 37.4. Extraction Functions
• 37.5. The Primitive Groups Library
• 37.6. The Transitive Groups Library
• 37.7. The Solvable Groups Library
• 37.8. The 2-Groups Library
• 37.9. The 3-Groups Library
• 37.10. The Irreducible Solvable Linear Groups Library
• 37.11. The Crystallographic Groups Library