GAP Manual: 52.1. Contents of the Table Libraries

As stated at the beginning of the chapter, there are three libraries of character tables: ordinary character tables, Brauer tables, and generic character tables.

Ordinary Character Tables

Two different aspects are useful to list up the ordinary character tables available to GAP: the aspect of source of the tables and that of connections between the tables.

As for the source, there are two big sources, the ATLAS (see ATLAS Tables) and the CAS library of character tables. Many ATLAS tables are contained in the CAS library, and difficulties may arise because the succession of characters or classes in CAS tables and ATLAS tables are different, so see CAS Tables and Character Table Records for the relations between the (at least) two forms of the same table. A large subset of the CAS tables is the set of tables of Sylow normalizers of sporadic simple groups as published in Ost86, so this may be viewed as another source.

To avoid confusions about the actual format of a table, authorship and so on, the text component of the table contains the information

origin: ATLAS of finite groups:
for ATLAS tables (see ATLAS Tables)

origin: Ostermann:
for tables of Ost86 and

origin: CAS library:
for any table of the CAS table library that is contained neither in the ATLAS nor in Ost86.

If one is interested in the aspect of connections between the tables, i.e., the internal structure of the library of ordinary tables (which corresponds to the access to character tables, as described in CharTable), the contents can be listed up the following way:

We have itemall ATLAS tables (see ATLAS Tables), i.e. the tables of the simple groups which are contained in the ATLAS, and the tables of cyclic and bicyclic extensions of these groups; itemmost tables of maximal subgroups of sporadic simple groups (not all for HN, F3+, B, M); itemsome tables of maximal subgroups of other ATLAS tables (which?) itemmost nontrivial Sylow normalizers of sporadic simple groups as printed in Ost86, where nontrivial means that the group is not contained in p:(p-1) (not J_4N2, Co_1N2, Co_1N5, all of Fi_(23), Fi_(24)^(prime), B, M, HN, and Fi_(22)N2) itemsome tables of element centralizers itemsome tables of Sylow subgroups itema few other tables, e.g. W(F4)
namely which?

Brauer Tables

This library contains the tables of the modular ATLAS which are yet known. Some of them still contain unknowns (see Unknown). Since there is ongoing work in computing new tables, this library is changed nearly every day.

These Brauer tables contain the information 

    origin: modular ATLAS of finite groups

in their text component.

Generic Character Tables

At the moment, generic tables of the following groups are available in GAP (see CharTable):

itemalternating groups itemcyclic groups, itemdihedral groups, itemsome linear groups, itemquaternionic (dicyclic) groups itemSuzuki groups, itemsymmetric groups, itemwreath products of a group with a symmetric group (see CharTableWreathSymmetric), itemWeyl groups of types B_n and D_n

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