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
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 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:
origin: Ostermann:
origin: CAS library: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
item all 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;
item most tables of maximal subgroups of sporadic simple groups (not
all for HN, F3+, B, M);
item some tables of maximal subgroups of other ATLAS tables
(which?)
item most 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)
item some tables of element centralizers
item some tables of Sylow subgroups
item a 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):
item alternating groups item cyclic groups, item dihedral groups, item some linear groups, item quaternionic (dicyclic) groups item Suzuki groups, item symmetric groups, item wreath products of a group with a symmetric group (see CharTableWreathSymmetric), item Weyl groups of types B_n and D_n
GAP 3.4.4