GAP Manual: 48.11. Getting Character Tables

There are in general four different ways to get a character table which GAP already ``knows'': You can either

read a file that contains the table record,
construct the table using generic formulae,
derive it from known tables or
use a presentation or representation of the group.

The first two methods are used by CharTable CharTable. For the conception of generic character tables, see chapter Generic Character Tables. Note that library files often contain something that is much different from the tables returned by CharTable, see chapter Character Table Libraries. Especially see Selecting Library Tables.

As for the third method, some generic ways to derive a character table are implemented::
One can obtain it as table of a factor group where the table of the group is given (see CharTableFactorGroup),
for given tables the table of the direct product can be constructed (see CharTableDirectProduct),
the restriction of a table to the p-regular classes can be formed (see CharTableRegular),
for special cases, an isoclinic table of a given table can be constructed (see CharTableIsoclinic),
the splitting and fusion of classes may be viewed as a generic process (see CharTableSplitClasses, CharTableCollapsedClasses).

At the moment, for the last method there are algorithms dealing with arbitrary groups (see CharTable), and with finite polycyclic groups with special properties (see CharTablePGroup).

Note that whenever fusions between tables occur in these functions, they are stored on the concerned tables, and the fusionsource fields are updated (see Character Table Records).