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
Character Table Libraries. Especially see Selecting Library Tables.
As for the third method, some generic ways to derive a character table
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).
GAP 3.4.4