Characters and Character Tables
Facilities for working with group characters can be found in Chapter Characters of Finite Groups. In this section we repeat a small number of character intrinsics that are used frequently when computing with \(K[G]\)-modules.
Ordinary Characters
In this section the various intrinsics for computing the table of absolutely irreducible complex characters for a finite group are described.
- Character(M): ModGrp -> AlgChtrElt
Given a \(K[G]\)-module \(M\) where \(K\) is the field of rationals or a number field, the character for \(M\) over the field \(K\) is returned.
- CharacterTable(G): Chtr -> SeqEnum
The table of irreducible complex characters for the group \(G\) is constructed.
Brauer Characters
In this section the intrinsic for computing the table of absolutely irreducible Brauer characters of a finite group are described.
- BrauerCharacterTable(G, p): Chtr -> SeqEnum
Construct the table of irreducible Brauer characters in characteristic \(p\) for the group \(G\). For soluble groups this is deduced from the ordinary character table. For non-soluble groups the absolutely irreducible \(p\)-modular representations are constructed.