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.

SymmetricCharacterTable(n) : RngIntElt -> SeqEnum

AlternatingCharacterTable(n) : RngIntElt -> SeqEnum

The table of irreducible complex characters for the symmetric (alternating) group of degree n is constructed.

RationalCharacterTable(G) : Chtr -> SeqEnum

The table of irreducible rational 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.

Character(M) : ModGrp -> AlgChtrElt

Given a K[G]-module M, where K is a finite field of characteristic p a prime, the p-modular Brauer character of M is constructed.