Class Functions
characters
group characters
virtual characters
generalized characters

This chapter describes operations for class functions of finite groups. For operations concerning character tables, see Chapter .

Several examples in this chapter require the &GAP; Character Table Library to be available. If it is not yet loaded then we load it now.

gap> LoadPackage( "ctbllib" ); true
Why Class Functions?
<#Include Label="[1]{ctblfuns}"> <#Include Label="IsClassFunction">

Basic Operations for Class Functions
<#Include Label="[2]{ctblfuns}"> <#Include Label="UnderlyingCharacterTable"> <#Include Label="ValuesOfClassFunction">

Comparison of Class Functions
<#Include Label="[3]{ctblfuns}">

Arithmetic Operations for Class Functions
<#Include Label="[4]{ctblfuns}">

Printing Class Functions
<#Include Label="[5]{ctblfuns}">

Creating Class Functions from Values Lists
<#Include Label="ClassFunction"> <#Include Label="VirtualCharacter"> <#Include Label="Character"> <#Include Label="ClassFunctionSameType">

Creating Class Functions using Groups
<#Include Label="TrivialCharacter"> <#Include Label="NaturalCharacter"> <#Include Label="PermutationCharacter">

Operations for Class Functions
<#Include Label="[6]{ctblfuns}"> <#Include Label="IsCharacter"> <#Include Label="IsVirtualCharacter"> <#Include Label="IsIrreducibleCharacter"> <#Include Label="DegreeOfCharacter"> <#Include Label="ScalarProduct:ctblfuns"> <#Include Label="MatScalarProducts"> <#Include Label="Norm:ctblfuns"> <#Include Label="ConstituentsOfCharacter"> <#Include Label="KernelOfCharacter"> <#Include Label="ClassPositionsOfKernel"> <#Include Label="CentreOfCharacter"> <#Include Label="ClassPositionsOfCentre:ctblfuns"> <#Include Label="InertiaSubgroup"> <#Include Label="CycleStructureClass"> <#Include Label="IsTransitive:ctblfuns"> <#Include Label="Transitivity:ctblfuns"> <#Include Label="CentralCharacter"> <#Include Label="DeterminantOfCharacter"> <#Include Label="EigenvaluesChar"> <#Include Label="Tensored">

Restricted and Induced Class Functions
<#Include Label="[7]{ctblfuns}"> <#Include Label="RestrictedClassFunction"> <#Include Label="RestrictedClassFunctions"> <#Include Label="InducedClassFunction"> <#Include Label="InducedClassFunctions"> <#Include Label="InducedClassFunctionsByFusionMap"> <#Include Label="InducedCyclic">

Reducing Virtual Characters
<#Include Label="[8]{ctblfuns}"> <#Include Label="ReducedClassFunctions"> <#Include Label="ReducedCharacters"> <#Include Label="IrreducibleDifferences"> <#Include Label="LLL"> <#Include Label="Extract"> <#Include Label="OrthogonalEmbeddingsSpecialDimension"> <#Include Label="Decreased"> <#Include Label="DnLattice"> <#Include Label="DnLatticeIterative">

Symmetrizations of Class Functions
<#Include Label="Symmetrizations"> <#Include Label="SymmetricParts"> <#Include Label="AntiSymmetricParts"> <#Include Label="OrthogonalComponents"> <#Include Label="SymplecticComponents">

Molien Series
<#Include Label="MolienSeries"> <#Include Label="MolienSeriesInfo"> <#Include Label="ValueMolienSeries"> <#Include Label="MolienSeriesWithGivenDenominator">

Possible Permutation Characters
<#Include Label="[1]{ctblpope}"> <#Include Label="PermCharInfo"> <#Include Label="PermCharInfoRelative">

Computing Possible Permutation Characters
<#Include Label="PermChars"> <#Include Label="TestPerm1"> <#Include Label="PermBounds"> <#Include Label="PermComb"> <#Include Label="Inequalities">

Operations for Brauer Characters
<#Include Label="FrobeniusCharacterValue"> <#Include Label="BrauerCharacterValue"> <#Include Label="SizeOfFieldOfDefinition"> <#Include Label="RealizableBrauerCharacters">

Domains Generated by Class Functions
<#Include Label="[9]{ctblfuns}">