This chapter introduces class functions and group characters in GAP.
First section Why Group Characters tells about the ideas why to use these structures besides the characters and character tables described in chapters Character Tables and Characters.
The subsequent section More about Class Functions tells details about the implementation of group characters and class functions in GAP.
Sections Operators for Class Functions and Functions for Class Functions tell about the operators and functions for class functions and (virtual) characters.
Sections ClassFunction, VirtualCharacter, Character, and Irr describe how to construct such class functions and group characters.
Sections IsClassFunction, IsVirtualCharacter, and IsCharacter describe the characteristic functions of class functions and virtual characters.
Then sections InertiaSubgroup and OrbitsCharacters describe other functions for characters.
Then sections Storing Subgroup Information, NormalSubgroupClasses, ClassesNormalSubgroup, and FactorGroupNormalSubgroupClasses tell about some functions and record components to access and store frequently used (normal) subgroups.
The final section Class Function Records describes the records that implement class functions.
In this chapter, all examples use irreducible characters of the symmetric group S_4. For running the examples, you must first define the group and its characters as follows.
gap> S4:= SolvableGroup( "S4" );; gap> irr:= Irr( S4 );;