gives the character table of a group.


  • The trace of the representation matrix TemplateBox[{T}, Gamma] of an element of a group is called character . The character systems of the irreducible representations of a finite group are conventionally displayed in the form of a "character table".
  • All elements in the same class have the same character.
  • The number of inequivalent irreducible representations is equal to the number of classes of a finite group .
  • For a finite group a necessary and sufficient condition for two representations to be equivalent is provided by the equality of their character systems.
  • If a group is finite, the sum of the squares of the dimensions of the inequivalent irreducible representations is equal to the order of .
  • The output of GTCharacterTable is a list of all classes, a list of the character system and a list of the names of the irreducible representations.
  • Attention: The names of the irreducible representations are generated automatically and may differ from tables in the literature!
  • The following options can be given:
  • GOIrepNotation"Bethe"Notation for irreducible representations
    GOVerboseTrueControls the output of information
    GOFastGOFastValueSkips the input vlidation
    GORealityFalseProvides information about the reality of the irreducible representations
    GOMethod"NumericalApproximant"Method for internal eigenvalue solution
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 5.8

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

First, load the package:

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As an example, we calculate the character table of the point group C3v.

Click for copyable input
Click for copyable input