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Character table

In group theory, a branch of abstract algebra, a character table is a two-dimensional table whose rows correspond to irreducible representations, and whose columns correspond to conjugacy classes of group elements. The entries consist of characters, the traces of the matrices representing group elements of the column's class in the given row's group…

Characters, Properties & Definition and example

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Overview

Definition and example

Orthogonality relations

Properties

Outer automorphisms

Finding the vibrational modes of a water molecule using character table

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Map overview Semantic statistics

Character table

Nodes74
Edges73
Triples54
Avg. degree1.97
Density0.027027
Components1

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Character table

Top relations

see also · 17
Character table → Applications, Character Theory, Dover Publications, Eric, Finite Groups, GroupNames, Irreducible, Isaacs, Lock-gray-alt-2, Lock-green, Lock-red-alt-2, Martin, MathWorld, Rowland, Todd, Weisstein, Wikisource-logo
related to Outer automorphisms · 10
Character table → Aut, For, Formally, GL, If, In, Note, Out, The, Thus
related to Definition and example · 6
Character table → Characters, Each, Here, It, Similarly, The
related to Finding Γreducible from the Character Table of H²O molecule · 6
Character table → Below, H2O, In, Mulliken, The, Water
related to Calculating the irreducible representation Γirreducible from the reducible representation Γreducible along with the character table · 4
Character table → From, Gamma, H2O, Using
related to Orthogonality relations · 2
Character table → The, With
related to Properties · 2
Character table → Certain, Complex
related to Rotational motion for water molecule · 2
Character table → As, Rotational
related to Translational motion for water molecule · 2
Character table → As, Translational
is a · 1
Character table → two-dimensional table whose rows correspond to irreducible representations

Important terminology Word statistics

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Important terminology

character group displaystyle irreducible table representation characters conjugacy molecule representations class symmetry γreducible functions axes first operation classes reducible linear

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Character tableis atwo-dimensional table whose rows correspond to irreducible representations0.90text
x 2instance ofthen the mode is IR activeIf there is a quadratic functions0.80text
Character tablerelated to Calculating the irreducible representation Γirreducible from the reducible representation Γreducible along with the character tableFrom0.60section
Character tablerelated to Calculating the irreducible representation Γirreducible from the reducible representation Γreducible along with the character tableUsing0.60section
Character tablerelated to Calculating the irreducible representation Γirreducible from the reducible representation Γreducible along with the character tableGamma0.60section
Character tablerelated to Calculating the irreducible representation Γirreducible from the reducible representation Γreducible along with the character tableH2O0.60section
Character tablerelated to Definition and exampleThe0.60section
Character tablerelated to Definition and exampleEach0.60section
Character tablerelated to Definition and exampleIt0.60section
Character tablerelated to Definition and exampleSimilarly0.60section
Character tablerelated to Definition and exampleCharacters0.60section
Character tablerelated to Definition and exampleHere0.60section

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