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The body of the tables contain the characters in the respective irreducible representations for each respective symmetry operation, or set of symmetry operations. The symbol i used in the body of the table denotes the imaginary unit: i 2 = −1. Used in a column heading, it denotes the operation of inversion.
[[Category:Character set table templates]] to the <includeonly> section at the bottom of that page. Otherwise, add <noinclude>[[Category:Character set table templates]]</noinclude> to the end of the template code, making sure it starts on the same line as the code's last character.
The irreducible complex characters of a finite group form a character table which encodes much useful information about the group G in a concise form. Each row is labelled by an irreducible character and the entries in the row are the values of that character on any representative of the respective conjugacy class of G (because characters are class functions).
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The following table lists several notations for point groups: Hermann–Mauguin notation (used in crystallography), Schönflies notation (used to describe molecular symmetry), orbifold notation, and Coxeter notation. The latter three are not only conveniently related to its properties, but also to the order of the group.
Template:chset-cell4 — Character cell with character + Unicode value + decimal + octal index; Template:chset-ctrl — Control character cell with name + Unicode value; Template:chset-ctrl3 — Control character cell with name + Unicode value + decimal index; Template:chset-ctrl4 — Control character cell with name + Unicode value + decimal ...
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The degree of translation is then added as a subscript showing how far along the axis the translation is, as a portion of the parallel lattice vector. For example, 2 1 is a 180° (twofold) rotation followed by a translation of 1 / 2 of the lattice vector. 3 1 is a 120° (threefold) rotation followed by a translation of 1 / 3 of ...