In group theory, a branch of abstract algebra, a character table is a two-dimensional table whose rows correspond to irreducible group representations, and whose columns correspond to classes of group elements. The entries consist of characters, the trace of the matrices representing group elements of the column's class in the given row's group representation.
In chemistry, crystallography, and spectroscopy, character tables of point groups are used to classify e.g. molecular vibrations according to their symmetry, and to predict whether a transition between two states is forbidden for symmetry reasons.
Read more about Character Table: Definition and Example, Orthogonality Relations, Properties, Outer Automorphisms
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