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This lists the character tables for the more common molecular point groups used in the study of molecular symmetry. These tables are based on the group-theoretical treatment of the symmetry operations present in common molecules, and are useful in molecular spectroscopy and quantum chemistry. Information regarding the use of the tables, as well ...
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).
In Schoenflies notation, point groups are denoted by a letter symbol with a subscript. The symbols used in crystallography mean the following: C n (for cyclic) indicates that the group has an n-fold rotation axis.
The irrep table for this symmetry group has the form below and, taking the 3D representations of the 4 operations in the order they appear in the diagram we obtain characters (3,-1,-3,1). The first column tells us there are 3 1D irreps, the second column (C 2 ) that there is 1 A and 2 B's while the third column reveals that they are all ...
Translations within the lattice in the form of screw axes and glide planes are also noted, giving a complete crystallographic space group. These are the Bravais lattices in three dimensions: P primitive; I body centered (from the German Innenzentriert) F face centered (from the German Flächenzentriert) A centered on A faces only; B centered on ...
English: Character tables of binary tetrahedral, octahedral and icosahedral subgroups from "Ueber die Composition der Charaktere einer Gruppe", Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin, Deutsche Akademie der Wissenschaften zu Berlin, 6 April 1899, page 339
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.
Used with Template:chset-tableformat to indicate a printable character table cell. For example, the first four ASCII digit characters "0" through "3" ( Unicode U+0030 through U+0033, decimal 48 through 51) are coded as rows in a character set table like this: