**Notation**

For each non-linear group, the tables give the most standard notation of the finite group isomorphic to the point group, followed by the order of the group (number of invariant symmetry operations). The finite group notation used is: Z_{n}: cyclic group of order *n*, D_{n}: dihedral group isomorphic to the symmetry group of an *n*–sided regular polygon, S_{n}: symmetric group on *n* letters, and A_{n}: alternating group on *n* letters.

The character tables then follow for all groups. The rows of the character tables correspond to the irreducible representations of the group, with their conventional names in the left margin. The naming conventions are as follows:

*A*and*B*are singly degenerate representations, with the former transforming symmetrically around the principal axis of the group, and the latter asymmetrically.*E*,*T*,*G*,*H*, ... are doubly, triply, quadruply, quintuply, ... degenerate representations.*g*and*u*subscripts denote symmetry and antisymmetry, respectively, with respect to a center of inversion. Subscripts "1" and "2" denote symmetry and antisymmetry, respectively, with respect to a nonprincipal rotation axis. Higher numbers denote additional representations with such asymmetry.- Single prime ( ' ) and double prime ( '' ) superscripts denote symmetry and antisymmetry, respectively, with respect to a horizontal mirror plane σ
_{h}, one perpendicular to the principal rotation axis.

All but the two rightmost columns correspond to the symmetry operations which are invariant in the group. In the case of sets of similar operations with the same characters for all representations, they are presented as one column, with the number of such similar operations noted in the heading.

The body of the tables contain the characters in the respective irreducible representations for each respective symmetry operation, or set of symmetry operations.

The two rightmost columns indicate which irreducible representations describe the symmetry transformations of the three Cartesian coordinates (*x*, *y* and *z*), rotations about those three coordinates (*R _{x}*,

*R*and

_{y}*R*), and functions of the quadratic terms of the coordinates(

_{z}*x*2,

*y*2,

*z*2,

*xy*,

*xz*, and

*yz*).

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. A superscripted uppercase "C" denotes complex conjugation.

Read more about this topic: List Of Character Tables For Chemically Important 3D Point Groups

### Other articles related to "notation":

**Notation**- Other Systems

... scorekeeping, to represent a game of baseball Chess

**notation**, to represent moves in a game of chess New Epoch Art

**Notation**, to represent the creation of a visual image using any physical media ...

**Notation**

...

**Notation**of gamakams is generally not found in the Indian music system ... the complex and fluid melodic movement of gamakas in a

**notation**system that uses fixed pitch signs ... In Carnatic music in particular, the

**notation**of gamakas is often unnecessary, as performers use

**notation**as a memory aid for compositions they already learned by hearing and imitating ...

**Notation**(RPN) (postfix

**Notation**)

... In reverse Polish

**notation**, also known as postfix

**notation**, all operations are entered after the operands on which the operation is performed ... Reverse Polish

**notation**is parenthesis-free which usually leads to fewer button presses needed to perform an operation ... + 0 ... + 12 Note example 1 which is one of the few examples where reverse Polish

**notation**does not use the fewest button presses – provided one does not rearrange operands ...

**Notation**- History

... An earlier form of music

**notation**from the Tang era survives in just one manuscript, dated to the seventh century CE, called Jieshi Diao Youlan ... is written in a longhand form called wenzi pu 〔文字譜〕 (literally "written

**notation**"), said to have been created by Yongmen Zhou (雍門周) during the Warring States Period, which gives all the details ... Later in the Tang dynasty Cao Rou (曹柔) and others simplified the

**notation**, using only the important elements of the characters (like string number, plucking technique, hui ...