## Categorisation of point groups by symmetry operations |

This table lists point group symmetries along with their symmetry
operations, the order of the group (i.e. the number of symmetry
operations) and common notations.
links to a correlation table, and links to tables of products of irreducible representations. The group produced by combination with inversion is listed under "x *i*". This, in the case of crystolographic point groups, is the *Laue class* which corresponds to the symmetry of reciprocal space. Isomorphic groups are also listed where
character tables are available.

Cubic* | ||||||||

Operations | Order | Schönflies Symbol |
International Symbol |
Full Symmetry Symbol |
Correlation Table |
Irred. Rep. products |
x i |
Isomorph. with |

E, 4C_{3}, 4C_{3}^{2}, 3C_{2} |
12 | T |
23 | 23 | T_{h} |
|||

E, 8C_{3}, 3C_{2}, 3_{v},
i, 8S_{6} |
24 | T_{h} |
m3 |
T_{h} |
||||

E, 6C_{4}, 8C_{3}, 3C_{2}, 6C_{2}' |
24 | O |
432 | 432 | O_{h} |
T_{d} |
||

E, 8C_{3}, 3C_{2}, 6S_{4}, 6_{d} |
24 | T_{d} |
3m |
3m |
O_{h} |
O |
||

E, 8C_{3}, 6C_{2}, 6C_{4}, 3C_{2}',
i, 6S_{4}, 8S_{6}, 3_{h}, 6_{d} |
48 | O_{h} |
m3m |
O_{h} |
||||

Tetragonal | ||||||||

Orthorhombic | ||||||||

Monoclinic | ||||||||

Triclinic | ||||||||

Trigonal | ||||||||

Hexagonal | ||||||||

Non-Crystallographic | ||||||||

All |

- Symmetry pages index
- Categorisation by unit cell parameters
- Correlation table index
- 3D objects
- Stereographs
- A brief description of tables