|
Cubic |
(T Th O Td Oh) |
Tetragonal |
(C4 S4 C4h D4 C4v D2d D4h) |
Orthorhombic |
(D2 C2v D2h) |
Monoclinic |
(C2 Cs C2h) |
Triclinic |
(C1 Ci) |
Trigonal |
Operations |
Order |
Schönflies Symbol |
International Symbol |
Full Symmetry Symbol |
Correlation Table |
Irred. Rep. products |
× i |
Isomorph. with |
E, C3, C32 |
3 |
C3 |
3 |
3 |
|
⊗ |
S6 |
|
E, C3, C32, i, S65, S6 |
6 |
S6(C3i) |
|
|
|
⊗ |
S6 |
C6, C3h |
E, 2C3, 3C2 |
6 |
D3 |
32 |
32 |
|
⊗ |
D3d |
C3v |
E, 2C3, 3σv |
6 |
C3v |
3m |
3m |
|
⊗ |
D3d |
D3 |
E, 2C3, 3C2, i, 2S6, 3σd |
12 |
D3d |
m |
 |
|
⊗ |
D3d |
C6v, D6, D3h |
Hexagonal |
(C6 C3h C6h D6 C6v D3h D6h) |
Non-crystallographic |
(C∞ C∞h C∞v D∞h C5 S8 D5 C5v C5h D4d D5d D5h D6d I Ih) |
All |
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 "× 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. |