D3d grupa punktowa
nieabelowe, nieredukowalne reprezentacje 6(8)Podgrupy D3d grupy punktowej: Cs, Ci, C2, C3, D3, C3v, S6
Tabela charakterów dla grupy punktowej D3d
| E | 2C3 | 3C'2 | i | 2S6 | 3σd | linear, rotations | quadratic | |
|---|---|---|---|---|---|---|---|---|
| A1g | 1 | 1 | 1 | 1 | 1 | 1 | x2+y2, z2 | |
| A2g | 1 | 1 | -1 | 1 | 1 | -1 | Rz | |
| Eg | 2 | -1 | 0 | 2 | -1 | 0 | (Rx, Ry) | (x2-y2, xy) (xz, yz) |
| A1u | 1 | 1 | 1 | -1 | -1 | -1 | ||
| A2u | 1 | 1 | -1 | -1 | -1 | 1 | z | |
| Eu | 2 | -1 | 0 | -2 | 1 | 0 | (x, y) |
Tabela mnożenia grupy punktowej D3d
| A1g | A2g | Eg | A1u | A2u | Eu | |
|---|---|---|---|---|---|---|
| A1g | A1g | A2g | Eg | A1u | A2u | Eu |
| A2g | A2g | A1g | Eg | A2u | A1u | Eu |
| Eg | Eg | Eg | A1g+A2g+Eg | Eu | Eu | A1u+A2u+Eu |
| A1u | A1u | A2u | Eu | A1g | A2g | Eg |
| A2u | A2u | A1u | Eu | A2g | A1g | Eg |
| Eu | Eu | Eu | A1u+A2u+Eu | Eg | Eg | A1g+A2g+Eg |
| C1 | Cs | Ci | ||
| C2 | C3 | C4 | C5 | C6 |
| C2v | C3v | C4v | C5v | C6v |
| C2h | C3h | C4h | C5h | C6h |
| D2 | D3 | D4 | D5 | D6 |
| D2h | D3h | D4h | D5h | D6h |
| D2d | D3d | D4d | D5d | D6d |
| S4 | S6 | S8 | S10 | |
| Td | Oh | Ih | ||
| C∞v | D∞h |
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