D2h Point Group
Abelian, 8 irreducible representationsSubgroups of D2h point group: Cs, Ci, C2, C2v, C2h
Character table for D2h point group
| E | C2 (z) | C2 (y) | C2 (x) | i | σ (xy) | σ (xz) | σ (yz) | linear, rotations | quadratic | |
|---|---|---|---|---|---|---|---|---|---|---|
| Ag | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | x2, y2, z2 | |
| B1g | 1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | Rz | xy |
| B2g | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | Ry | xz |
| B3g | 1 | -1 | -1 | 1 | 1 | -1 | -1 | 1 | Rx | yz |
| Au | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | ||
| B1u | 1 | 1 | -1 | -1 | -1 | -1 | 1 | 1 | z | |
| B2u | 1 | -1 | 1 | -1 | -1 | 1 | -1 | 1 | y | |
| B3u | 1 | -1 | -1 | 1 | -1 | 1 | 1 | -1 | x |
Product table for D2h point group
| Ag | B1g | B2g | B3g | Au | B1u | B2u | B3u | |
|---|---|---|---|---|---|---|---|---|
| Ag | Ag | B1g | B2g | B3g | Au | B1u | B2u | B3u |
| B1g | B1g | Ag | B3g | B2g | B1u | Au | B3u | B2u |
| B2g | B2g | B3g | Ag | B1g | B2u | B3u | Au | B1u |
| B3g | B3g | B2g | B1g | Ag | B3u | B2u | B1u | Au |
| Au | Au | B1u | B2u | B3u | Ag | B1g | B2g | B3g |
| B1u | B1u | Au | B3u | B2u | B1g | Ag | B3g | B2g |
| B2u | B2u | B3u | Au | B1u | B2g | B3g | Ag | B1g |
| B3u | B3u | B2u | B1u | Au | B3g | B2g | B1g | Ag |
| 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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