D3h Point Group
not Abelian, 6(8) irreducible representationsSubgroups of D3h point group: Cs, C2, C3, D3, C2v, C3v, C3h
Character table for D3h point group
| E | 2C3 | 3C'2 | σh | 2S3 | 3σv | linear, rotations | quadratic | |
|---|---|---|---|---|---|---|---|---|
| A'1 | 1 | 1 | 1 | 1 | 1 | 1 | x2+y2, z2 | |
| A'2 | 1 | 1 | -1 | 1 | 1 | -1 | Rz | |
| E' | 2 | -1 | 0 | 2 | -1 | 0 | (x, y) | (x2-y2, xy) |
| A''1 | 1 | 1 | 1 | -1 | -1 | -1 | ||
| A''2 | 1 | 1 | -1 | -1 | -1 | 1 | z | |
| E'' | 2 | -1 | 0 | -2 | 1 | 0 | (Rx, Ry) | (xz, yz) |
Product table for D3h point group
| A'1 | A'2 | E' | A''1 | A''2 | E'' | |
|---|---|---|---|---|---|---|
| A'1 | A'1 | A'2 | E' | A''1 | A''2 | E'' |
| A'2 | A'2 | A'1 | E' | A''2 | A''1 | E'' |
| E' | E' | E' | A'1+A'2+E' | E'' | E'' | A''1+A''2+E'' |
| A''1 | A''1 | A''2 | E'' | A'1 | A'2 | E' |
| A''2 | A''2 | A''1 | E'' | A'2 | A'1 | E' |
| E'' | E'' | E'' | A''1+A''2+E'' | E' | E' | A'1+A'2+E' |
| 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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