D6d Point Group
not Abelian, 9(14) irreducible representationsSubgroups of D6d point group: Cs, C2, C3, C6, D2, D3, D6, C2v, C3v, C6v, S4, S12
Character table for D6d point group
| E | 2S12 | 2C6 | 2S4 | 2C3 | 2(S12)5 | C2 | 6C'2 | 6σd | linear, rotations | quadratic | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| A1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | x2+y2, z2 | |
| A2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | Rz | |
| B1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | 1 | -1 | ||
| B2 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | z | |
| E1 | 2 | (3)1/2 | 1 | 0 | -1 | -(3)1/2 | -2 | 0 | 0 | (x, y) | |
| E2 | 2 | 1 | -1 | -2 | -1 | 1 | 2 | 0 | 0 | (x2-y2, xy) | |
| E3 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 0 | ||
| E4 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | 0 | 0 | ||
| E5 | 2 | -(3)1/2 | 1 | 0 | -1 | (3)1/2 | -2 | 0 | 0 | (Rx, Ry) | (xz, yz) |
Product table for D6d point group
| A1 | A2 | B1 | B2 | E1 | E2 | E3 | E4 | E5 | |
|---|---|---|---|---|---|---|---|---|---|
| A1 | A1 | A2 | B1 | B2 | E1 | E2 | E3 | E4 | E5 |
| A2 | A2 | A1 | B2 | B1 | E1 | E2 | E3 | E4 | E5 |
| B1 | B1 | B2 | A1 | A2 | E5 | E4 | E3 | E2 | E1 |
| B2 | B2 | B1 | A2 | A1 | E5 | E4 | E3 | E2 | E1 |
| E1 | E1 | E1 | E5 | E5 | A1+A2+E2 | E1+E3 | E2+E4 | E3+E5 | B1+B2+E4 |
| E2 | E2 | E2 | E4 | E4 | E1+E3 | A1+A2+E4 | E1+E5 | B1+B2+E3 | E3+E5 |
| E3 | E3 | E3 | E3 | E3 | E2+E4 | E1+E5 | A1+A2+B1+B2 | E1+E5 | E2+E4 |
| E4 | E4 | E4 | E2 | E2 | E3+E5 | B1+B2+E2 | E1+E5 | A1+A2+E4 | E1+E3 |
| E5 | E5 | E5 | E1 | E1 | B1+B2+E4 | E3+E5 | E2+E4 | E1+E3 | A1+A2+E2 |
| 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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