C3v Point Group
not Abelian, 3(4) irreducible representationsSubgroups of C3v point group: Cs, C3
Character table for C3v point group
| E | 2C3 (z) | 3σv | linear, rotations | quadratic | |
|---|---|---|---|---|---|
| A1 | 1 | 1 | 1 | z | x2+y2, z2 |
| A2 | 1 | 1 | -1 | Rz | |
| E | 2 | -1 | 0 | (x, y) (Rx, Ry) | (x2-y2, xy) (xz, yz) |
Product table for C3v point group
| A1 | A2 | E | |
|---|---|---|---|
| A1 | A1 | A2 | E |
| A2 | A2 | A1 | E |
| E | E | E | A1+A2+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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