D5 Point Group
not Abelian, 4(6) irreducible representationsSubgroups of D5 point group: C2, C5
Character table for D5 point group
| E | 2C5 (z) | 2(C5)2 | 5C'2 | linear, rotations | quadratic | |
|---|---|---|---|---|---|---|
| A1 | 1 | 1 | 1 | 1 | x2+y2, z2 | |
| A2 | 1 | 1 | 1 | -1 | z, Rz | |
| E1 | 2 | 2cos(2π/5) | 2cos(4π/5) | 0 | (x, y) (Rx, Ry) | (xz, yz) |
| E2 | 2 | 2cos(4π/5) | 2cos(2π/5) | 0 |
Product table for D5 point group
| A1 | A2 | E1 | E2 | |
|---|---|---|---|---|
| A1 | A1 | A2 | E1 | E2 |
| A2 | A2 | A1 | E1 | E2 |
| E1 | E1 | E1 | A1+A2+E2 | E1+E2 |
| E2 | E2 | E2 | E1+E2 | 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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