D5h Point Group
not Abelian, 8(12) irreducible representationsSubgroups of D5h point group: Cs, C2, C5, D5, C2v, C5v, C5h
Character table for D5h point group
| E | 2C5 | 2(C5)2 | 5C'2 | σh | 2S5 | 2(S5)3 | 5σv | linear, rotations | quadratic | |
|---|---|---|---|---|---|---|---|---|---|---|
| A'1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | x2+y2, z2 | |
| A'2 | 1 | 1 | 1 | -1 | 1 | 1 | 1 | -1 | Rz | |
| E'1 | 2 | 2cos(2π/5) | 2cos(4π/5) | 0 | 2 | 2cos(2π/5) | 2cos(4π/5) | 0 | (x, y) | |
| E'2 | 2 | 2cos(4π/5) | 2cos(2π/5) | 0 | 2 | 2cos(4π/5) | 2cos(2π/5) | 0 | (x2-y2, xy) | |
| A''1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | ||
| A''2 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | 1 | z | |
| E''1 | 2 | 2cos(2π/5) | 2cos(4π/5) | 0 | -2 | -2cos(2π/5) | -2cos(4π/5) | 0 | (Rx, Ry) | (xz, yz) |
| E''2 | 2 | 2cos(4π/5) | 2cos(2π/5) | 0 | -2 | -2cos(4π/5) | -2cos(2π/5) | 0 |
Product table for D5h point group
| A'1 | A'2 | E'1 | E'2 | A''1 | A''2 | E''1 | E''2 | |
|---|---|---|---|---|---|---|---|---|
| A'1 | A'1 | A'2 | E'1 | E'2 | A''1 | A''2 | E''1 | E''2 |
| A'2 | A'2 | A'1 | E'1 | E'2 | A''2 | A''1 | E''1 | E''2 |
| E'1 | E'1 | E'1 | A'1+A'2+E'2 | E'1+E'2 | E''1 | E''1 | A''1+A''2+E''2 | E''1+E''2 |
| E'2 | E'2 | E'2 | E'1+E'2 | A'1+A'2+E'1 | E''2 | E''2 | E''1+E''2 | A''1+A''2+E''1 |
| A''1 | A''1 | A''2 | E''1 | E''2 | A'1 | A'2 | E'1 | E'2 |
| A''2 | A''2 | A''1 | E''1 | E''2 | A'2 | A'1 | E'1 | E'2 |
| E''1 | E''1 | E''1 | A''1+A''2+E''2 | E''1+E''2 | E'1 | E'1 | A'1+A'2+E'2 | E'1+E'2 |
| E''2 | E''2 | E''2 | E''1+E''2 | A''1+A''2+E''1 | E'2 | E'2 | E'1+E'2 | A'1+A'2+E'1 |
| 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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