C4h Point Group
Abelian, 6(8) irreducible representationsSubgroups of C4h point group: Cs, Ci, C2, C4, C2h, S4
Character table for C4h point group
| E | C4(z) | C2 | (C4)3 | i | (S4)3 | σh | S4 | linear, rotations | quadratic | |
|---|---|---|---|---|---|---|---|---|---|---|
| Ag | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | Rz | x2+y2, z2 |
| Bg | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | x2-y2, xy | |
| Eg | 1 1 | i -i | -1 -1 | -i i | 1 1 | i -i | -1 -1 | -i i | Rx+iRy Rx-iRy | (xz, yz) |
| Au | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | z | |
| Bu | 1 | -1 | 1 | -1 | -1 | 1 | -1 | 1 | ||
| Eu | 1 1 | i -i | -1 -1 | -i i | -1 -1 | -i i | 1 1 | i -i | x+iy x-iy |
Product table for C4h point group
| Ag | Bg | Eg | Au | Bu | Eu | |
|---|---|---|---|---|---|---|
| Ag | Ag | Bg | Eg | Au | Bu | Eu |
| Bg | Bg | Ag | Eg | Bu | Au | Eu |
| Eg | Eg | Eg | Ag+Bg+Eg | Eu | Eu | Au+Bu+Eu |
| Au | Au | Bu | Eu | Ag | Bg | Eg |
| Bu | Bu | Au | Eu | Bg | Ag | Eg |
| Eu | Eu | Eu | Au+Bu+Eu | Eg | Eg | Ag+Bg+Eg |
| 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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