C6h 점군
아벨, 8(12) 기약 표현C6h 점군의 하위 군: Cs, Ci, C2, C3, C6, C2h, C3h, S6
C6h 점군에 대한 지표표
| E | C6(z) | C3 | C2 | (C3)2 | (C6)5 | i | (S3)5 | (S6)5 | σh | S6 | S3 | linear, rotations | quadratic | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Ag | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | Rz | x2+y2, z2 | |
| Bg | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | ||
| E1g | 1 1 | e e* | -e* -e | -1 -1 | -e -e* | e* e | 1 1 | e e* | -e* -e | -1 -1 | -e -e* | e* e | Rx+iRy Rx-iRy | (xz, yz) |
| E2g | 1 1 | -e* -e | -e -e* | 1 1 | -e* -e | -e -e* | 1 1 | -e* -e | -e -e* | 1 1 | -e* -e | -e -e* | (x2-y2, xy) | |
| Au | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | z | |
| Bu | 1 | -1 | 1 | -1 | 1 | -1 | -1 | 1 | -1 | 1 | -1 | 1 | ||
| E1u | 1 1 | e e* | -e* -e | -1 -1 | -e -e* | e* e | -1 -1 | -e -e* | e* e | 1 1 | e e* | -e* -e | x+iy x-iy | |
| E2u | 1 1 | -e* -e | -e -e* | 1 1 | -e* -e | -e -e* | -1 -1 | e* e | e e* | -1 -1 | e* e | e e* |
C6h 점군의 곱셈표
| Ag | Bg | E1g | E2g | Au | Bu | E1u | E2u | |
|---|---|---|---|---|---|---|---|---|
| Ag | Ag | Bg | E1g | E2g | Au | Bu | E1u | E2u |
| Bg | Bg | Ag | E2g | E1g | Bu | Au | E2u | E1u |
| E1g | E1g | E2g | 2Ag+E2g | 2Bg+E1g | E1u | E2u | 2Au+E2u | 2Bu+E1u |
| E2g | E2g | E1g | 2Bg+E1g | 2Ag+E2g | E2u | E1u | 2Bu+E1u | 2Au+E2u |
| Au | Au | Bu | E1u | E2u | Ag | Bg | E1g | E2g |
| Bu | Bu | Au | E2u | E1u | Bg | Ag | E2g | E1g |
| E1u | E1u | E2u | 2Au+E2u | 2Bu+E1u | E1g | E2g | 2Ag+E2g | 2Bg+E1g |
| E2u | E2u | E1u | 2Bu+E1u | 2Au+E2u | E2g | E1g | 2Bg+E1g | 2Ag+E2g |
| 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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