S6 Point Group
Abelian, 4(6) irreducible representationsSubgroups of S6 point group: Ci, C3
Character table for S6 point group
| E | C3(z) | (C3)2 | i | (S6)5 | S6 | linear, rotations | quadratic | |
|---|---|---|---|---|---|---|---|---|
| Ag | 1 | 1 | 1 | 1 | 1 | 1 | Rz | x2+y2, z2 |
| Eg | 1 1 | e e* | e* e | 1 1 | e e* | e* e | Rx+iRy Rx-iRy | (x2-y2, xy) (xz, yz) |
| Au | 1 | 1 | 1 | -1 | -1 | -1 | z | |
| Eu | 1 1 | e e* | e* e | -1 -1 | -e -e* | -e* -e | x+iy x-iy |
Product table for S6 point group
| Ag | Eg | Au | Eu | |
|---|---|---|---|---|
| Ag | Ag | Eg | Au | Eu |
| Eg | Eg | 2Ag+Eg | Au | 2Au+Eu |
| Au | Au | Eu | Ag | Eg |
| Eu | Au | 2Au+Eu | Eg | 2Ag+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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