S8 Point Group
Abelian, 5(8) irreducible representationsSubgroups of S8 point group: C2, C4
Character table for S8 point group
| E | S8 | C4 (z) | (S8)3 | C2 | (S8)5 | (C4)3 | (S8)7 | linear, rotations | quadratic | |
|---|---|---|---|---|---|---|---|---|---|---|
| A | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | Rz | x2+y2, z2 |
| B | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | z | |
| E1 | 1 1 | e e* | i -i | -e* -e | -1 -1 | -e -e* | -i i | e* e | x+iy x-iy | |
| E2 | 1 1 | i -i | -1 -1 | -i i | 1 1 | i -i | -1 -1 | -i i | (x2-y2, xy) | |
| E3 | 1 1 | -e -e* | i -i | e* e | -1 -1 | e e* | -i i | -e* -e | Rx+iRy Rx-iRy | (xz, yz) |
Product table for S8 point group
| A | B | E1 | E2 | E3 | |
|---|---|---|---|---|---|
| A | A | B | E1 | E2 | E3 |
| B | B | A | E3 | E2 | E1 |
| E1 | E1 | E3 | 2A+E2 | E1+E3 | 2B+E2 |
| E2 | E2 | E2 | E1+E3 | 2A+2B | E1+E3 |
| E3 | E3 | E1 | 2B+E2 | E1+E3 | 2A+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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