S4 Point Group
Abelian, 3(4) irreducible representationsSubgroups of S4 point group: C2
Character table for S4 point group
| E | S4 | C2 | (S4)3 | linear, rotations | quadratic | |
|---|---|---|---|---|---|---|
| A | 1 | 1 | 1 | 1 | Rz | x2+y2, z2 |
| B | 1 | -1 | 1 | -1 | z | x2-y2, xy |
| E | 1 1 | i -i | -1 -1 | -i i | x+iy; Rx+iRy x-iy; Rx-iRy | (xz, yz) |
Product table for S4 point group
| A | B | E | |
|---|---|---|---|
| A | A | B | E |
| B | B | A | E |
| E | E | E | 2A+2B |
| 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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