Character Tables for Common Symmetry Groups - The Sn
Groups
| S4 | E | S4 | C2 | S43 | ||
|---|---|---|---|---|---|---|
| A | 1 | 1 | 1 | 1 | Rz | x2 + y2, z2 |
| B | 1 | -1 | 1 | -1 | z | x2 - y2, xy |
| E | { 1 i -1 -i }
1 -i -1 i | (x, y); (Rx, Ry) | (xy, yz) | |||
| S6 | E | C3 | C32 | i | S65 | S6 | ε = exp(2π/3) | |
|---|---|---|---|---|---|---|---|---|
| Ag | 1 | 1 | 1 | 1 | 1 | 1 | Rz | x2 + y2, z2 |
| En | { 1 ε ε+ 1 ε ε+ }
1 ε+ ε 1 ε+ ε | (Rx, Ry) | (x2 - y2, xy); (xz, yz) | |||||
| Au | 1 | 1 | 1 | -1 | -1 | -1 | z | |
| Eu | { 1 ε ε+ -1 -ε -ε+ }
1 ε+ ε -1 -ε+ -ε | (x, y) | ||||||
Reference: F.A. Cotton, "Chemical Applications of Group Theory," 3rd ed., Wiley-Interscience, NY, 1990.