Character Tables for Common Symmetry Groups - The Cnh
Groups
| C2h | E | C2 | i | σh | ||
|---|---|---|---|---|---|---|
| Ag | 1 | 1 | 1 | 1 | Rz | x2, y2, z2, xy |
| Bg | 1 | -1 | 1 | -1 | Rx, Ry | xz, yz |
| Au | 1 | 1 | -1 | -1 | z | |
| Bu | 1 | -1 | -1 | 1 | x, y |
| C3h | E | C3 | C32 | σh | S3 | S35 | ε = exp(2π/3) | |
|---|---|---|---|---|---|---|---|---|
| A | 1 | 1 | 1 | 1 | 1 | 1 | Rz | x2 + y2, z2 |
| E' | { 1 ε ε+ 1 ε ε+}
1 ε+ ε 1 ε+ ε | (x, y) | (x2 - y2, xy) | |||||
| A' | 1 | 1 | 1 | -1 | -1 | -1 | z | |
| E' | { 1 ε ε+ -1 -ε -ε+}
1 ε+ ε -1 -ε+ -ε | (Rx, Ry) | (xz, yz) | |||||
| C4h | E | C4 | C2 | C43 | i | S43 | σh | S4 | ||
|---|---|---|---|---|---|---|---|---|---|---|
| Ag | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | Rz | x2 + y2, z2 |
| Bg | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | x2 - y2, xy | |
| En | { 1 i -1 -i 1 i -1 -i }
1 -i -1 i 1 -i -1 i | (Rx, Ry) | (xz, yz) | |||||||
| Au | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | z | |
| Bu | 1 | -1 | 1 | -1 | -1 | 1 | -1 | 1 | ||
| Eu | { 1 i -1 -i -1 -i 1 i }
1 -1 -1 i -1 i 1 -i | (x, y) | ||||||||
Reference: F.A. Cotton, "Chemical Applications of Group Theory," 3rd ed., Wiley-Interscience, NY, 1990.