Character Tables for Common Symmetry Groups - The Dn
Groups
| D2 | E | C2(z) | C2(y) | C2(x) | ||
|---|---|---|---|---|---|---|
| A | 1 | 1 | 1 | 1 | x2, y2, z2 | |
| B1 | 1 | 1 | -1 | -1 | z, Rz | xy |
| B2 | 1 | -1 | 1 | -1 | y, Ry | xz |
| B3 | 1 | -1 | -1 | 1 | x, Rx | yz |
| D3 | E | 2C3 | 3C2 | ||
|---|---|---|---|---|---|
| A1 | 1 | 1 | 1 | x2 + y2, z2 | |
| A2 | 1 | 1 | -1 | z, Rz | |
| E | 2 | -10 | (x, y)(Rx, Ry) | (x2 - y2, xy)(xz, yz) |
| D4 | E | 2C4 | C2(=C42) | 2C2' | 2C2" | ||
|---|---|---|---|---|---|---|---|
| A1 | 1 | 1 | 1 | 1 | 1 | x2 + y2, z2 | |
| A2 | 1 | 1 | 1 | -1 | -1 | z, Rz | |
| B1 | 1 | -1 | 1 | 1 | -1 | x2 - y2 | |
| B2 | 1 | -1 | 1 | -1 | 1 | xy | |
| E | 2 | 0 | -2 | 0 | 0 | (x, y)(Rx, Ry) | (xz, yz) |
Reference: F.A. Cotton, "Chemical Applications of Group Theory," 3rd ed., Wiley-Interscience, NY, 1990.