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Molecular Symmetry and Group Theory |
| D3h | E | 2C3 | 3C2 | σh | 2S3 | 3σv | ||
| A1′ | 1 | 1 | 1 | 1 | 1 | 1 | x2+y2,z2 | |
| A2′ | 1 | 1 | -1 | 1 | 1 | -1 | Rz | |
| E′ | 2 | -1 | 0 | 2 | -1 | 0 | (x,y) | (x2-y2,xy) |
| A1″ | 1 | 1 | 1 | -1 | -1 | -1 | ||
| A2″ | 1 | 1 | -1 | -1 | -1 | 1 | z | |
| E″ | 2 | -1 | 0 | -2 | 1 | 0 | (Rx,Ry) | (xz,yz) |
| Td | E | 8C3 | 3C2 | 6S4 | 6σd | ||
| A1 | 1 | 1 | 1 | 1 | 1 | x2+y2+z2 | |
| A2 | 1 | 1 | 1 | -1 | -1 | ||
| E | 2 | -1 | 2 | 0 | 0 | (2z2-x2-y2,x2-y2) | |
| T1 | 3 | 0 | -1 | 1 | -1 | (Rx,Ry,Rz) | |
| T2 | 3 | 0 | -1 | -1 | 1 | (x,y,z) | (xy,xz,yz) |
| C2v | E | C2 | σv(xz) | σv′(xz) | ||
| A1 | 1 | 1 | 1 | 1 | z | x2,y2,z2 |
| A2 | 1 | 1 | -1 | -1 | Rz | xy |
| B1 | 1 | -1 | 1 | -1 | x,Ry | xz |
| B2 | 1 | -1 | -1 | 1 | y,Rx | yz |
| Oh | E | 8C3 | 6C2 | 6C4 | 3C2(=C42) | i | 6S4 | 8S6 | 3σh | 6σd | ||
| A1g | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | x2+y2+z2 | |
| A2g | 1 | 1 | -1 | -1 | 1 | 1 | -1 | 1 | 1 | -1 | ||
| Eg | 2 | -1 | 0 | 0 | 2 | 2 | 0 | -1 | 2 | 0 | (2z2-x2-y2,x2-y2) | |
| T1g | 3 | 0 | -1 | 1 | -1 | 3 | 1 | 0 | -1 | -1 | (Rx,Ry,Rz) | |
| T2g | 3 | 0 | 1 | -1 | -1 | 3 | -1 | 0 | -1 | 1 | (xz,yz,xy) | |
| A1u | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | ||
| A2u | 1 | 1 | -1 | -1 | 1 | -1 | 1 | -1 | -1 | 1 | ||
| Eu | 2 | -1 | 0 | 0 | 2 | -2 | 0 | 1 | -2 | 0 | ||
| T1u | 3 | 0 | -1 | 1 | -1 | -3 | -1 | 0 | 1 | -1 | (x,y,z) | |
| T2u | 3 | 0 | 1 | -1 | -1 | -3 | 1 | 0 | 1 | -1 |