D8h Character Table
| D8h | E | 2C8 | 2C83 | 2C4 | C2 | 4C2' | 4C2" | i | 2S8 | 2S83 | 2S4 | σh | 4σd | 4σv | Linear Functions |
Quadratic Functions |
| A1g | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | x2 + y2, z2 | |
| A2g | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | Rz | |
| B1g | 1 | -1 | -1 | 1 | 1 | 1 | -1 | 1 | -1 | -1 | 1 | 1 | 1 | -1 | ||
| B2g | 1 | -1 | -1 | 1 | 1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | 1 | ||
| E1g | 2 | 2½ | -(2½) | 0 | -2 | 0 | 0 | 2 | 2½ | -(2½) | 0 | -2 | 0 | 0 | (Rx,Ry) | (xz,yz) |
| E2g | 2 | 0 | 0 | -2 | 2 | 0 | 0 | 2 | 0 | 0 | -2 | 2 | 0 | 0 | (x2 - y2,xy) | |
| E3g | 2 | -(2½) | 2½ | 0 | -2 | 0 | 0 | 2 | -(2½) | 2½ | 0 | -2 | 0 | 0 | ||
| A1u | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | ||
| A2u | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 | z | |
| B1u | 1 | -1 | -1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | -1 | -1 | -1 | 1 | ||
| B2u | 1 | -1 | -1 | 1 | 1 | -1 | 1 | -1 | 1 | 1 | -1 | -1 | 1 | -1 | ||
| E1u | 2 | 2½ | -(2½) | 0 | -2 | 0 | 0 | -2 | -(2½) | 2½ | 0 | 2 | 0 | 0 | (x,y) | |
| E2u | 2 | 0 | 0 | -2 | 2 | 0 | 0 | -2 | 0 | 0 | 2 | -2 | 0 | 0 | ||
| E3u | 2 | -(2½) | 2½ | 0 | -2 | 0 | 0 | -2 | 2½ | -(2½) | 0 | 2 | 0 | 0 |
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