D7d Character Table
| D7d | E | 2C7 | 2C72 | 2C73 | 7C2' | i | 2S145 | 2S143 | 2S14 | 7σd | Linear Functions |
Quadratic Functions |
| 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 | Rz | |
| E1g | 2 | 2 cos (2π/7) | 2 cos (4π/7) | 2 cos (6π/7) | 0 | 2 | 2 cos (2π/7) | 2 cos (4π/7) | 2 cos (6π/7) | 0 | (Rx,Ry) | (xz,yz) |
| E2g | 2 | 2 cos (4π/7) | 2 cos (6π/7) | 2 cos (2π/7) | 0 | 2 | 2 cos (4π/7) | 2 cos (6π/7) | 2 cos (2π/7) | 0 | (x2 - y2,xy) | |
| E3g | 2 | 2 cos (6π/7) | 2 cos (2π/7) | 2 cos (4π/7) | 0 | 2 | 2 cos (6π/7) | 2 cos (2π/7) | 2 cos (4π/7) | 0 | ||
| A1u | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | ||
| A2u | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | 1 | z | |
| E1u | 2 | 2 cos (2π/7) | 2 cos (4π/7) | 2 cos (6π/7) | 0 | -2 | -2 cos (2π/7) | -2 cos (4π/7) | -2 cos (6π/7) | 0 | (x,y) | |
| E2u | 2 | 2 cos (4π/7) | 2 cos (6π/7) | 2 cos (2π/7) | 0 | -2 | -2 cos (4π/7) | -2 cos (6π/7) | -2 cos (2π/7) | 0 | ||
| E3u | 2 | 2 cos (6π/7) | 2 cos (2π/7) | 2 cos (4π/7) | 0 | -2 | -2 cos (6π/7) | -2 cos (2π/7) | -2 cos (4π/7) | 0 |
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