S18 | E | C9 | (C9)2 | C3 | (C9)4 | (C9)5 | (C3)2 | (C9)7 | (C9)8 | i | (S18)11 | (S18)13 | (S6)5 | (S18)17 | S18 | S6 | (S18)5 | (S18)7 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Ag | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
E1g* | 2 | 2cos(2π/9) | 2cos(4π/9) | -1 | 2cos(8π/9) | 2cos(8π/9) | -1 | 2cos(4π/9) | 2cos(2π/9) | 2 | 2cos(2π/9) | 2cos(4π/9) | -1 | 2cos(8π/9) | 2cos(8π/9) | -1 | 2cos(4π/9) | 2cos(2π/9) |
E2g* | 2 | 2cos(4π/9) | 2cos(8π/9) | -1 | 2cos(2π/9) | 2cos(2π/9) | -1 | 2cos(8π/9) | 2cos(4π/9) | 2 | 2cos(4π/9) | 2cos(8π/9) | -1 | 2cos(2π/9) | 2cos(2π/9) | -1 | 2cos(8π/9) | 2cos(4π/9) |
E3g* | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 |
E4g* | 2 | 2cos(8π/9) | 2cos(2π/9) | -1 | 2cos(4π/9) | 2cos(4π/9) | -1 | 2cos(2π/9) | 2cos(8π/9) | 2 | 2cos(8π/9) | 2cos(2π/9) | -1 | 2cos(4π/9) | 2cos(4π/9) | -1 | 2cos(2π/9) | 2cos(8π/9) |
Au | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 |
E1u* | 2 | 2cos(2π/9) | 2cos(4π/9) | -1 | 2cos(8π/9) | 2cos(8π/9) | -1 | 2cos(4π/9) | 2cos(2π/9) | -2 | -2cos(2π/9) | -2cos(4π/9) | 1 | -2cos(8π/9) | -2cos(8π/9) | 1 | -2cos(4π/9) | -2cos(2π/9) |
E2u* | 2 | 2cos(4π/9) | 2cos(8π/9) | -1 | 2cos(2π/9) | 2cos(2π/9) | -1 | 2cos(8π/9) | 2cos(4π/9) | -2 | -2cos(4π/9) | -2cos(8π/9) | 1 | -2cos(2π/9) | -2cos(2π/9) | 1 | -2cos(8π/9) | -2cos(4π/9) |
E3u* | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | -2 | 1 | 1 | -2 | 1 | 1 | -2 | 1 | 1 |
E4u* | 2 | 2cos(8π/9) | 2cos(2π/9) | -1 | 2cos(4π/9) | 2cos(4π/9) | -1 | 2cos(2π/9) | 2cos(8π/9) | -2 | -2cos(8π/9) | -2cos(2π/9) | 1 | -2cos(4π/9) | -2cos(4π/9) | 1 | -2cos(2π/9) | -2cos(8π/9) |
Number of symmetry elements | h = 18 |
Number of classes, irreps | n = 18 |
Number of real-valued irreducible representations | n = 10 |
Abelian group | yes |
Optical Isomerism (Chirality) | no |
Polar | no |
Parity | yes |