✅
D18h | E | 2C18 | 2C9 | 2C6 | 2(C9)2 | 2(C18)5 | 2C3 | 2(C18)7 | 2(C9)4 | C2 | 9C'2 | 9C''2 | i | 2(S9)5 | 2(S18)7 | 2S3 | 2(S18)5 | 2(S9)7 | 2S6 | 2S9 | 2S18 | σh | 9σd | 9σv |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A1g | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
A2g | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 |
B1g | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 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 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | -1 | 1 |
E1g | 2 | 2cos(π/9) | 2cos(2π/9) | 1 | 2cos(4π/9) | -2cos(4π/9) | -1 | -2cos(2π/9) | -2cos(π/9) | -2 | 0 | 0 | 2 | 2cos(π/9) | 2cos(2π/9) | 1 | 2cos(4π/9) | -2cos(4π/9) | -1 | -2cos(2π/9) | -2cos(π/9) | -2 | 0 | 0 |
E2g | 2 | 2cos(2π/9) | 2cos(4π/9) | -1 | -2cos(π/9) | -2cos(π/9) | -1 | 2cos(4π/9) | 2cos(2π/9) | 2 | 0 | 0 | 2 | 2cos(2π/9) | 2cos(4π/9) | -1 | -2cos(π/9) | -2cos(π/9) | -1 | 2cos(4π/9) | 2cos(2π/9) | 2 | 0 | 0 |
E3g | 2 | 1 | -1 | -2 | -1 | 1 | 2 | 1 | -1 | -2 | 0 | 0 | 2 | 1 | -1 | -2 | -1 | 1 | 2 | 1 | -1 | -2 | 0 | 0 |
E4g | 2 | 2cos(4π/9) | -2cos(π/9) | -1 | 2cos(2π/9) | 2cos(2π/9) | -1 | -2cos(π/9) | 2cos(4π/9) | 2 | 0 | 0 | 2 | 2cos(4π/9) | -2cos(π/9) | -1 | 2cos(2π/9) | 2cos(2π/9) | -1 | -2cos(π/9) | 2cos(4π/9) | 2 | 0 | 0 |
E5g | 2 | -2cos(4π/9) | -2cos(π/9) | 1 | 2cos(2π/9) | -2cos(2π/9) | -1 | 2cos(π/9) | 2cos(4π/9) | -2 | 0 | 0 | 2 | -2cos(4π/9) | -2cos(π/9) | 1 | 2cos(2π/9) | -2cos(2π/9) | -1 | 2cos(π/9) | 2cos(4π/9) | -2 | 0 | 0 |
E6g | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | 0 | 0 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | 0 | 0 |
E7g | 2 | -2cos(2π/9) | 2cos(4π/9) | 1 | -2cos(π/9) | 2cos(π/9) | -1 | -2cos(4π/9) | 2cos(2π/9) | -2 | 0 | 0 | 2 | -2cos(2π/9) | 2cos(4π/9) | 1 | -2cos(π/9) | 2cos(π/9) | -1 | -2cos(4π/9) | 2cos(2π/9) | -2 | 0 | 0 |
E8g | 2 | -2cos(π/9) | 2cos(2π/9) | -1 | 2cos(4π/9) | 2cos(4π/9) | -1 | 2cos(2π/9) | -2cos(π/9) | 2 | 0 | 0 | 2 | -2cos(π/9) | 2cos(2π/9) | -1 | 2cos(4π/9) | 2cos(4π/9) | -1 | 2cos(2π/9) | -2cos(π/9) | 2 | 0 | 0 |
A1u | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 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 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | 1 | 1 |
B1u | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 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 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | 1 | -1 |
E1u | 2 | 2cos(π/9) | 2cos(2π/9) | 1 | 2cos(4π/9) | -2cos(4π/9) | -1 | -2cos(2π/9) | -2cos(π/9) | -2 | 0 | 0 | -2 | -2cos(π/9) | -2cos(2π/9) | -1 | -2cos(4π/9) | 2cos(4π/9) | 1 | 2cos(2π/9) | 2cos(π/9) | 2 | 0 | 0 |
E2u | 2 | 2cos(2π/9) | 2cos(4π/9) | -1 | -2cos(π/9) | -2cos(π/9) | -1 | 2cos(4π/9) | 2cos(2π/9) | 2 | 0 | 0 | -2 | -2cos(2π/9) | -2cos(4π/9) | 1 | 2cos(π/9) | 2cos(π/9) | 1 | -2cos(4π/9) | -2cos(2π/9) | -2 | 0 | 0 |
E3u | 2 | 1 | -1 | -2 | -1 | 1 | 2 | 1 | -1 | -2 | 0 | 0 | -2 | -1 | 1 | 2 | 1 | -1 | -2 | -1 | 1 | 2 | 0 | 0 |
E4u | 2 | 2cos(4π/9) | -2cos(π/9) | -1 | 2cos(2π/9) | 2cos(2π/9) | -1 | -2cos(π/9) | 2cos(4π/9) | 2 | 0 | 0 | -2 | -2cos(4π/9) | 2cos(π/9) | 1 | -2cos(2π/9) | -2cos(2π/9) | 1 | 2cos(π/9) | -2cos(4π/9) | -2 | 0 | 0 |
E5u | 2 | -2cos(4π/9) | -2cos(π/9) | 1 | 2cos(2π/9) | -2cos(2π/9) | -1 | 2cos(π/9) | 2cos(4π/9) | -2 | 0 | 0 | -2 | 2cos(4π/9) | 2cos(π/9) | -1 | -2cos(2π/9) | 2cos(2π/9) | 1 | -2cos(π/9) | -2cos(4π/9) | 2 | 0 | 0 |
E6u | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | 0 | 0 | -2 | 1 | 1 | -2 | 1 | 1 | -2 | 1 | 1 | -2 | 0 | 0 |
E7u | 2 | -2cos(2π/9) | 2cos(4π/9) | 1 | -2cos(π/9) | 2cos(π/9) | -1 | -2cos(4π/9) | 2cos(2π/9) | -2 | 0 | 0 | -2 | 2cos(2π/9) | -2cos(4π/9) | -1 | 2cos(π/9) | -2cos(π/9) | 1 | 2cos(4π/9) | -2cos(2π/9) | 2 | 0 | 0 |
E8u | 2 | -2cos(π/9) | 2cos(2π/9) | -1 | 2cos(4π/9) | 2cos(4π/9) | -1 | 2cos(2π/9) | -2cos(π/9) | 2 | 0 | 0 | -2 | 2cos(π/9) | -2cos(2π/9) | 1 | -2cos(4π/9) | -2cos(4π/9) | 1 | -2cos(2π/9) | 2cos(π/9) | -2 | 0 | 0 |
Number of symmetry elements | h = 72 |
Number of classes, irreps | n = 24 |
Abelian group | no |
Optical Isomerism (Chirality) | no |
Polar | no |
Parity | yes |