C18h | E | 2C18 | 2C9 | 2C6 | 2(C9)2 | 2(C18)5 | 2C3 | 2(C18)7 | 2(C9)4 | C2 | i | 2(S9)13 | 2(S18)7 | 2S3 | 2(S18)5 | 2(S9)11 | 2S6 | 2S9 | 2S18 | σh |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Ag | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Bg | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 |
E1g* | 2 | 1.8794 | 1.5321 | 1 | 0.3473 | -0.3473 | -1 | -1.5321 | -1.8794 | -2 | 2 | 1.8794 | 1.5321 | 1 | 0.3473 | -0.3473 | -1 | -1.5321 | -1.8794 | -2 |
E2g* | 2 | 1.5321 | 0.3473 | -1 | -1.8794 | -1.8794 | -1 | 0.3473 | 1.5321 | 2 | 2 | 1.5321 | 0.3473 | -1 | -1.8794 | -1.8794 | -1 | 0.3473 | 1.5321 | 2 |
E3g* | 2 | 1 | -1 | -2 | -1 | 1 | 2 | 1 | -1 | -2 | 2 | 1 | -1 | -2 | -1 | 1 | 2 | 1 | -1 | -2 |
E4g* | 2 | 0.3473 | -1.8794 | -1 | 1.5321 | 1.5321 | -1 | -1.8794 | 0.3473 | 2 | 2 | 0.3473 | -1.8794 | -1 | 1.5321 | 1.5321 | -1 | -1.8794 | 0.3473 | 2 |
E5g* | 2 | -0.3473 | -1.8794 | 1 | 1.5321 | -1.5321 | -1 | 1.8794 | 0.3473 | -2 | 2 | -0.3473 | -1.8794 | 1 | 1.5321 | -1.5321 | -1 | 1.8794 | 0.3473 | -2 |
E6g* | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 |
E7g* | 2 | -1.5321 | 0.3473 | 1 | -1.8794 | 1.8794 | -1 | -0.3473 | 1.5321 | -2 | 2 | -1.5321 | 0.3473 | 1 | -1.8794 | 1.8794 | -1 | -0.3473 | 1.5321 | -2 |
E8g* | 2 | -1.8794 | 1.5321 | -1 | 0.3473 | 0.3473 | -1 | 1.5321 | -1.8794 | 2 | 2 | -1.8794 | 1.5321 | -1 | 0.3473 | 0.3473 | -1 | 1.5321 | -1.8794 | 2 |
Au | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 |
Bu | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 |
E1u* | 2 | 1.8794 | 1.5321 | 1 | 0.3473 | -0.3473 | -1 | -1.5321 | -1.8794 | -2 | -2 | -1.8794 | -1.5321 | -1 | -0.3473 | 0.3473 | 1 | 1.5321 | 1.8794 | 2 |
E2u* | 2 | 1.5321 | 0.3473 | -1 | -1.8794 | -1.8794 | -1 | 0.3473 | 1.5321 | 2 | -2 | -1.5321 | -0.3473 | 1 | 1.8794 | 1.8794 | 1 | -0.3473 | -1.5321 | -2 |
E3u* | 2 | 1 | -1 | -2 | -1 | 1 | 2 | 1 | -1 | -2 | -2 | -1 | 1 | 2 | 1 | -1 | -2 | -1 | 1 | 2 |
E4u* | 2 | 0.3473 | -1.8794 | -1 | 1.5321 | 1.5321 | -1 | -1.8794 | 0.3473 | 2 | -2 | -0.3473 | 1.8794 | 1 | -1.5321 | -1.5321 | 1 | 1.8794 | -0.3473 | -2 |
E5u* | 2 | -0.3473 | -1.8794 | 1 | 1.5321 | -1.5321 | -1 | 1.8794 | 0.3473 | -2 | -2 | 0.3473 | 1.8794 | -1 | -1.5321 | 1.5321 | 1 | -1.8794 | -0.3473 | 2 |
E6u* | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -2 | 1 | 1 | -2 | 1 | 1 | -2 | 1 | 1 | -2 |
E7u* | 2 | -1.5321 | 0.3473 | 1 | -1.8794 | 1.8794 | -1 | -0.3473 | 1.5321 | -2 | -2 | 1.5321 | -0.3473 | -1 | 1.8794 | -1.8794 | 1 | 0.3473 | -1.5321 | 2 |
E8u* | 2 | -1.8794 | 1.5321 | -1 | 0.3473 | 0.3473 | -1 | 1.5321 | -1.8794 | 2 | -2 | 1.8794 | -1.5321 | 1 | -0.3473 | -0.3473 | 1 | -1.5321 | 1.8794 | -2 |
Number of symmetry elements | h = 36 |
Number of classes, irreps | n = 36 |
Number of real-valued irreducible representations | n = 20 |
Abelian group | yes |
Optical Isomerism (Chirality) | no |
Polar | no |
Parity | yes |