C12h | E | C12 | C6 | C4 | C3 | (C12)5 | C2 | (C12)7 | (C3)2 | (C4)3 | (C6)5 | (C12)11 | i | (S12)7 | (S3)5 | (S4)3 | (S6)5 | (S12)11 | σh | S12 | S6 | S4 | S3 | (S12)5 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Ag | 1 | 1 | 1 | 1 | 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 | 1 | -1 | 1 | -1 |
E1g* | 2 | 1.7321 | 1 | 0 | -1 | -1.7321 | -2 | -1.7321 | -1 | 0 | 1 | 1.7321 | 2 | 1.7321 | 1 | 0 | -1 | -1.7321 | -2 | -1.7321 | -1 | 0 | 1 | 1.7321 |
E2g* | 2 | 1 | -1 | -2 | -1 | 1 | 2 | 1 | -1 | -2 | -1 | 1 | 2 | 1 | -1 | -2 | -1 | 1 | 2 | 1 | -1 | -2 | -1 | 1 |
E3g* | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 |
E4g* | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 |
E5g* | 2 | -1.7321 | 1 | 0 | -1 | 1.7321 | -2 | 1.7321 | -1 | 0 | 1 | -1.7321 | 2 | -1.7321 | 1 | 0 | -1 | 1.7321 | -2 | 1.7321 | -1 | 0 | 1 | -1.7321 |
Au | 1 | 1 | 1 | 1 | 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 | -1 | 1 | -1 | 1 |
E1u* | 2 | 1.7321 | 1 | 0 | -1 | -1.7321 | -2 | -1.7321 | -1 | 0 | 1 | 1.7321 | -2 | -1.7321 | -1 | 0 | 1 | 1.7321 | 2 | 1.7321 | 1 | 0 | -1 | -1.7321 |
E2u* | 2 | 1 | -1 | -2 | -1 | 1 | 2 | 1 | -1 | -2 | -1 | 1 | -2 | -1 | 1 | 2 | 1 | -1 | -2 | -1 | 1 | 2 | 1 | -1 |
E3u* | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 |
E4u* | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | -2 | 1 | 1 | -2 | 1 | 1 | -2 | 1 | 1 | -2 | 1 | 1 |
E5u* | 2 | -1.7321 | 1 | 0 | -1 | 1.7321 | -2 | 1.7321 | -1 | 0 | 1 | -1.7321 | -2 | 1.7321 | -1 | 0 | 1 | -1.7321 | 2 | -1.7321 | 1 | 0 | -1 | 1.7321 |
Number of symmetry elements | h = 24 |
Number of classes, irreps | n = 24 |
Number of real-valued irreducible representations | n = 14 |
Abelian group | yes |
Optical Isomerism (Chirality) | no |
Polar | no |
Parity | yes |