C20h | E | C20 | C10 | (C20)3 | C5 | C4 | (C10)3 | (C20)7 | (C5)2 | (C20)9 | C2 | (C20)11 | (C5)3 | (C20)13 | (C10)7 | (C4)3 | (C5)4 | (C20)17 | (C10)9 | (C20)19 | i | (S20)11 | (S5)3 | (S20)13 | (S10)7 | (S4)3 | (S5)9 | (S20)17 | (S10)9 | (S20)19 | σh | S20 | S10 | (S20)3 | S5 | S4 | (S10)3 | (S20)7 | (S5)7 | (S20)9 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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 | 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 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 |
E1g* | 2 | 1.9021 | 1.6180 | 1.1756 | 0.6180 | 0 | -0.6180 | -1.1756 | -1.6180 | -1.9021 | -2 | -1.9021 | -1.6180 | -1.1756 | -0.6180 | 0 | 0.6180 | 1.1756 | 1.6180 | 1.9021 | 2 | 1.9021 | 1.6180 | 1.1756 | 0.6180 | 0 | -0.6180 | -1.1756 | -1.6180 | -1.9021 | -2 | -1.9021 | -1.6180 | -1.1756 | -0.6180 | 0 | 0.6180 | 1.1756 | 1.6180 | 1.9021 |
E2g* | 2 | 1.6180 | 0.6180 | -0.6180 | -1.6180 | -2 | -1.6180 | -0.6180 | 0.6180 | 1.6180 | 2 | 1.6180 | 0.6180 | -0.6180 | -1.6180 | -2 | -1.6180 | -0.6180 | 0.6180 | 1.6180 | 2 | 1.6180 | 0.6180 | -0.6180 | -1.6180 | -2 | -1.6180 | -0.6180 | 0.6180 | 1.6180 | 2 | 1.6180 | 0.6180 | -0.6180 | -1.6180 | -2 | -1.6180 | -0.6180 | 0.6180 | 1.6180 |
E3g* | 2 | 1.1756 | -0.6180 | -1.9021 | -1.6180 | 0 | 1.6180 | 1.9021 | 0.6180 | -1.1756 | -2 | -1.1756 | 0.6180 | 1.9021 | 1.6180 | 0 | -1.6180 | -1.9021 | -0.6180 | 1.1756 | 2 | 1.1756 | -0.6180 | -1.9021 | -1.6180 | 0 | 1.6180 | 1.9021 | 0.6180 | -1.1756 | -2 | -1.1756 | 0.6180 | 1.9021 | 1.6180 | 0 | -1.6180 | -1.9021 | -0.6180 | 1.1756 |
E4g* | 2 | 0.6180 | -1.6180 | -1.6180 | 0.6180 | 2 | 0.6180 | -1.6180 | -1.6180 | 0.6180 | 2 | 0.6180 | -1.6180 | -1.6180 | 0.6180 | 2 | 0.6180 | -1.6180 | -1.6180 | 0.6180 | 2 | 0.6180 | -1.6180 | -1.6180 | 0.6180 | 2 | 0.6180 | -1.6180 | -1.6180 | 0.6180 | 2 | 0.6180 | -1.6180 | -1.6180 | 0.6180 | 2 | 0.6180 | -1.6180 | -1.6180 | 0.6180 |
E5g* | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 |
E6g* | 2 | -0.6180 | -1.6180 | 1.6180 | 0.6180 | -2 | 0.6180 | 1.6180 | -1.6180 | -0.6180 | 2 | -0.6180 | -1.6180 | 1.6180 | 0.6180 | -2 | 0.6180 | 1.6180 | -1.6180 | -0.6180 | 2 | -0.6180 | -1.6180 | 1.6180 | 0.6180 | -2 | 0.6180 | 1.6180 | -1.6180 | -0.6180 | 2 | -0.6180 | -1.6180 | 1.6180 | 0.6180 | -2 | 0.6180 | 1.6180 | -1.6180 | -0.6180 |
E7g* | 2 | -1.1756 | -0.6180 | 1.9021 | -1.6180 | 0 | 1.6180 | -1.9021 | 0.6180 | 1.1756 | -2 | 1.1756 | 0.6180 | -1.9021 | 1.6180 | 0 | -1.6180 | 1.9021 | -0.6180 | -1.1756 | 2 | -1.1756 | -0.6180 | 1.9021 | -1.6180 | 0 | 1.6180 | -1.9021 | 0.6180 | 1.1756 | -2 | 1.1756 | 0.6180 | -1.9021 | 1.6180 | 0 | -1.6180 | 1.9021 | -0.6180 | -1.1756 |
E8g* | 2 | -1.6180 | 0.6180 | 0.6180 | -1.6180 | 2 | -1.6180 | 0.6180 | 0.6180 | -1.6180 | 2 | -1.6180 | 0.6180 | 0.6180 | -1.6180 | 2 | -1.6180 | 0.6180 | 0.6180 | -1.6180 | 2 | -1.6180 | 0.6180 | 0.6180 | -1.6180 | 2 | -1.6180 | 0.6180 | 0.6180 | -1.6180 | 2 | -1.6180 | 0.6180 | 0.6180 | -1.6180 | 2 | -1.6180 | 0.6180 | 0.6180 | -1.6180 |
E9g* | 2 | -1.9021 | 1.6180 | -1.1756 | 0.6180 | 0 | -0.6180 | 1.1756 | -1.6180 | 1.9021 | -2 | 1.9021 | -1.6180 | 1.1756 | -0.6180 | 0 | 0.6180 | -1.1756 | 1.6180 | -1.9021 | 2 | -1.9021 | 1.6180 | -1.1756 | 0.6180 | 0 | -0.6180 | 1.1756 | -1.6180 | 1.9021 | -2 | 1.9021 | -1.6180 | 1.1756 | -0.6180 | 0 | 0.6180 | -1.1756 | 1.6180 | -1.9021 |
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 | -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 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 |
E1u* | 2 | 1.9021 | 1.6180 | 1.1756 | 0.6180 | 0 | -0.6180 | -1.1756 | -1.6180 | -1.9021 | -2 | -1.9021 | -1.6180 | -1.1756 | -0.6180 | 0 | 0.6180 | 1.1756 | 1.6180 | 1.9021 | -2 | -1.9021 | -1.6180 | -1.1756 | -0.6180 | 0 | 0.6180 | 1.1756 | 1.6180 | 1.9021 | 2 | 1.9021 | 1.6180 | 1.1756 | 0.6180 | 0 | -0.6180 | -1.1756 | -1.6180 | -1.9021 |
E2u* | 2 | 1.6180 | 0.6180 | -0.6180 | -1.6180 | -2 | -1.6180 | -0.6180 | 0.6180 | 1.6180 | 2 | 1.6180 | 0.6180 | -0.6180 | -1.6180 | -2 | -1.6180 | -0.6180 | 0.6180 | 1.6180 | -2 | -1.6180 | -0.6180 | 0.6180 | 1.6180 | 2 | 1.6180 | 0.6180 | -0.6180 | -1.6180 | -2 | -1.6180 | -0.6180 | 0.6180 | 1.6180 | 2 | 1.6180 | 0.6180 | -0.6180 | -1.6180 |
E3u* | 2 | 1.1756 | -0.6180 | -1.9021 | -1.6180 | 0 | 1.6180 | 1.9021 | 0.6180 | -1.1756 | -2 | -1.1756 | 0.6180 | 1.9021 | 1.6180 | 0 | -1.6180 | -1.9021 | -0.6180 | 1.1756 | -2 | -1.1756 | 0.6180 | 1.9021 | 1.6180 | 0 | -1.6180 | -1.9021 | -0.6180 | 1.1756 | 2 | 1.1756 | -0.6180 | -1.9021 | -1.6180 | 0 | 1.6180 | 1.9021 | 0.6180 | -1.1756 |
E4u* | 2 | 0.6180 | -1.6180 | -1.6180 | 0.6180 | 2 | 0.6180 | -1.6180 | -1.6180 | 0.6180 | 2 | 0.6180 | -1.6180 | -1.6180 | 0.6180 | 2 | 0.6180 | -1.6180 | -1.6180 | 0.6180 | -2 | -0.6180 | 1.6180 | 1.6180 | -0.6180 | -2 | -0.6180 | 1.6180 | 1.6180 | -0.6180 | -2 | -0.6180 | 1.6180 | 1.6180 | -0.6180 | -2 | -0.6180 | 1.6180 | 1.6180 | -0.6180 |
E5u* | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 |
E6u* | 2 | -0.6180 | -1.6180 | 1.6180 | 0.6180 | -2 | 0.6180 | 1.6180 | -1.6180 | -0.6180 | 2 | -0.6180 | -1.6180 | 1.6180 | 0.6180 | -2 | 0.6180 | 1.6180 | -1.6180 | -0.6180 | -2 | 0.6180 | 1.6180 | -1.6180 | -0.6180 | 2 | -0.6180 | -1.6180 | 1.6180 | 0.6180 | -2 | 0.6180 | 1.6180 | -1.6180 | -0.6180 | 2 | -0.6180 | -1.6180 | 1.6180 | 0.6180 |
E7u* | 2 | -1.1756 | -0.6180 | 1.9021 | -1.6180 | 0 | 1.6180 | -1.9021 | 0.6180 | 1.1756 | -2 | 1.1756 | 0.6180 | -1.9021 | 1.6180 | 0 | -1.6180 | 1.9021 | -0.6180 | -1.1756 | -2 | 1.1756 | 0.6180 | -1.9021 | 1.6180 | 0 | -1.6180 | 1.9021 | -0.6180 | -1.1756 | 2 | -1.1756 | -0.6180 | 1.9021 | -1.6180 | 0 | 1.6180 | -1.9021 | 0.6180 | 1.1756 |
E8u* | 2 | -1.6180 | 0.6180 | 0.6180 | -1.6180 | 2 | -1.6180 | 0.6180 | 0.6180 | -1.6180 | 2 | -1.6180 | 0.6180 | 0.6180 | -1.6180 | 2 | -1.6180 | 0.6180 | 0.6180 | -1.6180 | -2 | 1.6180 | -0.6180 | -0.6180 | 1.6180 | -2 | 1.6180 | -0.6180 | -0.6180 | 1.6180 | -2 | 1.6180 | -0.6180 | -0.6180 | 1.6180 | -2 | 1.6180 | -0.6180 | -0.6180 | 1.6180 |
E9u* | 2 | -1.9021 | 1.6180 | -1.1756 | 0.6180 | 0 | -0.6180 | 1.1756 | -1.6180 | 1.9021 | -2 | 1.9021 | -1.6180 | 1.1756 | -0.6180 | 0 | 0.6180 | -1.1756 | 1.6180 | -1.9021 | -2 | 1.9021 | -1.6180 | 1.1756 | -0.6180 | 0 | 0.6180 | -1.1756 | 1.6180 | -1.9021 | 2 | -1.9021 | 1.6180 | -1.1756 | 0.6180 | 0 | -0.6180 | 1.1756 | -1.6180 | 1.9021 |
Number of symmetry elements | h = 40 |
Number of classes, irreps | n = 40 |
Number of real-valued irreducible representations | n = 22 |
Abelian group | yes |
Optical Isomerism (Chirality) | no |
Polar | no |
Parity | yes |