D20h | E | 2C20 | 2C10 | 2(C20)3 | 2C5 | 2C4 | 2(C10)3 | 2(C20)7 | 2(C5)2 | 2(C20)9 | C2 | 10C'2 | 10C''2 | i | 2(S20)9 | 2(S5)3 | 2(S20)7 | 2(S10)3 | 2S4 | 2S5 | 2(S20)3 | 2S10 | 2S20 | σh | 10σv | 10σd |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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 | 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 | -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 | 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 | -1 | 1 |
E1g | 2 | 1.9021 | 1.6180 | 1.1756 | 0.6180 | 0 | -0.6180 | -1.1756 | -1.6180 | -1.9021 | -2 | 0 | 0 | 2 | 1.9021 | 1.6180 | 1.1756 | 0.6180 | 0 | -0.6180 | -1.1756 | -1.6180 | -1.9021 | -2 | 0 | 0 |
E2g | 2 | 1.6180 | 0.6180 | -0.6180 | -1.6180 | -2 | -1.6180 | -0.6180 | 0.6180 | 1.6180 | 2 | 0 | 0 | 2 | 1.6180 | 0.6180 | -0.6180 | -1.6180 | -2 | -1.6180 | -0.6180 | 0.6180 | 1.6180 | 2 | 0 | 0 |
E3g | 2 | 1.1756 | -0.6180 | -1.9021 | -1.6180 | 0 | 1.6180 | 1.9021 | 0.6180 | -1.1756 | -2 | 0 | 0 | 2 | 1.1756 | -0.6180 | -1.9021 | -1.6180 | 0 | 1.6180 | 1.9021 | 0.6180 | -1.1756 | -2 | 0 | 0 |
E4g | 2 | 0.6180 | -1.6180 | -1.6180 | 0.6180 | 2 | 0.6180 | -1.6180 | -1.6180 | 0.6180 | 2 | 0 | 0 | 2 | 0.6180 | -1.6180 | -1.6180 | 0.6180 | 2 | 0.6180 | -1.6180 | -1.6180 | 0.6180 | 2 | 0 | 0 |
E5g | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 0 |
E6g | 2 | -0.6180 | -1.6180 | 1.6180 | 0.6180 | -2 | 0.6180 | 1.6180 | -1.6180 | -0.6180 | 2 | 0 | 0 | 2 | -0.6180 | -1.6180 | 1.6180 | 0.6180 | -2 | 0.6180 | 1.6180 | -1.6180 | -0.6180 | 2 | 0 | 0 |
E7g | 2 | -1.1756 | -0.6180 | 1.9021 | -1.6180 | 0 | 1.6180 | -1.9021 | 0.6180 | 1.1756 | -2 | 0 | 0 | 2 | -1.1756 | -0.6180 | 1.9021 | -1.6180 | 0 | 1.6180 | -1.9021 | 0.6180 | 1.1756 | -2 | 0 | 0 |
E8g | 2 | -1.6180 | 0.6180 | 0.6180 | -1.6180 | 2 | -1.6180 | 0.6180 | 0.6180 | -1.6180 | 2 | 0 | 0 | 2 | -1.6180 | 0.6180 | 0.6180 | -1.6180 | 2 | -1.6180 | 0.6180 | 0.6180 | -1.6180 | 2 | 0 | 0 |
E9g | 2 | -1.9021 | 1.6180 | -1.1756 | 0.6180 | 0 | -0.6180 | 1.1756 | -1.6180 | 1.9021 | -2 | 0 | 0 | 2 | -1.9021 | 1.6180 | -1.1756 | 0.6180 | 0 | -0.6180 | 1.1756 | -1.6180 | 1.9021 | -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 | -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 | 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 | -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 | 1 | -1 |
E1u | 2 | 1.9021 | 1.6180 | 1.1756 | 0.6180 | 0 | -0.6180 | -1.1756 | -1.6180 | -1.9021 | -2 | 0 | 0 | -2 | -1.9021 | -1.6180 | -1.1756 | -0.6180 | 0 | 0.6180 | 1.1756 | 1.6180 | 1.9021 | 2 | 0 | 0 |
E2u | 2 | 1.6180 | 0.6180 | -0.6180 | -1.6180 | -2 | -1.6180 | -0.6180 | 0.6180 | 1.6180 | 2 | 0 | 0 | -2 | -1.6180 | -0.6180 | 0.6180 | 1.6180 | 2 | 1.6180 | 0.6180 | -0.6180 | -1.6180 | -2 | 0 | 0 |
E3u | 2 | 1.1756 | -0.6180 | -1.9021 | -1.6180 | 0 | 1.6180 | 1.9021 | 0.6180 | -1.1756 | -2 | 0 | 0 | -2 | -1.1756 | 0.6180 | 1.9021 | 1.6180 | 0 | -1.6180 | -1.9021 | -0.6180 | 1.1756 | 2 | 0 | 0 |
E4u | 2 | 0.6180 | -1.6180 | -1.6180 | 0.6180 | 2 | 0.6180 | -1.6180 | -1.6180 | 0.6180 | 2 | 0 | 0 | -2 | -0.6180 | 1.6180 | 1.6180 | -0.6180 | -2 | -0.6180 | 1.6180 | 1.6180 | -0.6180 | -2 | 0 | 0 |
E5u | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | 0 |
E6u | 2 | -0.6180 | -1.6180 | 1.6180 | 0.6180 | -2 | 0.6180 | 1.6180 | -1.6180 | -0.6180 | 2 | 0 | 0 | -2 | 0.6180 | 1.6180 | -1.6180 | -0.6180 | 2 | -0.6180 | -1.6180 | 1.6180 | 0.6180 | -2 | 0 | 0 |
E7u | 2 | -1.1756 | -0.6180 | 1.9021 | -1.6180 | 0 | 1.6180 | -1.9021 | 0.6180 | 1.1756 | -2 | 0 | 0 | -2 | 1.1756 | 0.6180 | -1.9021 | 1.6180 | 0 | -1.6180 | 1.9021 | -0.6180 | -1.1756 | 2 | 0 | 0 |
E8u | 2 | -1.6180 | 0.6180 | 0.6180 | -1.6180 | 2 | -1.6180 | 0.6180 | 0.6180 | -1.6180 | 2 | 0 | 0 | -2 | 1.6180 | -0.6180 | -0.6180 | 1.6180 | -2 | 1.6180 | -0.6180 | -0.6180 | 1.6180 | -2 | 0 | 0 |
E9u | 2 | -1.9021 | 1.6180 | -1.1756 | 0.6180 | 0 | -0.6180 | 1.1756 | -1.6180 | 1.9021 | -2 | 0 | 0 | -2 | 1.9021 | -1.6180 | 1.1756 | -0.6180 | 0 | 0.6180 | -1.1756 | 1.6180 | -1.9021 | 2 | 0 | 0 |
Number of symmetry elements | h = 80 |
Number of classes, irreps | n = 26 |
Abelian group | no |
Optical Isomerism (Chirality) | no |
Polar | no |
Parity | yes |