C20 | 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 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
B | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 |
E1* | 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 |
E2* | 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 |
E3* | 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 |
E4* | 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 |
E5* | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 |
E6* | 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 |
E7* | 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 |
E8* | 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 |
E9* | 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 = 20 |
Number of classes, irreps | n = 20 |
Number of real-valued irreducible representations | n = 11 |
Abelian group | yes |
Optical Isomerism (Chirality) | yes |
Polar | yes |
Parity | no |