C10h | E | C10 | C5 | (C10)3 | (C5)2 | C2 | (C5)3 | (C10)7 | (C5)4 | (C10)9 | i | (S5)3 | (S10)7 | (S5)9 | (S10)9 | σh | S10 | S5 | (S10)3 | (S5)7 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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 | 1.6180 | 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 |
E2g* | 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 |
E3g* | 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 |
E4g* | 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 |
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 | 1.6180 | 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 |
E2u* | 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 |
E3u* | 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 |
E4u* | 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 |
Number of symmetry elements | h = 20 |
Number of classes, irreps | n = 20 |
Number of real-valued irreducible representations | n = 12 |
Abelian group | yes |
Optical Isomerism (Chirality) | no |
Polar | no |
Parity | yes |