✅
D15d | E | 2C15 | 2(C15)2 | 2C5 | 2(C15)4 | 2C3 | 2(C5)2 | 2(C15)7 | 15C'2 | i | 2(S30)13 | 2(S30)11 | 2(S10)3 | 2(S30)7 | 2S6 | 2S10 | 2S30 | 15σd |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A1g | 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 |
E1g | 2 | 2cos(2π/15) | 2cos(4π/15) | 2cos(2π/5) | 2cos(8π/15) | -1 | 2cos(4π/5) | 2cos(14π/15) | 0 | 2 | 2cos(2π/15) | 2cos(4π/15) | 2cos(2π/5) | 2cos(8π/15) | -1 | 2cos(4π/5) | 2cos(14π/15) | 0 |
E2g | 2 | 2cos(4π/15) | 2cos(8π/15) | 2cos(4π/5) | 2cos(14π/15) | -1 | 2cos(2π/5) | 2cos(2π/15) | 0 | 2 | 2cos(4π/15) | 2cos(8π/15) | 2cos(4π/5) | 2cos(14π/15) | -1 | 2cos(2π/5) | 2cos(2π/15) | 0 |
E3g | 2 | 2cos(2π/5) | 2cos(4π/5) | 2cos(4π/5) | 2cos(2π/5) | 2 | 2cos(2π/5) | 2cos(4π/5) | 0 | 2 | 2cos(2π/5) | 2cos(4π/5) | 2cos(4π/5) | 2cos(2π/5) | 2 | 2cos(2π/5) | 2cos(4π/5) | 0 |
E4g | 2 | 2cos(8π/15) | 2cos(14π/15) | 2cos(2π/5) | 2cos(2π/15) | -1 | 2cos(4π/5) | 2cos(4π/15) | 0 | 2 | 2cos(8π/15) | 2cos(14π/15) | 2cos(2π/5) | 2cos(2π/15) | -1 | 2cos(4π/5) | 2cos(4π/15) | 0 |
E5g | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | 0 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | 0 |
E6g | 2 | 2cos(4π/5) | 2cos(2π/5) | 2cos(2π/5) | 2cos(4π/5) | 2 | 2cos(4π/5) | 2cos(2π/5) | 0 | 2 | 2cos(4π/5) | 2cos(2π/5) | 2cos(2π/5) | 2cos(4π/5) | 2 | 2cos(4π/5) | 2cos(2π/5) | 0 |
E7g | 2 | 2cos(14π/15) | 2cos(2π/15) | 2cos(4π/5) | 2cos(4π/15) | -1 | 2cos(2π/5) | 2cos(8π/15) | 0 | 2 | 2cos(14π/15) | 2cos(2π/15) | 2cos(4π/5) | 2cos(4π/15) | -1 | 2cos(2π/5) | 2cos(8π/15) | 0 |
A1u | 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 |
E1u | 2 | 2cos(2π/15) | 2cos(4π/15) | 2cos(2π/5) | 2cos(8π/15) | -1 | 2cos(4π/5) | 2cos(14π/15) | 0 | -2 | -2cos(2π/15) | -2cos(4π/15) | -2cos(2π/5) | -2cos(8π/15) | 1 | -2cos(4π/5) | -2cos(14π/15) | 0 |
E2u | 2 | 2cos(4π/15) | 2cos(8π/15) | 2cos(4π/5) | 2cos(14π/15) | -1 | 2cos(2π/5) | 2cos(2π/15) | 0 | -2 | -2cos(4π/15) | -2cos(8π/15) | -2cos(4π/5) | -2cos(14π/15) | 1 | -2cos(2π/5) | -2cos(2π/15) | 0 |
E3u | 2 | 2cos(2π/5) | 2cos(4π/5) | 2cos(4π/5) | 2cos(2π/5) | 2 | 2cos(2π/5) | 2cos(4π/5) | 0 | -2 | -2cos(2π/5) | -2cos(4π/5) | -2cos(4π/5) | -2cos(2π/5) | -2 | -2cos(2π/5) | -2cos(4π/5) | 0 |
E4u | 2 | 2cos(8π/15) | 2cos(14π/15) | 2cos(2π/5) | 2cos(2π/15) | -1 | 2cos(4π/5) | 2cos(4π/15) | 0 | -2 | -2cos(8π/15) | -2cos(14π/15) | -2cos(2π/5) | -2cos(2π/15) | 1 | -2cos(4π/5) | -2cos(4π/15) | 0 |
E5u | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | 0 | -2 | 1 | 1 | -2 | 1 | 1 | -2 | 1 | 0 |
E6u | 2 | 2cos(4π/5) | 2cos(2π/5) | 2cos(2π/5) | 2cos(4π/5) | 2 | 2cos(4π/5) | 2cos(2π/5) | 0 | -2 | -2cos(4π/5) | -2cos(2π/5) | -2cos(2π/5) | -2cos(4π/5) | -2 | -2cos(4π/5) | -2cos(2π/5) | 0 |
E7u | 2 | 2cos(14π/15) | 2cos(2π/15) | 2cos(4π/5) | 2cos(4π/15) | -1 | 2cos(2π/5) | 2cos(8π/15) | 0 | -2 | -2cos(14π/15) | -2cos(2π/15) | -2cos(4π/5) | -2cos(4π/15) | 1 | -2cos(2π/5) | -2cos(8π/15) | 0 |
Number of symmetry elements | h = 60 |
Number of classes, irreps | n = 18 |
Abelian group | no |
Optical Isomerism (Chirality) | no |
Polar | no |
Parity | yes |