✅
D19d | E | 2C19 | 2(C19)2 | 2(C19)3 | 2(C19)4 | 2(C19)5 | 2(C19)6 | 2(C19)7 | 2(C19)8 | 2(C19)9 | 19C'2 | i | 2(S38)17 | 2(S38)15 | 2(S38)13 | 2(S38)11 | 2(S38)9 | 2(S38)7 | 2(S38)5 | 2(S38)3 | 2S38 | 19σd |
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A1g | 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 |
E1g | 2 | 2cos(2π/19) | 2cos(4π/19) | 2cos(6π/19) | 2cos(8π/19) | 2cos(10π/19) | 2cos(12π/19) | 2cos(14π/19) | 2cos(16π/19) | 2cos(18π/19) | 0 | 2 | 2cos(2π/19) | 2cos(4π/19) | 2cos(6π/19) | 2cos(8π/19) | 2cos(10π/19) | 2cos(12π/19) | 2cos(14π/19) | 2cos(16π/19) | 2cos(18π/19) | 0 |
E2g | 2 | 2cos(4π/19) | 2cos(8π/19) | 2cos(12π/19) | 2cos(16π/19) | 2cos(18π/19) | 2cos(14π/19) | 2cos(10π/19) | 2cos(6π/19) | 2cos(2π/19) | 0 | 2 | 2cos(4π/19) | 2cos(8π/19) | 2cos(12π/19) | 2cos(16π/19) | 2cos(18π/19) | 2cos(14π/19) | 2cos(10π/19) | 2cos(6π/19) | 2cos(2π/19) | 0 |
E3g | 2 | 2cos(6π/19) | 2cos(12π/19) | 2cos(18π/19) | 2cos(14π/19) | 2cos(8π/19) | 2cos(2π/19) | 2cos(4π/19) | 2cos(10π/19) | 2cos(16π/19) | 0 | 2 | 2cos(6π/19) | 2cos(12π/19) | 2cos(18π/19) | 2cos(14π/19) | 2cos(8π/19) | 2cos(2π/19) | 2cos(4π/19) | 2cos(10π/19) | 2cos(16π/19) | 0 |
E4g | 2 | 2cos(8π/19) | 2cos(16π/19) | 2cos(14π/19) | 2cos(6π/19) | 2cos(2π/19) | 2cos(10π/19) | 2cos(18π/19) | 2cos(12π/19) | 2cos(4π/19) | 0 | 2 | 2cos(8π/19) | 2cos(16π/19) | 2cos(14π/19) | 2cos(6π/19) | 2cos(2π/19) | 2cos(10π/19) | 2cos(18π/19) | 2cos(12π/19) | 2cos(4π/19) | 0 |
E5g | 2 | 2cos(10π/19) | 2cos(18π/19) | 2cos(8π/19) | 2cos(2π/19) | 2cos(12π/19) | 2cos(16π/19) | 2cos(6π/19) | 2cos(4π/19) | 2cos(14π/19) | 0 | 2 | 2cos(10π/19) | 2cos(18π/19) | 2cos(8π/19) | 2cos(2π/19) | 2cos(12π/19) | 2cos(16π/19) | 2cos(6π/19) | 2cos(4π/19) | 2cos(14π/19) | 0 |
E6g | 2 | 2cos(12π/19) | 2cos(14π/19) | 2cos(2π/19) | 2cos(10π/19) | 2cos(16π/19) | 2cos(4π/19) | 2cos(8π/19) | 2cos(18π/19) | 2cos(6π/19) | 0 | 2 | 2cos(12π/19) | 2cos(14π/19) | 2cos(2π/19) | 2cos(10π/19) | 2cos(16π/19) | 2cos(4π/19) | 2cos(8π/19) | 2cos(18π/19) | 2cos(6π/19) | 0 |
E7g | 2 | 2cos(14π/19) | 2cos(10π/19) | 2cos(4π/19) | 2cos(18π/19) | 2cos(6π/19) | 2cos(8π/19) | 2cos(16π/19) | 2cos(2π/19) | 2cos(12π/19) | 0 | 2 | 2cos(14π/19) | 2cos(10π/19) | 2cos(4π/19) | 2cos(18π/19) | 2cos(6π/19) | 2cos(8π/19) | 2cos(16π/19) | 2cos(2π/19) | 2cos(12π/19) | 0 |
E8g | 2 | 2cos(16π/19) | 2cos(6π/19) | 2cos(10π/19) | 2cos(12π/19) | 2cos(4π/19) | 2cos(18π/19) | 2cos(2π/19) | 2cos(14π/19) | 2cos(8π/19) | 0 | 2 | 2cos(16π/19) | 2cos(6π/19) | 2cos(10π/19) | 2cos(12π/19) | 2cos(4π/19) | 2cos(18π/19) | 2cos(2π/19) | 2cos(14π/19) | 2cos(8π/19) | 0 |
E9g | 2 | 2cos(18π/19) | 2cos(2π/19) | 2cos(16π/19) | 2cos(4π/19) | 2cos(14π/19) | 2cos(6π/19) | 2cos(12π/19) | 2cos(8π/19) | 2cos(10π/19) | 0 | 2 | 2cos(18π/19) | 2cos(2π/19) | 2cos(16π/19) | 2cos(4π/19) | 2cos(14π/19) | 2cos(6π/19) | 2cos(12π/19) | 2cos(8π/19) | 2cos(10π/19) | 0 |
A1u | 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 |
E1u | 2 | 2cos(2π/19) | 2cos(4π/19) | 2cos(6π/19) | 2cos(8π/19) | 2cos(10π/19) | 2cos(12π/19) | 2cos(14π/19) | 2cos(16π/19) | 2cos(18π/19) | 0 | -2 | -2cos(2π/19) | -2cos(4π/19) | -2cos(6π/19) | -2cos(8π/19) | -2cos(10π/19) | -2cos(12π/19) | -2cos(14π/19) | -2cos(16π/19) | -2cos(18π/19) | 0 |
E2u | 2 | 2cos(4π/19) | 2cos(8π/19) | 2cos(12π/19) | 2cos(16π/19) | 2cos(18π/19) | 2cos(14π/19) | 2cos(10π/19) | 2cos(6π/19) | 2cos(2π/19) | 0 | -2 | -2cos(4π/19) | -2cos(8π/19) | -2cos(12π/19) | -2cos(16π/19) | -2cos(18π/19) | -2cos(14π/19) | -2cos(10π/19) | -2cos(6π/19) | -2cos(2π/19) | 0 |
E3u | 2 | 2cos(6π/19) | 2cos(12π/19) | 2cos(18π/19) | 2cos(14π/19) | 2cos(8π/19) | 2cos(2π/19) | 2cos(4π/19) | 2cos(10π/19) | 2cos(16π/19) | 0 | -2 | -2cos(6π/19) | -2cos(12π/19) | -2cos(18π/19) | -2cos(14π/19) | -2cos(8π/19) | -2cos(2π/19) | -2cos(4π/19) | -2cos(10π/19) | -2cos(16π/19) | 0 |
E4u | 2 | 2cos(8π/19) | 2cos(16π/19) | 2cos(14π/19) | 2cos(6π/19) | 2cos(2π/19) | 2cos(10π/19) | 2cos(18π/19) | 2cos(12π/19) | 2cos(4π/19) | 0 | -2 | -2cos(8π/19) | -2cos(16π/19) | -2cos(14π/19) | -2cos(6π/19) | -2cos(2π/19) | -2cos(10π/19) | -2cos(18π/19) | -2cos(12π/19) | -2cos(4π/19) | 0 |
E5u | 2 | 2cos(10π/19) | 2cos(18π/19) | 2cos(8π/19) | 2cos(2π/19) | 2cos(12π/19) | 2cos(16π/19) | 2cos(6π/19) | 2cos(4π/19) | 2cos(14π/19) | 0 | -2 | -2cos(10π/19) | -2cos(18π/19) | -2cos(8π/19) | -2cos(2π/19) | -2cos(12π/19) | -2cos(16π/19) | -2cos(6π/19) | -2cos(4π/19) | -2cos(14π/19) | 0 |
E6u | 2 | 2cos(12π/19) | 2cos(14π/19) | 2cos(2π/19) | 2cos(10π/19) | 2cos(16π/19) | 2cos(4π/19) | 2cos(8π/19) | 2cos(18π/19) | 2cos(6π/19) | 0 | -2 | -2cos(12π/19) | -2cos(14π/19) | -2cos(2π/19) | -2cos(10π/19) | -2cos(16π/19) | -2cos(4π/19) | -2cos(8π/19) | -2cos(18π/19) | -2cos(6π/19) | 0 |
E7u | 2 | 2cos(14π/19) | 2cos(10π/19) | 2cos(4π/19) | 2cos(18π/19) | 2cos(6π/19) | 2cos(8π/19) | 2cos(16π/19) | 2cos(2π/19) | 2cos(12π/19) | 0 | -2 | -2cos(14π/19) | -2cos(10π/19) | -2cos(4π/19) | -2cos(18π/19) | -2cos(6π/19) | -2cos(8π/19) | -2cos(16π/19) | -2cos(2π/19) | -2cos(12π/19) | 0 |
E8u | 2 | 2cos(16π/19) | 2cos(6π/19) | 2cos(10π/19) | 2cos(12π/19) | 2cos(4π/19) | 2cos(18π/19) | 2cos(2π/19) | 2cos(14π/19) | 2cos(8π/19) | 0 | -2 | -2cos(16π/19) | -2cos(6π/19) | -2cos(10π/19) | -2cos(12π/19) | -2cos(4π/19) | -2cos(18π/19) | -2cos(2π/19) | -2cos(14π/19) | -2cos(8π/19) | 0 |
E9u | 2 | 2cos(18π/19) | 2cos(2π/19) | 2cos(16π/19) | 2cos(4π/19) | 2cos(14π/19) | 2cos(6π/19) | 2cos(12π/19) | 2cos(8π/19) | 2cos(10π/19) | 0 | -2 | -2cos(18π/19) | -2cos(2π/19) | -2cos(16π/19) | -2cos(4π/19) | -2cos(14π/19) | -2cos(6π/19) | -2cos(12π/19) | -2cos(8π/19) | -2cos(10π/19) | 0 |
Number of symmetry elements | h = 76 |
Number of classes, irreps | n = 22 |
Abelian group | no |
Optical Isomerism (Chirality) | no |
Polar | no |
Parity | yes |