C19 | E | C19 | (C19)2 | (C19)3 | (C19)4 | (C19)5 | (C19)6 | (C19)7 | (C19)8 | (C19)9 | (C19)10 | (C19)11 | (C19)12 | (C19)13 | (C19)14 | (C19)15 | (C19)16 | (C19)17 | (C19)18 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
E1* | 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) | 2cos(18π/19) | 2cos(16π/19) | 2cos(14π/19) | 2cos(12π/19) | 2cos(10π/19) | 2cos(8π/19) | 2cos(6π/19) | 2cos(4π/19) | 2cos(2π/19) |
E2* | 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) | 2cos(2π/19) | 2cos(6π/19) | 2cos(10π/19) | 2cos(14π/19) | 2cos(18π/19) | 2cos(16π/19) | 2cos(12π/19) | 2cos(8π/19) | 2cos(4π/19) |
E3* | 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) | 2cos(16π/19) | 2cos(10π/19) | 2cos(4π/19) | 2cos(2π/19) | 2cos(8π/19) | 2cos(14π/19) | 2cos(18π/19) | 2cos(12π/19) | 2cos(6π/19) |
E4* | 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) | 2cos(4π/19) | 2cos(12π/19) | 2cos(18π/19) | 2cos(10π/19) | 2cos(2π/19) | 2cos(6π/19) | 2cos(14π/19) | 2cos(16π/19) | 2cos(8π/19) |
E5* | 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) | 2cos(14π/19) | 2cos(4π/19) | 2cos(6π/19) | 2cos(16π/19) | 2cos(12π/19) | 2cos(2π/19) | 2cos(8π/19) | 2cos(18π/19) | 2cos(10π/19) |
E6* | 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) | 2cos(6π/19) | 2cos(18π/19) | 2cos(8π/19) | 2cos(4π/19) | 2cos(16π/19) | 2cos(10π/19) | 2cos(2π/19) | 2cos(14π/19) | 2cos(12π/19) |
E7* | 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) | 2cos(12π/19) | 2cos(2π/19) | 2cos(16π/19) | 2cos(8π/19) | 2cos(6π/19) | 2cos(18π/19) | 2cos(4π/19) | 2cos(10π/19) | 2cos(14π/19) |
E8* | 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) | 2cos(8π/19) | 2cos(14π/19) | 2cos(2π/19) | 2cos(18π/19) | 2cos(4π/19) | 2cos(12π/19) | 2cos(10π/19) | 2cos(6π/19) | 2cos(16π/19) |
E9* | 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) | 2cos(10π/19) | 2cos(8π/19) | 2cos(12π/19) | 2cos(6π/19) | 2cos(14π/19) | 2cos(4π/19) | 2cos(16π/19) | 2cos(2π/19) | 2cos(18π/19) |
Number of symmetry elements | h = 19 |
Number of classes, irreps | n = 19 |
Number of real-valued irreducible representations | n = 10 |
Abelian group | yes |
Optical Isomerism (Chirality) | yes |
Polar | yes |
Parity | no |