C19h | 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 | σh | S19 | (S19)21 | (S19)3 | (S19)23 | (S19)5 | (S19)25 | (S19)7 | (S19)27 | (S19)9 | (S19)29 | (S19)11 | (S19)31 | (S19)13 | (S19)33 | (S19)15 | (S19)35 | (S19)17 | (S19)37 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A' | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
E'1* | 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) | 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) |
E'2* | 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) | 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) |
E'3* | 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) | 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) |
E'4* | 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) | 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) |
E'5* | 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) | 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) |
E'6* | 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) | 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) |
E'7* | 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) | 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) |
E'8* | 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) | 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) |
E'9* | 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) | 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) |
A'' | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 |
E''1* | 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) | -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) |
E''2* | 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) | -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) |
E''3* | 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) | -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) |
E''4* | 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) | -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) |
E''5* | 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) | -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) |
E''6* | 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) | -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) |
E''7* | 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) | -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) |
E''8* | 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) | -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) |
E''9* | 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) | -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 = 38 |
Number of classes, irreps | n = 38 |
Number of real-valued irreducible representations | n = 20 |
Abelian group | yes |
Optical Isomerism (Chirality) | no |
Polar | no |
Parity | no |