✅
D19h | 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 | σh | 2S19 | 2(S19)17 | 2(S19)3 | 2(S19)15 | 2(S19)5 | 2(S19)13 | 2(S19)7 | 2(S19)11 | 2(S19)9 | 19σv |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A'1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
A'2 | 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) | 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 |
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) | 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 |
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) | 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 |
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) | 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 |
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) | 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 |
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) | 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 |
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) | 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 |
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) | 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 |
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) | 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 |
A''1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 |
A''2 | 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) | 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 |
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) | 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 |
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) | 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 |
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) | 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 |
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) | 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 |
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) | 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 |
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) | 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 |
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) | 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 |
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) | 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 | no |