✅
D13h | E | 2C13 | 2(C13)2 | 2(C13)3 | 2(C13)4 | 2(C13)5 | 2(C13)6 | 13C'2 | σh | 2S13 | 2(S13)11 | 2(S13)3 | 2(S13)9 | 2(S13)5 | 2(S13)7 | 13σv |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A'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 |
E'1 | 2 | 2cos(2π/13) | 2cos(4π/13) | 2cos(6π/13) | 2cos(8π/13) | 2cos(10π/13) | 2cos(12π/13) | 0 | 2 | 2cos(2π/13) | 2cos(4π/13) | 2cos(6π/13) | 2cos(8π/13) | 2cos(10π/13) | 2cos(12π/13) | 0 |
E'2 | 2 | 2cos(4π/13) | 2cos(8π/13) | 2cos(12π/13) | 2cos(10π/13) | 2cos(6π/13) | 2cos(2π/13) | 0 | 2 | 2cos(4π/13) | 2cos(8π/13) | 2cos(12π/13) | 2cos(10π/13) | 2cos(6π/13) | 2cos(2π/13) | 0 |
E'3 | 2 | 2cos(6π/13) | 2cos(12π/13) | 2cos(8π/13) | 2cos(2π/13) | 2cos(4π/13) | 2cos(10π/13) | 0 | 2 | 2cos(6π/13) | 2cos(12π/13) | 2cos(8π/13) | 2cos(2π/13) | 2cos(4π/13) | 2cos(10π/13) | 0 |
E'4 | 2 | 2cos(8π/13) | 2cos(10π/13) | 2cos(2π/13) | 2cos(6π/13) | 2cos(12π/13) | 2cos(4π/13) | 0 | 2 | 2cos(8π/13) | 2cos(10π/13) | 2cos(2π/13) | 2cos(6π/13) | 2cos(12π/13) | 2cos(4π/13) | 0 |
E'5 | 2 | 2cos(10π/13) | 2cos(6π/13) | 2cos(4π/13) | 2cos(12π/13) | 2cos(2π/13) | 2cos(8π/13) | 0 | 2 | 2cos(10π/13) | 2cos(6π/13) | 2cos(4π/13) | 2cos(12π/13) | 2cos(2π/13) | 2cos(8π/13) | 0 |
E'6 | 2 | 2cos(12π/13) | 2cos(2π/13) | 2cos(10π/13) | 2cos(4π/13) | 2cos(8π/13) | 2cos(6π/13) | 0 | 2 | 2cos(12π/13) | 2cos(2π/13) | 2cos(10π/13) | 2cos(4π/13) | 2cos(8π/13) | 2cos(6π/13) | 0 |
A''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 |
E''1 | 2 | 2cos(2π/13) | 2cos(4π/13) | 2cos(6π/13) | 2cos(8π/13) | 2cos(10π/13) | 2cos(12π/13) | 0 | -2 | -2cos(2π/13) | -2cos(4π/13) | -2cos(6π/13) | -2cos(8π/13) | -2cos(10π/13) | -2cos(12π/13) | 0 |
E''2 | 2 | 2cos(4π/13) | 2cos(8π/13) | 2cos(12π/13) | 2cos(10π/13) | 2cos(6π/13) | 2cos(2π/13) | 0 | -2 | -2cos(4π/13) | -2cos(8π/13) | -2cos(12π/13) | -2cos(10π/13) | -2cos(6π/13) | -2cos(2π/13) | 0 |
E''3 | 2 | 2cos(6π/13) | 2cos(12π/13) | 2cos(8π/13) | 2cos(2π/13) | 2cos(4π/13) | 2cos(10π/13) | 0 | -2 | -2cos(6π/13) | -2cos(12π/13) | -2cos(8π/13) | -2cos(2π/13) | -2cos(4π/13) | -2cos(10π/13) | 0 |
E''4 | 2 | 2cos(8π/13) | 2cos(10π/13) | 2cos(2π/13) | 2cos(6π/13) | 2cos(12π/13) | 2cos(4π/13) | 0 | -2 | -2cos(8π/13) | -2cos(10π/13) | -2cos(2π/13) | -2cos(6π/13) | -2cos(12π/13) | -2cos(4π/13) | 0 |
E''5 | 2 | 2cos(10π/13) | 2cos(6π/13) | 2cos(4π/13) | 2cos(12π/13) | 2cos(2π/13) | 2cos(8π/13) | 0 | -2 | -2cos(10π/13) | -2cos(6π/13) | -2cos(4π/13) | -2cos(12π/13) | -2cos(2π/13) | -2cos(8π/13) | 0 |
E''6 | 2 | 2cos(12π/13) | 2cos(2π/13) | 2cos(10π/13) | 2cos(4π/13) | 2cos(8π/13) | 2cos(6π/13) | 0 | -2 | -2cos(12π/13) | -2cos(2π/13) | -2cos(10π/13) | -2cos(4π/13) | -2cos(8π/13) | -2cos(6π/13) | 0 |
Number of symmetry elements | h = 52 |
Number of classes, irreps | n = 16 |
Abelian group | no |
Optical Isomerism (Chirality) | no |
Polar | no |
Parity | no |