✅
D13d | E | 2C13 | 2(C13)2 | 2(C13)3 | 2(C13)4 | 2(C13)5 | 2(C13)6 | 13C'2 | i | 2(S26)11 | 2(S26)9 | 2(S26)7 | 2(S26)5 | 2(S26)3 | 2S26 | 13σd |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A1g | 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 |
E1g | 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 |
E2g | 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 |
E3g | 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 |
E4g | 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 |
E5g | 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 |
E6g | 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 |
A1u | 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 |
E1u | 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 |
E2u | 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 |
E3u | 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 |
E4u | 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 |
E5u | 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 |
E6u | 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 | yes |