C13h | E | C13 | (C13)2 | (C13)3 | (C13)4 | (C13)5 | (C13)6 | (C13)7 | (C13)8 | (C13)9 | (C13)10 | (C13)11 | (C13)12 | σh | S13 | (S13)15 | (S13)3 | (S13)17 | (S13)5 | (S13)19 | (S13)7 | (S13)21 | (S13)9 | (S13)23 | (S13)11 | (S13)25 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
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 |
E'1* | 2 | 2cos(2π/13) | 2cos(4π/13) | 2cos(6π/13) | 2cos(8π/13) | 2cos(10π/13) | 2cos(12π/13) | 2cos(12π/13) | 2cos(10π/13) | 2cos(8π/13) | 2cos(6π/13) | 2cos(4π/13) | 2cos(2π/13) | 2 | 2cos(2π/13) | 2cos(4π/13) | 2cos(6π/13) | 2cos(8π/13) | 2cos(10π/13) | 2cos(12π/13) | 2cos(12π/13) | 2cos(10π/13) | 2cos(8π/13) | 2cos(6π/13) | 2cos(4π/13) | 2cos(2π/13) |
E'2* | 2 | 2cos(4π/13) | 2cos(8π/13) | 2cos(12π/13) | 2cos(10π/13) | 2cos(6π/13) | 2cos(2π/13) | 2cos(2π/13) | 2cos(6π/13) | 2cos(10π/13) | 2cos(12π/13) | 2cos(8π/13) | 2cos(4π/13) | 2 | 2cos(4π/13) | 2cos(8π/13) | 2cos(12π/13) | 2cos(10π/13) | 2cos(6π/13) | 2cos(2π/13) | 2cos(2π/13) | 2cos(6π/13) | 2cos(10π/13) | 2cos(12π/13) | 2cos(8π/13) | 2cos(4π/13) |
E'3* | 2 | 2cos(6π/13) | 2cos(12π/13) | 2cos(8π/13) | 2cos(2π/13) | 2cos(4π/13) | 2cos(10π/13) | 2cos(10π/13) | 2cos(4π/13) | 2cos(2π/13) | 2cos(8π/13) | 2cos(12π/13) | 2cos(6π/13) | 2 | 2cos(6π/13) | 2cos(12π/13) | 2cos(8π/13) | 2cos(2π/13) | 2cos(4π/13) | 2cos(10π/13) | 2cos(10π/13) | 2cos(4π/13) | 2cos(2π/13) | 2cos(8π/13) | 2cos(12π/13) | 2cos(6π/13) |
E'4* | 2 | 2cos(8π/13) | 2cos(10π/13) | 2cos(2π/13) | 2cos(6π/13) | 2cos(12π/13) | 2cos(4π/13) | 2cos(4π/13) | 2cos(12π/13) | 2cos(6π/13) | 2cos(2π/13) | 2cos(10π/13) | 2cos(8π/13) | 2 | 2cos(8π/13) | 2cos(10π/13) | 2cos(2π/13) | 2cos(6π/13) | 2cos(12π/13) | 2cos(4π/13) | 2cos(4π/13) | 2cos(12π/13) | 2cos(6π/13) | 2cos(2π/13) | 2cos(10π/13) | 2cos(8π/13) |
E'5* | 2 | 2cos(10π/13) | 2cos(6π/13) | 2cos(4π/13) | 2cos(12π/13) | 2cos(2π/13) | 2cos(8π/13) | 2cos(8π/13) | 2cos(2π/13) | 2cos(12π/13) | 2cos(4π/13) | 2cos(6π/13) | 2cos(10π/13) | 2 | 2cos(10π/13) | 2cos(6π/13) | 2cos(4π/13) | 2cos(12π/13) | 2cos(2π/13) | 2cos(8π/13) | 2cos(8π/13) | 2cos(2π/13) | 2cos(12π/13) | 2cos(4π/13) | 2cos(6π/13) | 2cos(10π/13) |
E'6* | 2 | 2cos(12π/13) | 2cos(2π/13) | 2cos(10π/13) | 2cos(4π/13) | 2cos(8π/13) | 2cos(6π/13) | 2cos(6π/13) | 2cos(8π/13) | 2cos(4π/13) | 2cos(10π/13) | 2cos(2π/13) | 2cos(12π/13) | 2 | 2cos(12π/13) | 2cos(2π/13) | 2cos(10π/13) | 2cos(4π/13) | 2cos(8π/13) | 2cos(6π/13) | 2cos(6π/13) | 2cos(8π/13) | 2cos(4π/13) | 2cos(10π/13) | 2cos(2π/13) | 2cos(12π/13) |
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 |
E''1* | 2 | 2cos(2π/13) | 2cos(4π/13) | 2cos(6π/13) | 2cos(8π/13) | 2cos(10π/13) | 2cos(12π/13) | 2cos(12π/13) | 2cos(10π/13) | 2cos(8π/13) | 2cos(6π/13) | 2cos(4π/13) | 2cos(2π/13) | -2 | -2cos(2π/13) | -2cos(4π/13) | -2cos(6π/13) | -2cos(8π/13) | -2cos(10π/13) | -2cos(12π/13) | -2cos(12π/13) | -2cos(10π/13) | -2cos(8π/13) | -2cos(6π/13) | -2cos(4π/13) | -2cos(2π/13) |
E''2* | 2 | 2cos(4π/13) | 2cos(8π/13) | 2cos(12π/13) | 2cos(10π/13) | 2cos(6π/13) | 2cos(2π/13) | 2cos(2π/13) | 2cos(6π/13) | 2cos(10π/13) | 2cos(12π/13) | 2cos(8π/13) | 2cos(4π/13) | -2 | -2cos(4π/13) | -2cos(8π/13) | -2cos(12π/13) | -2cos(10π/13) | -2cos(6π/13) | -2cos(2π/13) | -2cos(2π/13) | -2cos(6π/13) | -2cos(10π/13) | -2cos(12π/13) | -2cos(8π/13) | -2cos(4π/13) |
E''3* | 2 | 2cos(6π/13) | 2cos(12π/13) | 2cos(8π/13) | 2cos(2π/13) | 2cos(4π/13) | 2cos(10π/13) | 2cos(10π/13) | 2cos(4π/13) | 2cos(2π/13) | 2cos(8π/13) | 2cos(12π/13) | 2cos(6π/13) | -2 | -2cos(6π/13) | -2cos(12π/13) | -2cos(8π/13) | -2cos(2π/13) | -2cos(4π/13) | -2cos(10π/13) | -2cos(10π/13) | -2cos(4π/13) | -2cos(2π/13) | -2cos(8π/13) | -2cos(12π/13) | -2cos(6π/13) |
E''4* | 2 | 2cos(8π/13) | 2cos(10π/13) | 2cos(2π/13) | 2cos(6π/13) | 2cos(12π/13) | 2cos(4π/13) | 2cos(4π/13) | 2cos(12π/13) | 2cos(6π/13) | 2cos(2π/13) | 2cos(10π/13) | 2cos(8π/13) | -2 | -2cos(8π/13) | -2cos(10π/13) | -2cos(2π/13) | -2cos(6π/13) | -2cos(12π/13) | -2cos(4π/13) | -2cos(4π/13) | -2cos(12π/13) | -2cos(6π/13) | -2cos(2π/13) | -2cos(10π/13) | -2cos(8π/13) |
E''5* | 2 | 2cos(10π/13) | 2cos(6π/13) | 2cos(4π/13) | 2cos(12π/13) | 2cos(2π/13) | 2cos(8π/13) | 2cos(8π/13) | 2cos(2π/13) | 2cos(12π/13) | 2cos(4π/13) | 2cos(6π/13) | 2cos(10π/13) | -2 | -2cos(10π/13) | -2cos(6π/13) | -2cos(4π/13) | -2cos(12π/13) | -2cos(2π/13) | -2cos(8π/13) | -2cos(8π/13) | -2cos(2π/13) | -2cos(12π/13) | -2cos(4π/13) | -2cos(6π/13) | -2cos(10π/13) |
E''6* | 2 | 2cos(12π/13) | 2cos(2π/13) | 2cos(10π/13) | 2cos(4π/13) | 2cos(8π/13) | 2cos(6π/13) | 2cos(6π/13) | 2cos(8π/13) | 2cos(4π/13) | 2cos(10π/13) | 2cos(2π/13) | 2cos(12π/13) | -2 | -2cos(12π/13) | -2cos(2π/13) | -2cos(10π/13) | -2cos(4π/13) | -2cos(8π/13) | -2cos(6π/13) | -2cos(6π/13) | -2cos(8π/13) | -2cos(4π/13) | -2cos(10π/13) | -2cos(2π/13) | -2cos(12π/13) |
Number of symmetry elements | h = 26 |
Number of classes, irreps | n = 26 |
Number of real-valued irreducible representations | n = 14 |
Abelian group | yes |
Optical Isomerism (Chirality) | no |
Polar | no |
Parity | no |