C13 | E | C13 | (C13)2 | (C13)3 | (C13)4 | (C13)5 | (C13)6 | (C13)7 | (C13)8 | (C13)9 | (C13)10 | (C13)11 | (C13)12 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
E1* | 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) |
E2* | 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) |
E3* | 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) |
E4* | 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) |
E5* | 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) |
E6* | 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 = 13 |
Number of classes, irreps | n = 13 |
Number of real-valued irreducible representations | n = 7 |
Abelian group | yes |
Optical Isomerism (Chirality) | yes |
Polar | yes |
Parity | no |