C15 | E | C15 | (C15)2 | C5 | (C15)4 | C3 | (C5)2 | (C15)7 | (C15)8 | (C5)3 | (C3)2 | (C15)11 | (C5)4 | (C15)13 | (C15)14 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
E1* | 2 | 2cos(2π/15) | 2cos(4π/15) | 2cos(2π/5) | 2cos(8π/15) | -1 | 2cos(4π/5) | 2cos(14π/15) | 2cos(14π/15) | 2cos(4π/5) | -1 | 2cos(8π/15) | 2cos(2π/5) | 2cos(4π/15) | 2cos(2π/15) |
E2* | 2 | 2cos(4π/15) | 2cos(8π/15) | 2cos(4π/5) | 2cos(14π/15) | -1 | 2cos(2π/5) | 2cos(2π/15) | 2cos(2π/15) | 2cos(2π/5) | -1 | 2cos(14π/15) | 2cos(4π/5) | 2cos(8π/15) | 2cos(4π/15) |
E3* | 2 | 2cos(2π/5) | 2cos(4π/5) | 2cos(4π/5) | 2cos(2π/5) | 2 | 2cos(2π/5) | 2cos(4π/5) | 2cos(4π/5) | 2cos(2π/5) | 2 | 2cos(2π/5) | 2cos(4π/5) | 2cos(4π/5) | 2cos(2π/5) |
E4* | 2 | 2cos(8π/15) | 2cos(14π/15) | 2cos(2π/5) | 2cos(2π/15) | -1 | 2cos(4π/5) | 2cos(4π/15) | 2cos(4π/15) | 2cos(4π/5) | -1 | 2cos(2π/15) | 2cos(2π/5) | 2cos(14π/15) | 2cos(8π/15) |
E5* | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 |
E6* | 2 | 2cos(4π/5) | 2cos(2π/5) | 2cos(2π/5) | 2cos(4π/5) | 2 | 2cos(4π/5) | 2cos(2π/5) | 2cos(2π/5) | 2cos(4π/5) | 2 | 2cos(4π/5) | 2cos(2π/5) | 2cos(2π/5) | 2cos(4π/5) |
E7* | 2 | 2cos(14π/15) | 2cos(2π/15) | 2cos(4π/5) | 2cos(4π/15) | -1 | 2cos(2π/5) | 2cos(8π/15) | 2cos(8π/15) | 2cos(2π/5) | -1 | 2cos(4π/15) | 2cos(4π/5) | 2cos(2π/15) | 2cos(14π/15) |
Number of symmetry elements | h = 15 |
Number of classes, irreps | n = 15 |
Number of real-valued irreducible representations | n = 8 |
Abelian group | yes |
Optical Isomerism (Chirality) | yes |
Polar | yes |
Parity | no |