✅
| D28d | E | 2S56 | 2C28 | 2(S56)3 | 2C14 | 2(S56)5 | 2(C28)3 | 2S8 | 2C7 | 2(S56)9 | 2(C28)5 | 2(S56)11 | 2(C14)3 | 2(S56)13 | 2C4 | 2(S56)15 | 2(C7)2 | 2(S56)17 | 2(C28)9 | 2(S56)19 | 2(C14)5 | 2(S8)3 | 2(C28)11 | 2(S56)23 | 2(C7)3 | 2(S56)25 | 2(C28)13 | 2(S56)27 | C2 | 28C'2 | 28σd |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A1 | 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 | 1 | 1 | 1 | 1 | 1 |
| A2 | 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 | 1 | 1 | 1 | -1 | -1 |
| B1 | 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 | 1 | -1 | 1 | 1 | -1 |
| B2 | 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 | 1 | -1 | 1 | -1 | 1 |
| E1 | 2 | 2cos(π/28) | 2cos(π/14) | 2cos(3π/28) | 2cos(π/7) | 2cos(5π/28) | 2cos(3π/14) | 2cos(π/4) | 2cos(2π/7) | 2cos(9π/28) | 2cos(5π/14) | 2cos(11π/28) | 2cos(3π/7) | 2cos(13π/28) | 0 | -2cos(13π/28) | -2cos(3π/7) | -2cos(11π/28) | -2cos(5π/14) | -2cos(9π/28) | -2cos(2π/7) | -2cos(π/4) | -2cos(3π/14) | -2cos(5π/28) | -2cos(π/7) | -2cos(3π/28) | -2cos(π/14) | -2cos(π/28) | -2 | 0 | 0 |
| E2 | 2 | 2cos(π/14) | 2cos(π/7) | 2cos(3π/14) | 2cos(2π/7) | 2cos(5π/14) | 2cos(3π/7) | 0 | -2cos(3π/7) | -2cos(5π/14) | -2cos(2π/7) | -2cos(3π/14) | -2cos(π/7) | -2cos(π/14) | -2 | -2cos(π/14) | -2cos(π/7) | -2cos(3π/14) | -2cos(2π/7) | -2cos(5π/14) | -2cos(3π/7) | 0 | 2cos(3π/7) | 2cos(5π/14) | 2cos(2π/7) | 2cos(3π/14) | 2cos(π/7) | 2cos(π/14) | 2 | 0 | 0 |
| E3 | 2 | 2cos(3π/28) | 2cos(3π/14) | 2cos(9π/28) | 2cos(3π/7) | -2cos(13π/28) | -2cos(5π/14) | -2cos(π/4) | -2cos(π/7) | -2cos(π/28) | -2cos(π/14) | -2cos(5π/28) | -2cos(2π/7) | -2cos(11π/28) | 0 | 2cos(11π/28) | 2cos(2π/7) | 2cos(5π/28) | 2cos(π/14) | 2cos(π/28) | 2cos(π/7) | 2cos(π/4) | 2cos(5π/14) | 2cos(13π/28) | -2cos(3π/7) | -2cos(9π/28) | -2cos(3π/14) | -2cos(3π/28) | -2 | 0 | 0 |
| E4 | 2 | 2cos(π/7) | 2cos(2π/7) | 2cos(3π/7) | -2cos(3π/7) | -2cos(2π/7) | -2cos(π/7) | -2 | -2cos(π/7) | -2cos(2π/7) | -2cos(3π/7) | 2cos(3π/7) | 2cos(2π/7) | 2cos(π/7) | 2 | 2cos(π/7) | 2cos(2π/7) | 2cos(3π/7) | -2cos(3π/7) | -2cos(2π/7) | -2cos(π/7) | -2 | -2cos(π/7) | -2cos(2π/7) | -2cos(3π/7) | 2cos(3π/7) | 2cos(2π/7) | 2cos(π/7) | 2 | 0 | 0 |
| E5 | 2 | 2cos(5π/28) | 2cos(5π/14) | -2cos(13π/28) | -2cos(2π/7) | -2cos(3π/28) | -2cos(π/14) | -2cos(π/4) | -2cos(3π/7) | 2cos(11π/28) | 2cos(3π/14) | 2cos(π/28) | 2cos(π/7) | 2cos(9π/28) | 0 | -2cos(9π/28) | -2cos(π/7) | -2cos(π/28) | -2cos(3π/14) | -2cos(11π/28) | 2cos(3π/7) | 2cos(π/4) | 2cos(π/14) | 2cos(3π/28) | 2cos(2π/7) | 2cos(13π/28) | -2cos(5π/14) | -2cos(5π/28) | -2 | 0 | 0 |
| E6 | 2 | 2cos(3π/14) | 2cos(3π/7) | -2cos(5π/14) | -2cos(π/7) | -2cos(π/14) | -2cos(2π/7) | 0 | 2cos(2π/7) | 2cos(π/14) | 2cos(π/7) | 2cos(5π/14) | -2cos(3π/7) | -2cos(3π/14) | -2 | -2cos(3π/14) | -2cos(3π/7) | 2cos(5π/14) | 2cos(π/7) | 2cos(π/14) | 2cos(2π/7) | 0 | -2cos(2π/7) | -2cos(π/14) | -2cos(π/7) | -2cos(5π/14) | 2cos(3π/7) | 2cos(3π/14) | 2 | 0 | 0 |
| E7 | 2 | 2cos(π/4) | 0 | -2cos(π/4) | -2 | -2cos(π/4) | 0 | 2cos(π/4) | 2 | 2cos(π/4) | 0 | -2cos(π/4) | -2 | -2cos(π/4) | 0 | 2cos(π/4) | 2 | 2cos(π/4) | 0 | -2cos(π/4) | -2 | -2cos(π/4) | 0 | 2cos(π/4) | 2 | 2cos(π/4) | 0 | -2cos(π/4) | -2 | 0 | 0 |
| E8 | 2 | 2cos(2π/7) | -2cos(3π/7) | -2cos(π/7) | -2cos(π/7) | -2cos(3π/7) | 2cos(2π/7) | 2 | 2cos(2π/7) | -2cos(3π/7) | -2cos(π/7) | -2cos(π/7) | -2cos(3π/7) | 2cos(2π/7) | 2 | 2cos(2π/7) | -2cos(3π/7) | -2cos(π/7) | -2cos(π/7) | -2cos(3π/7) | 2cos(2π/7) | 2 | 2cos(2π/7) | -2cos(3π/7) | -2cos(π/7) | -2cos(π/7) | -2cos(3π/7) | 2cos(2π/7) | 2 | 0 | 0 |
| E9 | 2 | 2cos(9π/28) | -2cos(5π/14) | -2cos(π/28) | -2cos(2π/7) | 2cos(11π/28) | 2cos(π/14) | 2cos(π/4) | -2cos(3π/7) | -2cos(3π/28) | -2cos(3π/14) | 2cos(13π/28) | 2cos(π/7) | 2cos(5π/28) | 0 | -2cos(5π/28) | -2cos(π/7) | -2cos(13π/28) | 2cos(3π/14) | 2cos(3π/28) | 2cos(3π/7) | -2cos(π/4) | -2cos(π/14) | -2cos(11π/28) | 2cos(2π/7) | 2cos(π/28) | 2cos(5π/14) | -2cos(9π/28) | -2 | 0 | 0 |
| E10 | 2 | 2cos(5π/14) | -2cos(2π/7) | -2cos(π/14) | -2cos(3π/7) | 2cos(3π/14) | 2cos(π/7) | 0 | -2cos(π/7) | -2cos(3π/14) | 2cos(3π/7) | 2cos(π/14) | 2cos(2π/7) | -2cos(5π/14) | -2 | -2cos(5π/14) | 2cos(2π/7) | 2cos(π/14) | 2cos(3π/7) | -2cos(3π/14) | -2cos(π/7) | 0 | 2cos(π/7) | 2cos(3π/14) | -2cos(3π/7) | -2cos(π/14) | -2cos(2π/7) | 2cos(5π/14) | 2 | 0 | 0 |
| E11 | 2 | 2cos(11π/28) | -2cos(3π/14) | -2cos(5π/28) | 2cos(3π/7) | 2cos(π/28) | 2cos(5π/14) | -2cos(π/4) | -2cos(π/7) | 2cos(13π/28) | 2cos(π/14) | 2cos(9π/28) | -2cos(2π/7) | -2cos(3π/28) | 0 | 2cos(3π/28) | 2cos(2π/7) | -2cos(9π/28) | -2cos(π/14) | -2cos(13π/28) | 2cos(π/7) | 2cos(π/4) | -2cos(5π/14) | -2cos(π/28) | -2cos(3π/7) | 2cos(5π/28) | 2cos(3π/14) | -2cos(11π/28) | -2 | 0 | 0 |
| E12 | 2 | 2cos(3π/7) | -2cos(π/7) | -2cos(2π/7) | 2cos(2π/7) | 2cos(π/7) | -2cos(3π/7) | -2 | -2cos(3π/7) | 2cos(π/7) | 2cos(2π/7) | -2cos(2π/7) | -2cos(π/7) | 2cos(3π/7) | 2 | 2cos(3π/7) | -2cos(π/7) | -2cos(2π/7) | 2cos(2π/7) | 2cos(π/7) | -2cos(3π/7) | -2 | -2cos(3π/7) | 2cos(π/7) | 2cos(2π/7) | -2cos(2π/7) | -2cos(π/7) | 2cos(3π/7) | 2 | 0 | 0 |
| E13 | 2 | 2cos(13π/28) | -2cos(π/14) | -2cos(11π/28) | 2cos(π/7) | 2cos(9π/28) | -2cos(3π/14) | -2cos(π/4) | 2cos(2π/7) | 2cos(5π/28) | -2cos(5π/14) | -2cos(3π/28) | 2cos(3π/7) | 2cos(π/28) | 0 | -2cos(π/28) | -2cos(3π/7) | 2cos(3π/28) | 2cos(5π/14) | -2cos(5π/28) | -2cos(2π/7) | 2cos(π/4) | 2cos(3π/14) | -2cos(9π/28) | -2cos(π/7) | 2cos(11π/28) | 2cos(π/14) | -2cos(13π/28) | -2 | 0 | 0 |
| E14 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | 0 |
| E15 | 2 | -2cos(13π/28) | -2cos(π/14) | 2cos(11π/28) | 2cos(π/7) | -2cos(9π/28) | -2cos(3π/14) | 2cos(π/4) | 2cos(2π/7) | -2cos(5π/28) | -2cos(5π/14) | 2cos(3π/28) | 2cos(3π/7) | -2cos(π/28) | 0 | 2cos(π/28) | -2cos(3π/7) | -2cos(3π/28) | 2cos(5π/14) | 2cos(5π/28) | -2cos(2π/7) | -2cos(π/4) | 2cos(3π/14) | 2cos(9π/28) | -2cos(π/7) | -2cos(11π/28) | 2cos(π/14) | 2cos(13π/28) | -2 | 0 | 0 |
| E16 | 2 | -2cos(3π/7) | -2cos(π/7) | 2cos(2π/7) | 2cos(2π/7) | -2cos(π/7) | -2cos(3π/7) | 2 | -2cos(3π/7) | -2cos(π/7) | 2cos(2π/7) | 2cos(2π/7) | -2cos(π/7) | -2cos(3π/7) | 2 | -2cos(3π/7) | -2cos(π/7) | 2cos(2π/7) | 2cos(2π/7) | -2cos(π/7) | -2cos(3π/7) | 2 | -2cos(3π/7) | -2cos(π/7) | 2cos(2π/7) | 2cos(2π/7) | -2cos(π/7) | -2cos(3π/7) | 2 | 0 | 0 |
| E17 | 2 | -2cos(11π/28) | -2cos(3π/14) | 2cos(5π/28) | 2cos(3π/7) | -2cos(π/28) | 2cos(5π/14) | 2cos(π/4) | -2cos(π/7) | -2cos(13π/28) | 2cos(π/14) | -2cos(9π/28) | -2cos(2π/7) | 2cos(3π/28) | 0 | -2cos(3π/28) | 2cos(2π/7) | 2cos(9π/28) | -2cos(π/14) | 2cos(13π/28) | 2cos(π/7) | -2cos(π/4) | -2cos(5π/14) | 2cos(π/28) | -2cos(3π/7) | -2cos(5π/28) | 2cos(3π/14) | 2cos(11π/28) | -2 | 0 | 0 |
| E18 | 2 | -2cos(5π/14) | -2cos(2π/7) | 2cos(π/14) | -2cos(3π/7) | -2cos(3π/14) | 2cos(π/7) | 0 | -2cos(π/7) | 2cos(3π/14) | 2cos(3π/7) | -2cos(π/14) | 2cos(2π/7) | 2cos(5π/14) | -2 | 2cos(5π/14) | 2cos(2π/7) | -2cos(π/14) | 2cos(3π/7) | 2cos(3π/14) | -2cos(π/7) | 0 | 2cos(π/7) | -2cos(3π/14) | -2cos(3π/7) | 2cos(π/14) | -2cos(2π/7) | -2cos(5π/14) | 2 | 0 | 0 |
| E19 | 2 | -2cos(9π/28) | -2cos(5π/14) | 2cos(π/28) | -2cos(2π/7) | -2cos(11π/28) | 2cos(π/14) | -2cos(π/4) | -2cos(3π/7) | 2cos(3π/28) | -2cos(3π/14) | -2cos(13π/28) | 2cos(π/7) | -2cos(5π/28) | 0 | 2cos(5π/28) | -2cos(π/7) | 2cos(13π/28) | 2cos(3π/14) | -2cos(3π/28) | 2cos(3π/7) | 2cos(π/4) | -2cos(π/14) | 2cos(11π/28) | 2cos(2π/7) | -2cos(π/28) | 2cos(5π/14) | 2cos(9π/28) | -2 | 0 | 0 |
| E20 | 2 | -2cos(2π/7) | -2cos(3π/7) | 2cos(π/7) | -2cos(π/7) | 2cos(3π/7) | 2cos(2π/7) | -2 | 2cos(2π/7) | 2cos(3π/7) | -2cos(π/7) | 2cos(π/7) | -2cos(3π/7) | -2cos(2π/7) | 2 | -2cos(2π/7) | -2cos(3π/7) | 2cos(π/7) | -2cos(π/7) | 2cos(3π/7) | 2cos(2π/7) | -2 | 2cos(2π/7) | 2cos(3π/7) | -2cos(π/7) | 2cos(π/7) | -2cos(3π/7) | -2cos(2π/7) | 2 | 0 | 0 |
| E21 | 2 | -2cos(π/4) | 0 | 2cos(π/4) | -2 | 2cos(π/4) | 0 | -2cos(π/4) | 2 | -2cos(π/4) | 0 | 2cos(π/4) | -2 | 2cos(π/4) | 0 | -2cos(π/4) | 2 | -2cos(π/4) | 0 | 2cos(π/4) | -2 | 2cos(π/4) | 0 | -2cos(π/4) | 2 | -2cos(π/4) | 0 | 2cos(π/4) | -2 | 0 | 0 |
| E22 | 2 | -2cos(3π/14) | 2cos(3π/7) | 2cos(5π/14) | -2cos(π/7) | 2cos(π/14) | -2cos(2π/7) | 0 | 2cos(2π/7) | -2cos(π/14) | 2cos(π/7) | -2cos(5π/14) | -2cos(3π/7) | 2cos(3π/14) | -2 | 2cos(3π/14) | -2cos(3π/7) | -2cos(5π/14) | 2cos(π/7) | -2cos(π/14) | 2cos(2π/7) | 0 | -2cos(2π/7) | 2cos(π/14) | -2cos(π/7) | 2cos(5π/14) | 2cos(3π/7) | -2cos(3π/14) | 2 | 0 | 0 |
| E23 | 2 | -2cos(5π/28) | 2cos(5π/14) | 2cos(13π/28) | -2cos(2π/7) | 2cos(3π/28) | -2cos(π/14) | 2cos(π/4) | -2cos(3π/7) | -2cos(11π/28) | 2cos(3π/14) | -2cos(π/28) | 2cos(π/7) | -2cos(9π/28) | 0 | 2cos(9π/28) | -2cos(π/7) | 2cos(π/28) | -2cos(3π/14) | 2cos(11π/28) | 2cos(3π/7) | -2cos(π/4) | 2cos(π/14) | -2cos(3π/28) | 2cos(2π/7) | -2cos(13π/28) | -2cos(5π/14) | 2cos(5π/28) | -2 | 0 | 0 |
| E24 | 2 | -2cos(π/7) | 2cos(2π/7) | -2cos(3π/7) | -2cos(3π/7) | 2cos(2π/7) | -2cos(π/7) | 2 | -2cos(π/7) | 2cos(2π/7) | -2cos(3π/7) | -2cos(3π/7) | 2cos(2π/7) | -2cos(π/7) | 2 | -2cos(π/7) | 2cos(2π/7) | -2cos(3π/7) | -2cos(3π/7) | 2cos(2π/7) | -2cos(π/7) | 2 | -2cos(π/7) | 2cos(2π/7) | -2cos(3π/7) | -2cos(3π/7) | 2cos(2π/7) | -2cos(π/7) | 2 | 0 | 0 |
| E25 | 2 | -2cos(3π/28) | 2cos(3π/14) | -2cos(9π/28) | 2cos(3π/7) | 2cos(13π/28) | -2cos(5π/14) | 2cos(π/4) | -2cos(π/7) | 2cos(π/28) | -2cos(π/14) | 2cos(5π/28) | -2cos(2π/7) | 2cos(11π/28) | 0 | -2cos(11π/28) | 2cos(2π/7) | -2cos(5π/28) | 2cos(π/14) | -2cos(π/28) | 2cos(π/7) | -2cos(π/4) | 2cos(5π/14) | -2cos(13π/28) | -2cos(3π/7) | 2cos(9π/28) | -2cos(3π/14) | 2cos(3π/28) | -2 | 0 | 0 |
| E26 | 2 | -2cos(π/14) | 2cos(π/7) | -2cos(3π/14) | 2cos(2π/7) | -2cos(5π/14) | 2cos(3π/7) | 0 | -2cos(3π/7) | 2cos(5π/14) | -2cos(2π/7) | 2cos(3π/14) | -2cos(π/7) | 2cos(π/14) | -2 | 2cos(π/14) | -2cos(π/7) | 2cos(3π/14) | -2cos(2π/7) | 2cos(5π/14) | -2cos(3π/7) | 0 | 2cos(3π/7) | -2cos(5π/14) | 2cos(2π/7) | -2cos(3π/14) | 2cos(π/7) | -2cos(π/14) | 2 | 0 | 0 |
| E27 | 2 | -2cos(π/28) | 2cos(π/14) | -2cos(3π/28) | 2cos(π/7) | -2cos(5π/28) | 2cos(3π/14) | -2cos(π/4) | 2cos(2π/7) | -2cos(9π/28) | 2cos(5π/14) | -2cos(11π/28) | 2cos(3π/7) | -2cos(13π/28) | 0 | 2cos(13π/28) | -2cos(3π/7) | 2cos(11π/28) | -2cos(5π/14) | 2cos(9π/28) | -2cos(2π/7) | 2cos(π/4) | -2cos(3π/14) | 2cos(5π/28) | -2cos(π/7) | 2cos(3π/28) | -2cos(π/14) | 2cos(π/28) | -2 | 0 | 0 |
| Number of symmetry elements | h = 112 |
| Number of classes, irreps | n = 31 |
| Abelian group | no |
| Optical Isomerism (Chirality) | no |
| Polar | no |
| Parity | no |