✅
| D28h | E | 2C28 | 2C14 | 2(C28)3 | 2C7 | 2(C28)5 | 2(C14)3 | 2C4 | 2(C7)2 | 2(C28)9 | 2(C14)5 | 2(C28)11 | 2(C7)3 | 2(C28)13 | C2 | 14C'2 | 14C''2 | i | 2(S28)13 | 2(S7)3 | 2(S28)11 | 2(S14)5 | 2(S28)9 | 2(S7)5 | 2S4 | 2(S14)3 | 2(S28)5 | 2S7 | 2(S28)3 | 2S14 | 2S28 | σh | 14σv | 14σd |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A1g | 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 | 1 | 1 | 1 |
| A2g | 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 | 1 | -1 | -1 |
| B1g | 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 | 1 | 1 | -1 |
| B2g | 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 | 1 | -1 | 1 |
| E1g | 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 | 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 |
| E2g | 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 | 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 |
| E3g | 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 | 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 |
| E4g | 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 | 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 |
| E5g | 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 | 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 |
| E6g | 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 | 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 |
| E7g | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 0 |
| E8g | 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 | 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 |
| E9g | 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 | 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 |
| E10g | 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 | 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 |
| E11g | 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 | 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 |
| E12g | 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 | 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 |
| E13g | 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 | 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 |
| A1u | 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 | -1 | -1 | -1 |
| A2u | 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 | -1 | 1 | 1 |
| B1u | 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 | -1 | -1 | 1 |
| B2u | 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 | -1 | 1 | -1 |
| E1u | 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 | -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 |
| E2u | 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 | -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 |
| E3u | 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 | -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 |
| E4u | 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 | -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 |
| E5u | 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 | -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 |
| E6u | 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 | -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 |
| E7u | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | 0 |
| E8u | 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 | -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 |
| E9u | 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 | -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 |
| E10u | 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 | -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 |
| E11u | 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 | -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 |
| E12u | 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 | -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 |
| E13u | 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 | -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 |
| Number of symmetry elements | h = 112 |
| Number of classes, irreps | n = 34 |
| Abelian group | no |
| Optical Isomerism (Chirality) | no |
| Polar | no |
| Parity | yes |