✅
| D29d | E | 2C29 | 2(C29)2 | 2(C29)3 | 2(C29)4 | 2(C29)5 | 2(C29)6 | 2(C29)7 | 2(C29)8 | 2(C29)9 | 2(C29)10 | 2(C29)11 | 2(C29)12 | 2(C29)13 | 2(C29)14 | 29C'2 | i | 2(S58)27 | 2(S58)25 | 2(S58)23 | 2(S58)21 | 2(S58)19 | 2(S58)17 | 2(S58)15 | 2(S58)13 | 2(S58)11 | 2(S58)9 | 2(S58)7 | 2(S58)5 | 2(S58)3 | 2S58 | 29σd |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 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 |
| 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 |
| E1g | 2 | 2cos(2π/29) | 2cos(4π/29) | 2cos(6π/29) | 2cos(8π/29) | 2cos(10π/29) | 2cos(12π/29) | 2cos(14π/29) | 2cos(16π/29) | 2cos(18π/29) | 2cos(20π/29) | 2cos(22π/29) | 2cos(24π/29) | 2cos(26π/29) | 2cos(28π/29) | 0 | 2 | 2cos(2π/29) | 2cos(4π/29) | 2cos(6π/29) | 2cos(8π/29) | 2cos(10π/29) | 2cos(12π/29) | 2cos(14π/29) | 2cos(16π/29) | 2cos(18π/29) | 2cos(20π/29) | 2cos(22π/29) | 2cos(24π/29) | 2cos(26π/29) | 2cos(28π/29) | 0 |
| E2g | 2 | 2cos(4π/29) | 2cos(8π/29) | 2cos(12π/29) | 2cos(16π/29) | 2cos(20π/29) | 2cos(24π/29) | 2cos(28π/29) | 2cos(26π/29) | 2cos(22π/29) | 2cos(18π/29) | 2cos(14π/29) | 2cos(10π/29) | 2cos(6π/29) | 2cos(2π/29) | 0 | 2 | 2cos(4π/29) | 2cos(8π/29) | 2cos(12π/29) | 2cos(16π/29) | 2cos(20π/29) | 2cos(24π/29) | 2cos(28π/29) | 2cos(26π/29) | 2cos(22π/29) | 2cos(18π/29) | 2cos(14π/29) | 2cos(10π/29) | 2cos(6π/29) | 2cos(2π/29) | 0 |
| E3g | 2 | 2cos(6π/29) | 2cos(12π/29) | 2cos(18π/29) | 2cos(24π/29) | 2cos(28π/29) | 2cos(22π/29) | 2cos(16π/29) | 2cos(10π/29) | 2cos(4π/29) | 2cos(2π/29) | 2cos(8π/29) | 2cos(14π/29) | 2cos(20π/29) | 2cos(26π/29) | 0 | 2 | 2cos(6π/29) | 2cos(12π/29) | 2cos(18π/29) | 2cos(24π/29) | 2cos(28π/29) | 2cos(22π/29) | 2cos(16π/29) | 2cos(10π/29) | 2cos(4π/29) | 2cos(2π/29) | 2cos(8π/29) | 2cos(14π/29) | 2cos(20π/29) | 2cos(26π/29) | 0 |
| E4g | 2 | 2cos(8π/29) | 2cos(16π/29) | 2cos(24π/29) | 2cos(26π/29) | 2cos(18π/29) | 2cos(10π/29) | 2cos(2π/29) | 2cos(6π/29) | 2cos(14π/29) | 2cos(22π/29) | 2cos(28π/29) | 2cos(20π/29) | 2cos(12π/29) | 2cos(4π/29) | 0 | 2 | 2cos(8π/29) | 2cos(16π/29) | 2cos(24π/29) | 2cos(26π/29) | 2cos(18π/29) | 2cos(10π/29) | 2cos(2π/29) | 2cos(6π/29) | 2cos(14π/29) | 2cos(22π/29) | 2cos(28π/29) | 2cos(20π/29) | 2cos(12π/29) | 2cos(4π/29) | 0 |
| E5g | 2 | 2cos(10π/29) | 2cos(20π/29) | 2cos(28π/29) | 2cos(18π/29) | 2cos(8π/29) | 2cos(2π/29) | 2cos(12π/29) | 2cos(22π/29) | 2cos(26π/29) | 2cos(16π/29) | 2cos(6π/29) | 2cos(4π/29) | 2cos(14π/29) | 2cos(24π/29) | 0 | 2 | 2cos(10π/29) | 2cos(20π/29) | 2cos(28π/29) | 2cos(18π/29) | 2cos(8π/29) | 2cos(2π/29) | 2cos(12π/29) | 2cos(22π/29) | 2cos(26π/29) | 2cos(16π/29) | 2cos(6π/29) | 2cos(4π/29) | 2cos(14π/29) | 2cos(24π/29) | 0 |
| E6g | 2 | 2cos(12π/29) | 2cos(24π/29) | 2cos(22π/29) | 2cos(10π/29) | 2cos(2π/29) | 2cos(14π/29) | 2cos(26π/29) | 2cos(20π/29) | 2cos(8π/29) | 2cos(4π/29) | 2cos(16π/29) | 2cos(28π/29) | 2cos(18π/29) | 2cos(6π/29) | 0 | 2 | 2cos(12π/29) | 2cos(24π/29) | 2cos(22π/29) | 2cos(10π/29) | 2cos(2π/29) | 2cos(14π/29) | 2cos(26π/29) | 2cos(20π/29) | 2cos(8π/29) | 2cos(4π/29) | 2cos(16π/29) | 2cos(28π/29) | 2cos(18π/29) | 2cos(6π/29) | 0 |
| E7g | 2 | 2cos(14π/29) | 2cos(28π/29) | 2cos(16π/29) | 2cos(2π/29) | 2cos(12π/29) | 2cos(26π/29) | 2cos(18π/29) | 2cos(4π/29) | 2cos(10π/29) | 2cos(24π/29) | 2cos(20π/29) | 2cos(6π/29) | 2cos(8π/29) | 2cos(22π/29) | 0 | 2 | 2cos(14π/29) | 2cos(28π/29) | 2cos(16π/29) | 2cos(2π/29) | 2cos(12π/29) | 2cos(26π/29) | 2cos(18π/29) | 2cos(4π/29) | 2cos(10π/29) | 2cos(24π/29) | 2cos(20π/29) | 2cos(6π/29) | 2cos(8π/29) | 2cos(22π/29) | 0 |
| E8g | 2 | 2cos(16π/29) | 2cos(26π/29) | 2cos(10π/29) | 2cos(6π/29) | 2cos(22π/29) | 2cos(20π/29) | 2cos(4π/29) | 2cos(12π/29) | 2cos(28π/29) | 2cos(14π/29) | 2cos(2π/29) | 2cos(18π/29) | 2cos(24π/29) | 2cos(8π/29) | 0 | 2 | 2cos(16π/29) | 2cos(26π/29) | 2cos(10π/29) | 2cos(6π/29) | 2cos(22π/29) | 2cos(20π/29) | 2cos(4π/29) | 2cos(12π/29) | 2cos(28π/29) | 2cos(14π/29) | 2cos(2π/29) | 2cos(18π/29) | 2cos(24π/29) | 2cos(8π/29) | 0 |
| E9g | 2 | 2cos(18π/29) | 2cos(22π/29) | 2cos(4π/29) | 2cos(14π/29) | 2cos(26π/29) | 2cos(8π/29) | 2cos(10π/29) | 2cos(28π/29) | 2cos(12π/29) | 2cos(6π/29) | 2cos(24π/29) | 2cos(16π/29) | 2cos(2π/29) | 2cos(20π/29) | 0 | 2 | 2cos(18π/29) | 2cos(22π/29) | 2cos(4π/29) | 2cos(14π/29) | 2cos(26π/29) | 2cos(8π/29) | 2cos(10π/29) | 2cos(28π/29) | 2cos(12π/29) | 2cos(6π/29) | 2cos(24π/29) | 2cos(16π/29) | 2cos(2π/29) | 2cos(20π/29) | 0 |
| E10g | 2 | 2cos(20π/29) | 2cos(18π/29) | 2cos(2π/29) | 2cos(22π/29) | 2cos(16π/29) | 2cos(4π/29) | 2cos(24π/29) | 2cos(14π/29) | 2cos(6π/29) | 2cos(26π/29) | 2cos(12π/29) | 2cos(8π/29) | 2cos(28π/29) | 2cos(10π/29) | 0 | 2 | 2cos(20π/29) | 2cos(18π/29) | 2cos(2π/29) | 2cos(22π/29) | 2cos(16π/29) | 2cos(4π/29) | 2cos(24π/29) | 2cos(14π/29) | 2cos(6π/29) | 2cos(26π/29) | 2cos(12π/29) | 2cos(8π/29) | 2cos(28π/29) | 2cos(10π/29) | 0 |
| E11g | 2 | 2cos(22π/29) | 2cos(14π/29) | 2cos(8π/29) | 2cos(28π/29) | 2cos(6π/29) | 2cos(16π/29) | 2cos(20π/29) | 2cos(2π/29) | 2cos(24π/29) | 2cos(12π/29) | 2cos(10π/29) | 2cos(26π/29) | 2cos(4π/29) | 2cos(18π/29) | 0 | 2 | 2cos(22π/29) | 2cos(14π/29) | 2cos(8π/29) | 2cos(28π/29) | 2cos(6π/29) | 2cos(16π/29) | 2cos(20π/29) | 2cos(2π/29) | 2cos(24π/29) | 2cos(12π/29) | 2cos(10π/29) | 2cos(26π/29) | 2cos(4π/29) | 2cos(18π/29) | 0 |
| E12g | 2 | 2cos(24π/29) | 2cos(10π/29) | 2cos(14π/29) | 2cos(20π/29) | 2cos(4π/29) | 2cos(28π/29) | 2cos(6π/29) | 2cos(18π/29) | 2cos(16π/29) | 2cos(8π/29) | 2cos(26π/29) | 2cos(2π/29) | 2cos(22π/29) | 2cos(12π/29) | 0 | 2 | 2cos(24π/29) | 2cos(10π/29) | 2cos(14π/29) | 2cos(20π/29) | 2cos(4π/29) | 2cos(28π/29) | 2cos(6π/29) | 2cos(18π/29) | 2cos(16π/29) | 2cos(8π/29) | 2cos(26π/29) | 2cos(2π/29) | 2cos(22π/29) | 2cos(12π/29) | 0 |
| E13g | 2 | 2cos(26π/29) | 2cos(6π/29) | 2cos(20π/29) | 2cos(12π/29) | 2cos(14π/29) | 2cos(18π/29) | 2cos(8π/29) | 2cos(24π/29) | 2cos(2π/29) | 2cos(28π/29) | 2cos(4π/29) | 2cos(22π/29) | 2cos(10π/29) | 2cos(16π/29) | 0 | 2 | 2cos(26π/29) | 2cos(6π/29) | 2cos(20π/29) | 2cos(12π/29) | 2cos(14π/29) | 2cos(18π/29) | 2cos(8π/29) | 2cos(24π/29) | 2cos(2π/29) | 2cos(28π/29) | 2cos(4π/29) | 2cos(22π/29) | 2cos(10π/29) | 2cos(16π/29) | 0 |
| E14g | 2 | 2cos(28π/29) | 2cos(2π/29) | 2cos(26π/29) | 2cos(4π/29) | 2cos(24π/29) | 2cos(6π/29) | 2cos(22π/29) | 2cos(8π/29) | 2cos(20π/29) | 2cos(10π/29) | 2cos(18π/29) | 2cos(12π/29) | 2cos(16π/29) | 2cos(14π/29) | 0 | 2 | 2cos(28π/29) | 2cos(2π/29) | 2cos(26π/29) | 2cos(4π/29) | 2cos(24π/29) | 2cos(6π/29) | 2cos(22π/29) | 2cos(8π/29) | 2cos(20π/29) | 2cos(10π/29) | 2cos(18π/29) | 2cos(12π/29) | 2cos(16π/29) | 2cos(14π/29) | 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 |
| 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 |
| E1u | 2 | 2cos(2π/29) | 2cos(4π/29) | 2cos(6π/29) | 2cos(8π/29) | 2cos(10π/29) | 2cos(12π/29) | 2cos(14π/29) | 2cos(16π/29) | 2cos(18π/29) | 2cos(20π/29) | 2cos(22π/29) | 2cos(24π/29) | 2cos(26π/29) | 2cos(28π/29) | 0 | -2 | -2cos(2π/29) | -2cos(4π/29) | -2cos(6π/29) | -2cos(8π/29) | -2cos(10π/29) | -2cos(12π/29) | -2cos(14π/29) | -2cos(16π/29) | -2cos(18π/29) | -2cos(20π/29) | -2cos(22π/29) | -2cos(24π/29) | -2cos(26π/29) | -2cos(28π/29) | 0 |
| E2u | 2 | 2cos(4π/29) | 2cos(8π/29) | 2cos(12π/29) | 2cos(16π/29) | 2cos(20π/29) | 2cos(24π/29) | 2cos(28π/29) | 2cos(26π/29) | 2cos(22π/29) | 2cos(18π/29) | 2cos(14π/29) | 2cos(10π/29) | 2cos(6π/29) | 2cos(2π/29) | 0 | -2 | -2cos(4π/29) | -2cos(8π/29) | -2cos(12π/29) | -2cos(16π/29) | -2cos(20π/29) | -2cos(24π/29) | -2cos(28π/29) | -2cos(26π/29) | -2cos(22π/29) | -2cos(18π/29) | -2cos(14π/29) | -2cos(10π/29) | -2cos(6π/29) | -2cos(2π/29) | 0 |
| E3u | 2 | 2cos(6π/29) | 2cos(12π/29) | 2cos(18π/29) | 2cos(24π/29) | 2cos(28π/29) | 2cos(22π/29) | 2cos(16π/29) | 2cos(10π/29) | 2cos(4π/29) | 2cos(2π/29) | 2cos(8π/29) | 2cos(14π/29) | 2cos(20π/29) | 2cos(26π/29) | 0 | -2 | -2cos(6π/29) | -2cos(12π/29) | -2cos(18π/29) | -2cos(24π/29) | -2cos(28π/29) | -2cos(22π/29) | -2cos(16π/29) | -2cos(10π/29) | -2cos(4π/29) | -2cos(2π/29) | -2cos(8π/29) | -2cos(14π/29) | -2cos(20π/29) | -2cos(26π/29) | 0 |
| E4u | 2 | 2cos(8π/29) | 2cos(16π/29) | 2cos(24π/29) | 2cos(26π/29) | 2cos(18π/29) | 2cos(10π/29) | 2cos(2π/29) | 2cos(6π/29) | 2cos(14π/29) | 2cos(22π/29) | 2cos(28π/29) | 2cos(20π/29) | 2cos(12π/29) | 2cos(4π/29) | 0 | -2 | -2cos(8π/29) | -2cos(16π/29) | -2cos(24π/29) | -2cos(26π/29) | -2cos(18π/29) | -2cos(10π/29) | -2cos(2π/29) | -2cos(6π/29) | -2cos(14π/29) | -2cos(22π/29) | -2cos(28π/29) | -2cos(20π/29) | -2cos(12π/29) | -2cos(4π/29) | 0 |
| E5u | 2 | 2cos(10π/29) | 2cos(20π/29) | 2cos(28π/29) | 2cos(18π/29) | 2cos(8π/29) | 2cos(2π/29) | 2cos(12π/29) | 2cos(22π/29) | 2cos(26π/29) | 2cos(16π/29) | 2cos(6π/29) | 2cos(4π/29) | 2cos(14π/29) | 2cos(24π/29) | 0 | -2 | -2cos(10π/29) | -2cos(20π/29) | -2cos(28π/29) | -2cos(18π/29) | -2cos(8π/29) | -2cos(2π/29) | -2cos(12π/29) | -2cos(22π/29) | -2cos(26π/29) | -2cos(16π/29) | -2cos(6π/29) | -2cos(4π/29) | -2cos(14π/29) | -2cos(24π/29) | 0 |
| E6u | 2 | 2cos(12π/29) | 2cos(24π/29) | 2cos(22π/29) | 2cos(10π/29) | 2cos(2π/29) | 2cos(14π/29) | 2cos(26π/29) | 2cos(20π/29) | 2cos(8π/29) | 2cos(4π/29) | 2cos(16π/29) | 2cos(28π/29) | 2cos(18π/29) | 2cos(6π/29) | 0 | -2 | -2cos(12π/29) | -2cos(24π/29) | -2cos(22π/29) | -2cos(10π/29) | -2cos(2π/29) | -2cos(14π/29) | -2cos(26π/29) | -2cos(20π/29) | -2cos(8π/29) | -2cos(4π/29) | -2cos(16π/29) | -2cos(28π/29) | -2cos(18π/29) | -2cos(6π/29) | 0 |
| E7u | 2 | 2cos(14π/29) | 2cos(28π/29) | 2cos(16π/29) | 2cos(2π/29) | 2cos(12π/29) | 2cos(26π/29) | 2cos(18π/29) | 2cos(4π/29) | 2cos(10π/29) | 2cos(24π/29) | 2cos(20π/29) | 2cos(6π/29) | 2cos(8π/29) | 2cos(22π/29) | 0 | -2 | -2cos(14π/29) | -2cos(28π/29) | -2cos(16π/29) | -2cos(2π/29) | -2cos(12π/29) | -2cos(26π/29) | -2cos(18π/29) | -2cos(4π/29) | -2cos(10π/29) | -2cos(24π/29) | -2cos(20π/29) | -2cos(6π/29) | -2cos(8π/29) | -2cos(22π/29) | 0 |
| E8u | 2 | 2cos(16π/29) | 2cos(26π/29) | 2cos(10π/29) | 2cos(6π/29) | 2cos(22π/29) | 2cos(20π/29) | 2cos(4π/29) | 2cos(12π/29) | 2cos(28π/29) | 2cos(14π/29) | 2cos(2π/29) | 2cos(18π/29) | 2cos(24π/29) | 2cos(8π/29) | 0 | -2 | -2cos(16π/29) | -2cos(26π/29) | -2cos(10π/29) | -2cos(6π/29) | -2cos(22π/29) | -2cos(20π/29) | -2cos(4π/29) | -2cos(12π/29) | -2cos(28π/29) | -2cos(14π/29) | -2cos(2π/29) | -2cos(18π/29) | -2cos(24π/29) | -2cos(8π/29) | 0 |
| E9u | 2 | 2cos(18π/29) | 2cos(22π/29) | 2cos(4π/29) | 2cos(14π/29) | 2cos(26π/29) | 2cos(8π/29) | 2cos(10π/29) | 2cos(28π/29) | 2cos(12π/29) | 2cos(6π/29) | 2cos(24π/29) | 2cos(16π/29) | 2cos(2π/29) | 2cos(20π/29) | 0 | -2 | -2cos(18π/29) | -2cos(22π/29) | -2cos(4π/29) | -2cos(14π/29) | -2cos(26π/29) | -2cos(8π/29) | -2cos(10π/29) | -2cos(28π/29) | -2cos(12π/29) | -2cos(6π/29) | -2cos(24π/29) | -2cos(16π/29) | -2cos(2π/29) | -2cos(20π/29) | 0 |
| E10u | 2 | 2cos(20π/29) | 2cos(18π/29) | 2cos(2π/29) | 2cos(22π/29) | 2cos(16π/29) | 2cos(4π/29) | 2cos(24π/29) | 2cos(14π/29) | 2cos(6π/29) | 2cos(26π/29) | 2cos(12π/29) | 2cos(8π/29) | 2cos(28π/29) | 2cos(10π/29) | 0 | -2 | -2cos(20π/29) | -2cos(18π/29) | -2cos(2π/29) | -2cos(22π/29) | -2cos(16π/29) | -2cos(4π/29) | -2cos(24π/29) | -2cos(14π/29) | -2cos(6π/29) | -2cos(26π/29) | -2cos(12π/29) | -2cos(8π/29) | -2cos(28π/29) | -2cos(10π/29) | 0 |
| E11u | 2 | 2cos(22π/29) | 2cos(14π/29) | 2cos(8π/29) | 2cos(28π/29) | 2cos(6π/29) | 2cos(16π/29) | 2cos(20π/29) | 2cos(2π/29) | 2cos(24π/29) | 2cos(12π/29) | 2cos(10π/29) | 2cos(26π/29) | 2cos(4π/29) | 2cos(18π/29) | 0 | -2 | -2cos(22π/29) | -2cos(14π/29) | -2cos(8π/29) | -2cos(28π/29) | -2cos(6π/29) | -2cos(16π/29) | -2cos(20π/29) | -2cos(2π/29) | -2cos(24π/29) | -2cos(12π/29) | -2cos(10π/29) | -2cos(26π/29) | -2cos(4π/29) | -2cos(18π/29) | 0 |
| E12u | 2 | 2cos(24π/29) | 2cos(10π/29) | 2cos(14π/29) | 2cos(20π/29) | 2cos(4π/29) | 2cos(28π/29) | 2cos(6π/29) | 2cos(18π/29) | 2cos(16π/29) | 2cos(8π/29) | 2cos(26π/29) | 2cos(2π/29) | 2cos(22π/29) | 2cos(12π/29) | 0 | -2 | -2cos(24π/29) | -2cos(10π/29) | -2cos(14π/29) | -2cos(20π/29) | -2cos(4π/29) | -2cos(28π/29) | -2cos(6π/29) | -2cos(18π/29) | -2cos(16π/29) | -2cos(8π/29) | -2cos(26π/29) | -2cos(2π/29) | -2cos(22π/29) | -2cos(12π/29) | 0 |
| E13u | 2 | 2cos(26π/29) | 2cos(6π/29) | 2cos(20π/29) | 2cos(12π/29) | 2cos(14π/29) | 2cos(18π/29) | 2cos(8π/29) | 2cos(24π/29) | 2cos(2π/29) | 2cos(28π/29) | 2cos(4π/29) | 2cos(22π/29) | 2cos(10π/29) | 2cos(16π/29) | 0 | -2 | -2cos(26π/29) | -2cos(6π/29) | -2cos(20π/29) | -2cos(12π/29) | -2cos(14π/29) | -2cos(18π/29) | -2cos(8π/29) | -2cos(24π/29) | -2cos(2π/29) | -2cos(28π/29) | -2cos(4π/29) | -2cos(22π/29) | -2cos(10π/29) | -2cos(16π/29) | 0 |
| E14u | 2 | 2cos(28π/29) | 2cos(2π/29) | 2cos(26π/29) | 2cos(4π/29) | 2cos(24π/29) | 2cos(6π/29) | 2cos(22π/29) | 2cos(8π/29) | 2cos(20π/29) | 2cos(10π/29) | 2cos(18π/29) | 2cos(12π/29) | 2cos(16π/29) | 2cos(14π/29) | 0 | -2 | -2cos(28π/29) | -2cos(2π/29) | -2cos(26π/29) | -2cos(4π/29) | -2cos(24π/29) | -2cos(6π/29) | -2cos(22π/29) | -2cos(8π/29) | -2cos(20π/29) | -2cos(10π/29) | -2cos(18π/29) | -2cos(12π/29) | -2cos(16π/29) | -2cos(14π/29) | 0 |
| Number of symmetry elements | h = 116 |
| Number of classes, irreps | n = 32 |
| Abelian group | no |
| Optical Isomerism (Chirality) | no |
| Polar | no |
| Parity | yes |