✅
| D29h | 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 | σh | 2S29 | 2(S29)27 | 2(S29)3 | 2(S29)25 | 2(S29)5 | 2(S29)23 | 2(S29)7 | 2(S29)21 | 2(S29)9 | 2(S29)19 | 2(S29)11 | 2(S29)17 | 2(S29)13 | 2(S29)15 | 29σv |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| A'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 |
| A'2 | 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 |
| E'1 | 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 |
| E'2 | 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 |
| E'3 | 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 |
| E'4 | 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 |
| E'5 | 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 |
| E'6 | 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 |
| E'7 | 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 |
| E'8 | 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 |
| E'9 | 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 |
| E'10 | 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 |
| E'11 | 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 |
| E'12 | 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 |
| E'13 | 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 |
| E'14 | 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 |
| A''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 |
| A''2 | 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 |
| E''1 | 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 |
| E''2 | 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 |
| E''3 | 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 |
| E''4 | 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 |
| E''5 | 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 |
| E''6 | 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 |
| E''7 | 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 |
| E''8 | 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 |
| E''9 | 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 |
| E''10 | 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 |
| E''11 | 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 |
| E''12 | 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 |
| E''13 | 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 |
| E''14 | 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 | no |