✅
D15h | E | 2C15 | 2(C15)2 | 2C5 | 2(C15)4 | 2C3 | 2(C5)2 | 2(C15)7 | 15C'2 | σh | 2S15 | 2(S15)13 | 2S5 | 2(S15)11 | 2S3 | 2(S5)3 | 2(S15)7 | 15σv |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A'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 |
E'1 | 2 | 2cos(2π/15) | 2cos(4π/15) | 2cos(2π/5) | 2cos(8π/15) | -1 | 2cos(4π/5) | 2cos(14π/15) | 0 | 2 | 2cos(2π/15) | 2cos(4π/15) | 2cos(2π/5) | 2cos(8π/15) | -1 | 2cos(4π/5) | 2cos(14π/15) | 0 |
E'2 | 2 | 2cos(4π/15) | 2cos(8π/15) | 2cos(4π/5) | 2cos(14π/15) | -1 | 2cos(2π/5) | 2cos(2π/15) | 0 | 2 | 2cos(4π/15) | 2cos(8π/15) | 2cos(4π/5) | 2cos(14π/15) | -1 | 2cos(2π/5) | 2cos(2π/15) | 0 |
E'3 | 2 | 2cos(2π/5) | 2cos(4π/5) | 2cos(4π/5) | 2cos(2π/5) | 2 | 2cos(2π/5) | 2cos(4π/5) | 0 | 2 | 2cos(2π/5) | 2cos(4π/5) | 2cos(4π/5) | 2cos(2π/5) | 2 | 2cos(2π/5) | 2cos(4π/5) | 0 |
E'4 | 2 | 2cos(8π/15) | 2cos(14π/15) | 2cos(2π/5) | 2cos(2π/15) | -1 | 2cos(4π/5) | 2cos(4π/15) | 0 | 2 | 2cos(8π/15) | 2cos(14π/15) | 2cos(2π/5) | 2cos(2π/15) | -1 | 2cos(4π/5) | 2cos(4π/15) | 0 |
E'5 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | 0 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | 0 |
E'6 | 2 | 2cos(4π/5) | 2cos(2π/5) | 2cos(2π/5) | 2cos(4π/5) | 2 | 2cos(4π/5) | 2cos(2π/5) | 0 | 2 | 2cos(4π/5) | 2cos(2π/5) | 2cos(2π/5) | 2cos(4π/5) | 2 | 2cos(4π/5) | 2cos(2π/5) | 0 |
E'7 | 2 | 2cos(14π/15) | 2cos(2π/15) | 2cos(4π/5) | 2cos(4π/15) | -1 | 2cos(2π/5) | 2cos(8π/15) | 0 | 2 | 2cos(14π/15) | 2cos(2π/15) | 2cos(4π/5) | 2cos(4π/15) | -1 | 2cos(2π/5) | 2cos(8π/15) | 0 |
A''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 |
E''1 | 2 | 2cos(2π/15) | 2cos(4π/15) | 2cos(2π/5) | 2cos(8π/15) | -1 | 2cos(4π/5) | 2cos(14π/15) | 0 | -2 | -2cos(2π/15) | -2cos(4π/15) | -2cos(2π/5) | -2cos(8π/15) | 1 | -2cos(4π/5) | -2cos(14π/15) | 0 |
E''2 | 2 | 2cos(4π/15) | 2cos(8π/15) | 2cos(4π/5) | 2cos(14π/15) | -1 | 2cos(2π/5) | 2cos(2π/15) | 0 | -2 | -2cos(4π/15) | -2cos(8π/15) | -2cos(4π/5) | -2cos(14π/15) | 1 | -2cos(2π/5) | -2cos(2π/15) | 0 |
E''3 | 2 | 2cos(2π/5) | 2cos(4π/5) | 2cos(4π/5) | 2cos(2π/5) | 2 | 2cos(2π/5) | 2cos(4π/5) | 0 | -2 | -2cos(2π/5) | -2cos(4π/5) | -2cos(4π/5) | -2cos(2π/5) | -2 | -2cos(2π/5) | -2cos(4π/5) | 0 |
E''4 | 2 | 2cos(8π/15) | 2cos(14π/15) | 2cos(2π/5) | 2cos(2π/15) | -1 | 2cos(4π/5) | 2cos(4π/15) | 0 | -2 | -2cos(8π/15) | -2cos(14π/15) | -2cos(2π/5) | -2cos(2π/15) | 1 | -2cos(4π/5) | -2cos(4π/15) | 0 |
E''5 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | 0 | -2 | 1 | 1 | -2 | 1 | 1 | -2 | 1 | 0 |
E''6 | 2 | 2cos(4π/5) | 2cos(2π/5) | 2cos(2π/5) | 2cos(4π/5) | 2 | 2cos(4π/5) | 2cos(2π/5) | 0 | -2 | -2cos(4π/5) | -2cos(2π/5) | -2cos(2π/5) | -2cos(4π/5) | -2 | -2cos(4π/5) | -2cos(2π/5) | 0 |
E''7 | 2 | 2cos(14π/15) | 2cos(2π/15) | 2cos(4π/5) | 2cos(4π/15) | -1 | 2cos(2π/5) | 2cos(8π/15) | 0 | -2 | -2cos(14π/15) | -2cos(2π/15) | -2cos(4π/5) | -2cos(4π/15) | 1 | -2cos(2π/5) | -2cos(8π/15) | 0 |
Number of symmetry elements | h = 60 |
Number of classes, irreps | n = 18 |
Abelian group | no |
Optical Isomerism (Chirality) | no |
Polar | no |
Parity | no |