✅
D18d | E | 2S36 | 2C18 | 2S12 | 2C9 | 2(S36)5 | 2C6 | 2(S36)7 | 2(C9)2 | 2S4 | 2(C18)5 | 2(S36)11 | 2C3 | 2(S36)13 | 2(C18)7 | 2(S12)5 | 2(C9)4 | 2(S36)17 | C2 | 18C'2 | 18σd |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A1 | 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 |
B1 | 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 |
E1 | 2 | 2cos(π/18) | 2cos(π/9) | 2cos(π/6) | 2cos(2π/9) | 2cos(5π/18) | 1 | 2cos(7π/18) | 2cos(4π/9) | 0 | -2cos(4π/9) | -2cos(7π/18) | -1 | -2cos(5π/18) | -2cos(2π/9) | -2cos(π/6) | -2cos(π/9) | -2cos(π/18) | -2 | 0 | 0 |
E2 | 2 | 2cos(π/9) | 2cos(2π/9) | 1 | 2cos(4π/9) | -2cos(4π/9) | -1 | -2cos(2π/9) | -2cos(π/9) | -2 | -2cos(π/9) | -2cos(2π/9) | -1 | -2cos(4π/9) | 2cos(4π/9) | 1 | 2cos(2π/9) | 2cos(π/9) | 2 | 0 | 0 |
E3 | 2 | 2cos(π/6) | 1 | 0 | -1 | -2cos(π/6) | -2 | -2cos(π/6) | -1 | 0 | 1 | 2cos(π/6) | 2 | 2cos(π/6) | 1 | 0 | -1 | -2cos(π/6) | -2 | 0 | 0 |
E4 | 2 | 2cos(2π/9) | 2cos(4π/9) | -1 | -2cos(π/9) | -2cos(π/9) | -1 | 2cos(4π/9) | 2cos(2π/9) | 2 | 2cos(2π/9) | 2cos(4π/9) | -1 | -2cos(π/9) | -2cos(π/9) | -1 | 2cos(4π/9) | 2cos(2π/9) | 2 | 0 | 0 |
E5 | 2 | 2cos(5π/18) | -2cos(4π/9) | -2cos(π/6) | -2cos(π/9) | -2cos(7π/18) | 1 | 2cos(π/18) | 2cos(2π/9) | 0 | -2cos(2π/9) | -2cos(π/18) | -1 | 2cos(7π/18) | 2cos(π/9) | 2cos(π/6) | 2cos(4π/9) | -2cos(5π/18) | -2 | 0 | 0 |
E6 | 2 | 1 | -1 | -2 | -1 | 1 | 2 | 1 | -1 | -2 | -1 | 1 | 2 | 1 | -1 | -2 | -1 | 1 | 2 | 0 | 0 |
E7 | 2 | 2cos(7π/18) | -2cos(2π/9) | -2cos(π/6) | 2cos(4π/9) | 2cos(π/18) | 1 | -2cos(5π/18) | -2cos(π/9) | 0 | 2cos(π/9) | 2cos(5π/18) | -1 | -2cos(π/18) | -2cos(4π/9) | 2cos(π/6) | 2cos(2π/9) | -2cos(7π/18) | -2 | 0 | 0 |
E8 | 2 | 2cos(4π/9) | -2cos(π/9) | -1 | 2cos(2π/9) | 2cos(2π/9) | -1 | -2cos(π/9) | 2cos(4π/9) | 2 | 2cos(4π/9) | -2cos(π/9) | -1 | 2cos(2π/9) | 2cos(2π/9) | -1 | -2cos(π/9) | 2cos(4π/9) | 2 | 0 | 0 |
E9 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 0 |
E10 | 2 | -2cos(4π/9) | -2cos(π/9) | 1 | 2cos(2π/9) | -2cos(2π/9) | -1 | 2cos(π/9) | 2cos(4π/9) | -2 | 2cos(4π/9) | 2cos(π/9) | -1 | -2cos(2π/9) | 2cos(2π/9) | 1 | -2cos(π/9) | -2cos(4π/9) | 2 | 0 | 0 |
E11 | 2 | -2cos(7π/18) | -2cos(2π/9) | 2cos(π/6) | 2cos(4π/9) | -2cos(π/18) | 1 | 2cos(5π/18) | -2cos(π/9) | 0 | 2cos(π/9) | -2cos(5π/18) | -1 | 2cos(π/18) | -2cos(4π/9) | -2cos(π/6) | 2cos(2π/9) | 2cos(7π/18) | -2 | 0 | 0 |
E12 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | -1 | -1 | 2 | 0 | 0 |
E13 | 2 | -2cos(5π/18) | -2cos(4π/9) | 2cos(π/6) | -2cos(π/9) | 2cos(7π/18) | 1 | -2cos(π/18) | 2cos(2π/9) | 0 | -2cos(2π/9) | 2cos(π/18) | -1 | -2cos(7π/18) | 2cos(π/9) | -2cos(π/6) | 2cos(4π/9) | 2cos(5π/18) | -2 | 0 | 0 |
E14 | 2 | -2cos(2π/9) | 2cos(4π/9) | 1 | -2cos(π/9) | 2cos(π/9) | -1 | -2cos(4π/9) | 2cos(2π/9) | -2 | 2cos(2π/9) | -2cos(4π/9) | -1 | 2cos(π/9) | -2cos(π/9) | 1 | 2cos(4π/9) | -2cos(2π/9) | 2 | 0 | 0 |
E15 | 2 | -2cos(π/6) | 1 | 0 | -1 | 2cos(π/6) | -2 | 2cos(π/6) | -1 | 0 | 1 | -2cos(π/6) | 2 | -2cos(π/6) | 1 | 0 | -1 | 2cos(π/6) | -2 | 0 | 0 |
E16 | 2 | -2cos(π/9) | 2cos(2π/9) | -1 | 2cos(4π/9) | 2cos(4π/9) | -1 | 2cos(2π/9) | -2cos(π/9) | 2 | -2cos(π/9) | 2cos(2π/9) | -1 | 2cos(4π/9) | 2cos(4π/9) | -1 | 2cos(2π/9) | -2cos(π/9) | 2 | 0 | 0 |
E17 | 2 | -2cos(π/18) | 2cos(π/9) | -2cos(π/6) | 2cos(2π/9) | -2cos(5π/18) | 1 | -2cos(7π/18) | 2cos(4π/9) | 0 | -2cos(4π/9) | 2cos(7π/18) | -1 | 2cos(5π/18) | -2cos(2π/9) | 2cos(π/6) | -2cos(π/9) | 2cos(π/18) | -2 | 0 | 0 |
Number of symmetry elements | h = 72 |
Number of classes, irreps | n = 21 |
Abelian group | no |
Optical Isomerism (Chirality) | no |
Polar | no |
Parity | no |