C16h | E | 2C16 | 2C8 | 2(C16)3 | 2C4 | 2(C16)5 | 2(C8)3 | 2(C16)7 | C2 | i | 2(S16)7 | 2(S8)3 | 2(S16)5 | 2S4 | 2(S16)3 | 2S8 | 2S16 | σh |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Ag | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Bg | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 |
E1g* | 2 | 2cos(π/8) | 2cos(π/4) | 2cos(3π/8) | 0 | -2cos(3π/8) | -2cos(π/4) | -2cos(π/8) | -2 | 2 | 2cos(π/8) | 2cos(π/4) | 2cos(3π/8) | 0 | -2cos(3π/8) | -2cos(π/4) | -2cos(π/8) | -2 |
E2g* | 2 | 2cos(π/4) | 0 | -2cos(π/4) | -2 | -2cos(π/4) | 0 | 2cos(π/4) | 2 | 2 | 2cos(π/4) | 0 | -2cos(π/4) | -2 | -2cos(π/4) | 0 | 2cos(π/4) | 2 |
E3g* | 2 | 2cos(3π/8) | -2cos(π/4) | -2cos(π/8) | 0 | 2cos(π/8) | 2cos(π/4) | -2cos(3π/8) | -2 | 2 | 2cos(3π/8) | -2cos(π/4) | -2cos(π/8) | 0 | 2cos(π/8) | 2cos(π/4) | -2cos(3π/8) | -2 |
E4g* | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 |
E5g* | 2 | -2cos(3π/8) | -2cos(π/4) | 2cos(π/8) | 0 | -2cos(π/8) | 2cos(π/4) | 2cos(3π/8) | -2 | 2 | -2cos(3π/8) | -2cos(π/4) | 2cos(π/8) | 0 | -2cos(π/8) | 2cos(π/4) | 2cos(3π/8) | -2 |
E6g* | 2 | -2cos(π/4) | 0 | 2cos(π/4) | -2 | 2cos(π/4) | 0 | -2cos(π/4) | 2 | 2 | -2cos(π/4) | 0 | 2cos(π/4) | -2 | 2cos(π/4) | 0 | -2cos(π/4) | 2 |
E7g* | 2 | -2cos(π/8) | 2cos(π/4) | -2cos(3π/8) | 0 | 2cos(3π/8) | -2cos(π/4) | 2cos(π/8) | -2 | 2 | -2cos(π/8) | 2cos(π/4) | -2cos(3π/8) | 0 | 2cos(3π/8) | -2cos(π/4) | 2cos(π/8) | -2 |
Au | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 |
Bu | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 |
E1u* | 2 | 2cos(π/8) | 2cos(π/4) | 2cos(3π/8) | 0 | -2cos(3π/8) | -2cos(π/4) | -2cos(π/8) | -2 | -2 | -2cos(π/8) | -2cos(π/4) | -2cos(3π/8) | 0 | 2cos(3π/8) | 2cos(π/4) | 2cos(π/8) | 2 |
E2u* | 2 | 2cos(π/4) | 0 | -2cos(π/4) | -2 | -2cos(π/4) | 0 | 2cos(π/4) | 2 | -2 | -2cos(π/4) | 0 | 2cos(π/4) | 2 | 2cos(π/4) | 0 | -2cos(π/4) | -2 |
E3u* | 2 | 2cos(3π/8) | -2cos(π/4) | -2cos(π/8) | 0 | 2cos(π/8) | 2cos(π/4) | -2cos(3π/8) | -2 | -2 | -2cos(3π/8) | 2cos(π/4) | 2cos(π/8) | 0 | -2cos(π/8) | -2cos(π/4) | 2cos(3π/8) | 2 |
E4u* | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 |
E5u* | 2 | -2cos(3π/8) | -2cos(π/4) | 2cos(π/8) | 0 | -2cos(π/8) | 2cos(π/4) | 2cos(3π/8) | -2 | -2 | 2cos(3π/8) | 2cos(π/4) | -2cos(π/8) | 0 | 2cos(π/8) | -2cos(π/4) | -2cos(3π/8) | 2 |
E6u* | 2 | -2cos(π/4) | 0 | 2cos(π/4) | -2 | 2cos(π/4) | 0 | -2cos(π/4) | 2 | -2 | 2cos(π/4) | 0 | -2cos(π/4) | 2 | -2cos(π/4) | 0 | 2cos(π/4) | -2 |
E7u* | 2 | -2cos(π/8) | 2cos(π/4) | -2cos(3π/8) | 0 | 2cos(3π/8) | -2cos(π/4) | 2cos(π/8) | -2 | -2 | 2cos(π/8) | -2cos(π/4) | 2cos(3π/8) | 0 | -2cos(3π/8) | 2cos(π/4) | -2cos(π/8) | 2 |
Number of symmetry elements | h = 32 |
Number of classes, irreps | n = 32 |
Number of real-valued irreducible representations | n = 18 |
Abelian group | yes |
Optical Isomerism (Chirality) | no |
Polar | no |
Parity | yes |