D16h | E | 2C16 | 2C8 | 2(C16)3 | 2C4 | 2(C16)5 | 2(C8)3 | 2(C16)7 | C2 | 8C'2 | 8C''2 | i | 2(S16)7 | 2(S8)3 | 2(S16)5 | 2S4 | 2(S16)3 | 2S8 | 2S16 | σh | 8σv | 8σd |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A1g | 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 |
B1g | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | 1 | -1 |
B2g | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 |
E1g | 2 | 1.8478 | 1.4142 | 0.7654 | 0 | -0.7654 | -1.4142 | -1.8478 | -2 | 0 | 0 | 2 | 1.8478 | 1.4142 | 0.7654 | 0 | -0.7654 | -1.4142 | -1.8478 | -2 | 0 | 0 |
E2g | 2 | 1.4142 | 0 | -1.4142 | -2 | -1.4142 | 0 | 1.4142 | 2 | 0 | 0 | 2 | 1.4142 | 0 | -1.4142 | -2 | -1.4142 | 0 | 1.4142 | 2 | 0 | 0 |
E3g | 2 | 0.7654 | -1.4142 | -1.8478 | 0 | 1.8478 | 1.4142 | -0.7654 | -2 | 0 | 0 | 2 | 0.7654 | -1.4142 | -1.8478 | 0 | 1.8478 | 1.4142 | -0.7654 | -2 | 0 | 0 |
E4g | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | 0 |
E5g | 2 | -0.7654 | -1.4142 | 1.8478 | 0 | -1.8478 | 1.4142 | 0.7654 | -2 | 0 | 0 | 2 | -0.7654 | -1.4142 | 1.8478 | 0 | -1.8478 | 1.4142 | 0.7654 | -2 | 0 | 0 |
E6g | 2 | -1.4142 | 0 | 1.4142 | -2 | 1.4142 | 0 | -1.4142 | 2 | 0 | 0 | 2 | -1.4142 | 0 | 1.4142 | -2 | 1.4142 | 0 | -1.4142 | 2 | 0 | 0 |
E7g | 2 | -1.8478 | 1.4142 | -0.7654 | 0 | 0.7654 | -1.4142 | 1.8478 | -2 | 0 | 0 | 2 | -1.8478 | 1.4142 | -0.7654 | 0 | 0.7654 | -1.4142 | 1.8478 | -2 | 0 | 0 |
A1u | 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 |
B1u | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | 1 | -1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | -1 | 1 |
B2u | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 |
E1u | 2 | 1.8478 | 1.4142 | 0.7654 | 0 | -0.7654 | -1.4142 | -1.8478 | -2 | 0 | 0 | -2 | -1.8478 | -1.4142 | -0.7654 | 0 | 0.7654 | 1.4142 | 1.8478 | 2 | 0 | 0 |
E2u | 2 | 1.4142 | 0 | -1.4142 | -2 | -1.4142 | 0 | 1.4142 | 2 | 0 | 0 | -2 | -1.4142 | 0 | 1.4142 | 2 | 1.4142 | 0 | -1.4142 | -2 | 0 | 0 |
E3u | 2 | 0.7654 | -1.4142 | -1.8478 | 0 | 1.8478 | 1.4142 | -0.7654 | -2 | 0 | 0 | -2 | -0.7654 | 1.4142 | 1.8478 | 0 | -1.8478 | -1.4142 | 0.7654 | 2 | 0 | 0 |
E4u | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 0 |
E5u | 2 | -0.7654 | -1.4142 | 1.8478 | 0 | -1.8478 | 1.4142 | 0.7654 | -2 | 0 | 0 | -2 | 0.7654 | 1.4142 | -1.8478 | 0 | 1.8478 | -1.4142 | -0.7654 | 2 | 0 | 0 |
E6u | 2 | -1.4142 | 0 | 1.4142 | -2 | 1.4142 | 0 | -1.4142 | 2 | 0 | 0 | -2 | 1.4142 | 0 | -1.4142 | 2 | -1.4142 | 0 | 1.4142 | -2 | 0 | 0 |
E7u | 2 | -1.8478 | 1.4142 | -0.7654 | 0 | 0.7654 | -1.4142 | 1.8478 | -2 | 0 | 0 | -2 | 1.8478 | -1.4142 | 0.7654 | 0 | -0.7654 | 1.4142 | -1.8478 | 2 | 0 | 0 |
Number of symmetry elements | h = 64 |
Number of classes, irreps | n = 22 |
Abelian group | no |
Optical Isomerism (Chirality) | no |
Polar | no |
Parity | yes |