S16 | E | S16 | C8 | (S16)3 | C4 | (S16)5 | (C8)3 | (S16)7 | C2 | (S16)9 | (C8)5 | (S16)11 | (C4)3 | (S16)13 | (C8)7 | (S16)15 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
B | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 |
E1* | 2 | 2cos(π/8) | 2cos(π/4) | 2cos(3π/8) | 0 | -2cos(3π/8) | -2cos(π/4) | -2cos(π/8) | -2 | -2cos(π/8) | -2cos(π/4) | -2cos(3π/8) | 0 | 2cos(3π/8) | 2cos(π/4) | 2cos(π/8) |
E2* | 2 | 2cos(π/4) | 0 | -2cos(π/4) | -2 | -2cos(π/4) | 0 | 2cos(π/4) | 2 | 2cos(π/4) | 0 | -2cos(π/4) | -2 | -2cos(π/4) | 0 | 2cos(π/4) |
E3* | 2 | 2cos(3π/8) | -2cos(π/4) | -2cos(π/8) | 0 | 2cos(π/8) | 2cos(π/4) | -2cos(3π/8) | -2 | -2cos(3π/8) | 2cos(π/4) | 2cos(π/8) | 0 | -2cos(π/8) | -2cos(π/4) | 2cos(3π/8) |
E4* | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 |
E5* | 2 | -2cos(3π/8) | -2cos(π/4) | 2cos(π/8) | 0 | -2cos(π/8) | 2cos(π/4) | 2cos(3π/8) | -2 | 2cos(3π/8) | 2cos(π/4) | -2cos(π/8) | 0 | 2cos(π/8) | -2cos(π/4) | -2cos(3π/8) |
E6* | 2 | -2cos(π/4) | 0 | 2cos(π/4) | -2 | 2cos(π/4) | 0 | -2cos(π/4) | 2 | -2cos(π/4) | 0 | 2cos(π/4) | -2 | 2cos(π/4) | 0 | -2cos(π/4) |
E7* | 2 | -2cos(π/8) | 2cos(π/4) | -2cos(3π/8) | 0 | 2cos(3π/8) | -2cos(π/4) | 2cos(π/8) | -2 | 2cos(π/8) | -2cos(π/4) | 2cos(3π/8) | 0 | -2cos(3π/8) | 2cos(π/4) | -2cos(π/8) |
Number of symmetry elements | h = 16 |
Number of classes, irreps | n = 16 |
Number of real-valued irreducible representations | n = 9 |
Abelian group | yes |
Optical Isomerism (Chirality) | no |
Polar | no |
Parity | no |