✅
D16d | E | 2S32 | 2C16 | 2(S32)3 | 2C8 | 2(S32)5 | 2(C16)3 | 2(S32)7 | 2C4 | 2(S32)9 | 2(C16)5 | 2(S32)11 | 2(C8)3 | 2(S32)13 | 2(C16)7 | 2(S32)15 | C2 | 16C'2 | 16σd |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A1 | 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 |
B1 | 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 |
E1 | 2 | 2cos(π/16) | 2cos(π/8) | 2cos(3π/16) | 2cos(π/4) | 2cos(5π/16) | 2cos(3π/8) | 2cos(7π/16) | 0 | -2cos(7π/16) | -2cos(3π/8) | -2cos(5π/16) | -2cos(π/4) | -2cos(3π/16) | -2cos(π/8) | -2cos(π/16) | -2 | 0 | 0 |
E2 | 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) | 2 | 0 | 0 |
E3 | 2 | 2cos(3π/16) | 2cos(3π/8) | -2cos(7π/16) | -2cos(π/4) | -2cos(π/16) | -2cos(π/8) | -2cos(5π/16) | 0 | 2cos(5π/16) | 2cos(π/8) | 2cos(π/16) | 2cos(π/4) | 2cos(7π/16) | -2cos(3π/8) | -2cos(3π/16) | -2 | 0 | 0 |
E4 | 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) | 2 | 0 | 0 |
E5 | 2 | 2cos(5π/16) | -2cos(3π/8) | -2cos(π/16) | -2cos(π/4) | 2cos(7π/16) | 2cos(π/8) | 2cos(3π/16) | 0 | -2cos(3π/16) | -2cos(π/8) | -2cos(7π/16) | 2cos(π/4) | 2cos(π/16) | 2cos(3π/8) | -2cos(5π/16) | -2 | 0 | 0 |
E6 | 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) | 2 | 0 | 0 |
E7 | 2 | 2cos(7π/16) | -2cos(π/8) | -2cos(5π/16) | 2cos(π/4) | 2cos(3π/16) | -2cos(3π/8) | -2cos(π/16) | 0 | 2cos(π/16) | 2cos(3π/8) | -2cos(3π/16) | -2cos(π/4) | 2cos(5π/16) | 2cos(π/8) | -2cos(7π/16) | -2 | 0 | 0 |
E8 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 2 | 0 | 0 |
E9 | 2 | -2cos(7π/16) | -2cos(π/8) | 2cos(5π/16) | 2cos(π/4) | -2cos(3π/16) | -2cos(3π/8) | 2cos(π/16) | 0 | -2cos(π/16) | 2cos(3π/8) | 2cos(3π/16) | -2cos(π/4) | -2cos(5π/16) | 2cos(π/8) | 2cos(7π/16) | -2 | 0 | 0 |
E10 | 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) | 2 | 0 | 0 |
E11 | 2 | -2cos(5π/16) | -2cos(3π/8) | 2cos(π/16) | -2cos(π/4) | -2cos(7π/16) | 2cos(π/8) | -2cos(3π/16) | 0 | 2cos(3π/16) | -2cos(π/8) | 2cos(7π/16) | 2cos(π/4) | -2cos(π/16) | 2cos(3π/8) | 2cos(5π/16) | -2 | 0 | 0 |
E12 | 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) | 2 | 0 | 0 |
E13 | 2 | -2cos(3π/16) | 2cos(3π/8) | 2cos(7π/16) | -2cos(π/4) | 2cos(π/16) | -2cos(π/8) | 2cos(5π/16) | 0 | -2cos(5π/16) | 2cos(π/8) | -2cos(π/16) | 2cos(π/4) | -2cos(7π/16) | -2cos(3π/8) | 2cos(3π/16) | -2 | 0 | 0 |
E14 | 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) | 2 | 0 | 0 |
E15 | 2 | -2cos(π/16) | 2cos(π/8) | -2cos(3π/16) | 2cos(π/4) | -2cos(5π/16) | 2cos(3π/8) | -2cos(7π/16) | 0 | 2cos(7π/16) | -2cos(3π/8) | 2cos(5π/16) | -2cos(π/4) | 2cos(3π/16) | -2cos(π/8) | 2cos(π/16) | -2 | 0 | 0 |
Number of symmetry elements | h = 64 |
Number of classes, irreps | n = 19 |
Abelian group | no |
Optical Isomerism (Chirality) | no |
Polar | no |
Parity | no |