C14h | E | C14 | C7 | (C14)3 | (C7)2 | (C14)5 | (C7)3 | C2 | (C7)4 | (C14)9 | (C7)5 | (C14)11 | (C7)6 | (C14)13 | i | (S7)11 | (S14)9 | (S7)5 | (S14)11 | (S7)13 | (S14)13 | σh | S14 | S7 | (S14)3 | (S7)9 | (S14)5 | (S7)3 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Ag | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 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 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 |
E1g* | 2 | 2cos(π/7) | 2cos(2π/7) | 2cos(3π/7) | -2cos(3π/7) | -2cos(2π/7) | -2cos(π/7) | -2 | -2cos(π/7) | -2cos(2π/7) | -2cos(3π/7) | 2cos(3π/7) | 2cos(2π/7) | 2cos(π/7) | 2 | 2cos(π/7) | 2cos(2π/7) | 2cos(3π/7) | -2cos(3π/7) | -2cos(2π/7) | -2cos(π/7) | -2 | -2cos(π/7) | -2cos(2π/7) | -2cos(3π/7) | 2cos(3π/7) | 2cos(2π/7) | 2cos(π/7) |
E2g* | 2 | 2cos(2π/7) | -2cos(3π/7) | -2cos(π/7) | -2cos(π/7) | -2cos(3π/7) | 2cos(2π/7) | 2 | 2cos(2π/7) | -2cos(3π/7) | -2cos(π/7) | -2cos(π/7) | -2cos(3π/7) | 2cos(2π/7) | 2 | 2cos(2π/7) | -2cos(3π/7) | -2cos(π/7) | -2cos(π/7) | -2cos(3π/7) | 2cos(2π/7) | 2 | 2cos(2π/7) | -2cos(3π/7) | -2cos(π/7) | -2cos(π/7) | -2cos(3π/7) | 2cos(2π/7) |
E3g* | 2 | 2cos(3π/7) | -2cos(π/7) | -2cos(2π/7) | 2cos(2π/7) | 2cos(π/7) | -2cos(3π/7) | -2 | -2cos(3π/7) | 2cos(π/7) | 2cos(2π/7) | -2cos(2π/7) | -2cos(π/7) | 2cos(3π/7) | 2 | 2cos(3π/7) | -2cos(π/7) | -2cos(2π/7) | 2cos(2π/7) | 2cos(π/7) | -2cos(3π/7) | -2 | -2cos(3π/7) | 2cos(π/7) | 2cos(2π/7) | -2cos(2π/7) | -2cos(π/7) | 2cos(3π/7) |
E4g* | 2 | -2cos(3π/7) | -2cos(π/7) | 2cos(2π/7) | 2cos(2π/7) | -2cos(π/7) | -2cos(3π/7) | 2 | -2cos(3π/7) | -2cos(π/7) | 2cos(2π/7) | 2cos(2π/7) | -2cos(π/7) | -2cos(3π/7) | 2 | -2cos(3π/7) | -2cos(π/7) | 2cos(2π/7) | 2cos(2π/7) | -2cos(π/7) | -2cos(3π/7) | 2 | -2cos(3π/7) | -2cos(π/7) | 2cos(2π/7) | 2cos(2π/7) | -2cos(π/7) | -2cos(3π/7) |
E5g* | 2 | -2cos(2π/7) | -2cos(3π/7) | 2cos(π/7) | -2cos(π/7) | 2cos(3π/7) | 2cos(2π/7) | -2 | 2cos(2π/7) | 2cos(3π/7) | -2cos(π/7) | 2cos(π/7) | -2cos(3π/7) | -2cos(2π/7) | 2 | -2cos(2π/7) | -2cos(3π/7) | 2cos(π/7) | -2cos(π/7) | 2cos(3π/7) | 2cos(2π/7) | -2 | 2cos(2π/7) | 2cos(3π/7) | -2cos(π/7) | 2cos(π/7) | -2cos(3π/7) | -2cos(2π/7) |
E6g* | 2 | -2cos(π/7) | 2cos(2π/7) | -2cos(3π/7) | -2cos(3π/7) | 2cos(2π/7) | -2cos(π/7) | 2 | -2cos(π/7) | 2cos(2π/7) | -2cos(3π/7) | -2cos(3π/7) | 2cos(2π/7) | -2cos(π/7) | 2 | -2cos(π/7) | 2cos(2π/7) | -2cos(3π/7) | -2cos(3π/7) | 2cos(2π/7) | -2cos(π/7) | 2 | -2cos(π/7) | 2cos(2π/7) | -2cos(3π/7) | -2cos(3π/7) | 2cos(2π/7) | -2cos(π/7) |
Au | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 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 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 |
E1u* | 2 | 2cos(π/7) | 2cos(2π/7) | 2cos(3π/7) | -2cos(3π/7) | -2cos(2π/7) | -2cos(π/7) | -2 | -2cos(π/7) | -2cos(2π/7) | -2cos(3π/7) | 2cos(3π/7) | 2cos(2π/7) | 2cos(π/7) | -2 | -2cos(π/7) | -2cos(2π/7) | -2cos(3π/7) | 2cos(3π/7) | 2cos(2π/7) | 2cos(π/7) | 2 | 2cos(π/7) | 2cos(2π/7) | 2cos(3π/7) | -2cos(3π/7) | -2cos(2π/7) | -2cos(π/7) |
E2u* | 2 | 2cos(2π/7) | -2cos(3π/7) | -2cos(π/7) | -2cos(π/7) | -2cos(3π/7) | 2cos(2π/7) | 2 | 2cos(2π/7) | -2cos(3π/7) | -2cos(π/7) | -2cos(π/7) | -2cos(3π/7) | 2cos(2π/7) | -2 | -2cos(2π/7) | 2cos(3π/7) | 2cos(π/7) | 2cos(π/7) | 2cos(3π/7) | -2cos(2π/7) | -2 | -2cos(2π/7) | 2cos(3π/7) | 2cos(π/7) | 2cos(π/7) | 2cos(3π/7) | -2cos(2π/7) |
E3u* | 2 | 2cos(3π/7) | -2cos(π/7) | -2cos(2π/7) | 2cos(2π/7) | 2cos(π/7) | -2cos(3π/7) | -2 | -2cos(3π/7) | 2cos(π/7) | 2cos(2π/7) | -2cos(2π/7) | -2cos(π/7) | 2cos(3π/7) | -2 | -2cos(3π/7) | 2cos(π/7) | 2cos(2π/7) | -2cos(2π/7) | -2cos(π/7) | 2cos(3π/7) | 2 | 2cos(3π/7) | -2cos(π/7) | -2cos(2π/7) | 2cos(2π/7) | 2cos(π/7) | -2cos(3π/7) |
E4u* | 2 | -2cos(3π/7) | -2cos(π/7) | 2cos(2π/7) | 2cos(2π/7) | -2cos(π/7) | -2cos(3π/7) | 2 | -2cos(3π/7) | -2cos(π/7) | 2cos(2π/7) | 2cos(2π/7) | -2cos(π/7) | -2cos(3π/7) | -2 | 2cos(3π/7) | 2cos(π/7) | -2cos(2π/7) | -2cos(2π/7) | 2cos(π/7) | 2cos(3π/7) | -2 | 2cos(3π/7) | 2cos(π/7) | -2cos(2π/7) | -2cos(2π/7) | 2cos(π/7) | 2cos(3π/7) |
E5u* | 2 | -2cos(2π/7) | -2cos(3π/7) | 2cos(π/7) | -2cos(π/7) | 2cos(3π/7) | 2cos(2π/7) | -2 | 2cos(2π/7) | 2cos(3π/7) | -2cos(π/7) | 2cos(π/7) | -2cos(3π/7) | -2cos(2π/7) | -2 | 2cos(2π/7) | 2cos(3π/7) | -2cos(π/7) | 2cos(π/7) | -2cos(3π/7) | -2cos(2π/7) | 2 | -2cos(2π/7) | -2cos(3π/7) | 2cos(π/7) | -2cos(π/7) | 2cos(3π/7) | 2cos(2π/7) |
E6u* | 2 | -2cos(π/7) | 2cos(2π/7) | -2cos(3π/7) | -2cos(3π/7) | 2cos(2π/7) | -2cos(π/7) | 2 | -2cos(π/7) | 2cos(2π/7) | -2cos(3π/7) | -2cos(3π/7) | 2cos(2π/7) | -2cos(π/7) | -2 | 2cos(π/7) | -2cos(2π/7) | 2cos(3π/7) | 2cos(3π/7) | -2cos(2π/7) | 2cos(π/7) | -2 | 2cos(π/7) | -2cos(2π/7) | 2cos(3π/7) | 2cos(3π/7) | -2cos(2π/7) | 2cos(π/7) |
Number of symmetry elements | h = 28 |
Number of classes, irreps | n = 28 |
Number of real-valued irreducible representations | n = 16 |
Abelian group | yes |
Optical Isomerism (Chirality) | no |
Polar | no |
Parity | yes |