✅
C20 | E | C20 | C10 | (C20)3 | C5 | C4 | (C10)3 | (C20)7 | (C5)2 | (C20)9 | C2 | (C20)11 | (C5)3 | (C20)13 | (C10)7 | (C4)3 | (C5)4 | (C20)17 | (C10)9 | (C20)19 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A | 1 | 1 | 1 | 1 | 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 | 1 | -1 | 1 | -1 |
E1* | 1 1 |
ε* ε* |
ε2* ε2* |
ε3* ε3* |
ε4* ε4* |
i -i |
-ε4* -ε4* |
-ε3* -ε3* |
-ε2* -ε2* |
-ε* -ε* |
-1 -1 |
-ε* -ε* |
-ε2* -ε2* |
-ε3* -ε3* |
-ε4* -ε4* |
-i i |
ε4* ε4* |
ε3* ε3* |
ε2* ε2* |
ε* ε* |
E2* | 1 1 |
ε2* ε2* |
ε4* ε4* |
-ε4* -ε4* |
-ε2* -ε2* |
-1 -1 |
-ε2* -ε2* |
-ε4* -ε4* |
ε4* ε4* |
ε2* ε2* |
1 1 |
ε2* ε2* |
ε4* ε4* |
-ε4* -ε4* |
-ε2* -ε2* |
-1 -1 |
-ε2* -ε2* |
-ε4* -ε4* |
ε4* ε4* |
ε2* ε2* |
E3* | 1 1 |
ε3* ε3* |
-ε4* -ε4* |
-ε* -ε* |
-ε2* -ε2* |
-i i |
ε2* ε2* |
ε* ε* |
ε4* ε4* |
-ε3* -ε3* |
-1 -1 |
-ε3* -ε3* |
ε4* ε4* |
ε* ε* |
ε2* ε2* |
i -i |
-ε2* -ε2* |
-ε* -ε* |
-ε4* -ε4* |
ε3* ε3* |
E4* | 1 1 |
ε4* ε4* |
-ε2* -ε2* |
-ε2* -ε2* |
ε4* ε4* |
1 1 |
ε4* ε4* |
-ε2* -ε2* |
-ε2* -ε2* |
ε4* ε4* |
1 1 |
ε4* ε4* |
-ε2* -ε2* |
-ε2* -ε2* |
ε4* ε4* |
1 1 |
ε4* ε4* |
-ε2* -ε2* |
-ε2* -ε2* |
ε4* ε4* |
E5* | 1 1 |
i -i |
-1 -1 |
-i i |
1 1 |
i -i |
-1 -1 |
-i i |
1 1 |
i -i |
-1 -1 |
-i i |
1 1 |
i -i |
-1 -1 |
-i i |
1 1 |
i -i |
-1 -1 |
-i i |
E6* | 1 1 |
-ε4* -ε4* |
-ε2* -ε2* |
ε2* ε2* |
ε4* ε4* |
-1 -1 |
ε4* ε4* |
ε2* ε2* |
-ε2* -ε2* |
-ε4* -ε4* |
1 1 |
-ε4* -ε4* |
-ε2* -ε2* |
ε2* ε2* |
ε4* ε4* |
-1 -1 |
ε4* ε4* |
ε2* ε2* |
-ε2* -ε2* |
-ε4* -ε4* |
E7* | 1 1 |
-ε3* -ε3* |
-ε4* -ε4* |
ε* ε* |
-ε2* -ε2* |
-i i |
ε2* ε2* |
-ε* -ε* |
ε4* ε4* |
ε3* ε3* |
-1 -1 |
ε3* ε3* |
ε4* ε4* |
-ε* -ε* |
ε2* ε2* |
i -i |
-ε2* -ε2* |
ε* ε* |
-ε4* -ε4* |
-ε3* -ε3* |
E8* | 1 1 |
-ε2* -ε2* |
ε4* ε4* |
ε4* ε4* |
-ε2* -ε2* |
1 1 |
-ε2* -ε2* |
ε4* ε4* |
ε4* ε4* |
-ε2* -ε2* |
1 1 |
-ε2* -ε2* |
ε4* ε4* |
ε4* ε4* |
-ε2* -ε2* |
1 1 |
-ε2* -ε2* |
ε4* ε4* |
ε4* ε4* |
-ε2* -ε2* |
E9* | 1 1 |
-ε* -ε* |
ε2* ε2* |
-ε3* -ε3* |
ε4* ε4* |
i -i |
-ε4* -ε4* |
ε3* ε3* |
-ε2* -ε2* |
ε* ε* |
-1 -1 |
ε* ε* |
-ε2* -ε2* |
ε3* ε3* |
-ε4* -ε4* |
-i i |
ε4* ε4* |
-ε3* -ε3* |
ε2* ε2* |
-ε* -ε* |
Number of symmetry elements | h = 20 |
Number of classes, irreps | n = 20 |
Number of real-valued irreducible representations | n = 11 |
Abelian group | yes |
Optical Isomerism (Chirality) | yes |
Polar | yes |
Parity | no |