Point Group D28h



D28h E 2C28 2C14 2(C28)3 2C7 2(C28)5 2(C14)3 2C4 2(C7)2 2(C28)9 2(C14)5 2(C28)11 2(C7)3 2(C28)13 C2 14C'2 14C''2 i 2(S28)13 2(S7)3 2(S28)11 2(S14)5 2(S28)9 2(S7)5 2S4 2(S14)3 2(S28)5 2S7 2(S28)3 2S14 2S28 σh 14σv 14σd
A1g 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 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 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 -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 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1
E1g 2 1.9499 1.8019 1.5637 1.2470 0.8678 0.4450 0 -0.4450 -0.8678 -1.2470 -1.5637 -1.8019 -1.9499 -2 0 0 2 1.9499 1.8019 1.5637 1.2470 0.8678 0.4450 0 -0.4450 -0.8678 -1.2470 -1.5637 -1.8019 -1.9499 -2 0 0
E2g 2 1.8019 1.2470 0.4450 -0.4450 -1.2470 -1.8019 -2 -1.8019 -1.2470 -0.4450 0.4450 1.2470 1.8019 2 0 0 2 1.8019 1.2470 0.4450 -0.4450 -1.2470 -1.8019 -2 -1.8019 -1.2470 -0.4450 0.4450 1.2470 1.8019 2 0 0
E3g 2 1.5637 0.4450 -0.8678 -1.8019 -1.9499 -1.2470 0 1.2470 1.9499 1.8019 0.8678 -0.4450 -1.5637 -2 0 0 2 1.5637 0.4450 -0.8678 -1.8019 -1.9499 -1.2470 0 1.2470 1.9499 1.8019 0.8678 -0.4450 -1.5637 -2 0 0
E4g 2 1.2470 -0.4450 -1.8019 -1.8019 -0.4450 1.2470 2 1.2470 -0.4450 -1.8019 -1.8019 -0.4450 1.2470 2 0 0 2 1.2470 -0.4450 -1.8019 -1.8019 -0.4450 1.2470 2 1.2470 -0.4450 -1.8019 -1.8019 -0.4450 1.2470 2 0 0
E5g 2 0.8678 -1.2470 -1.9499 -0.4450 1.5637 1.8019 0 -1.8019 -1.5637 0.4450 1.9499 1.2470 -0.8678 -2 0 0 2 0.8678 -1.2470 -1.9499 -0.4450 1.5637 1.8019 0 -1.8019 -1.5637 0.4450 1.9499 1.2470 -0.8678 -2 0 0
E6g 2 0.4450 -1.8019 -1.2470 1.2470 1.8019 -0.4450 -2 -0.4450 1.8019 1.2470 -1.2470 -1.8019 0.4450 2 0 0 2 0.4450 -1.8019 -1.2470 1.2470 1.8019 -0.4450 -2 -0.4450 1.8019 1.2470 -1.2470 -1.8019 0.4450 2 0 0
E7g 2 0 -2 0 2 0 -2 0 2 0 -2 0 2 0 -2 0 0 2 0 -2 0 2 0 -2 0 2 0 -2 0 2 0 -2 0 0
E8g 2 -0.4450 -1.8019 1.2470 1.2470 -1.8019 -0.4450 2 -0.4450 -1.8019 1.2470 1.2470 -1.8019 -0.4450 2 0 0 2 -0.4450 -1.8019 1.2470 1.2470 -1.8019 -0.4450 2 -0.4450 -1.8019 1.2470 1.2470 -1.8019 -0.4450 2 0 0
E9g 2 -0.8678 -1.2470 1.9499 -0.4450 -1.5637 1.8019 0 -1.8019 1.5637 0.4450 -1.9499 1.2470 0.8678 -2 0 0 2 -0.8678 -1.2470 1.9499 -0.4450 -1.5637 1.8019 0 -1.8019 1.5637 0.4450 -1.9499 1.2470 0.8678 -2 0 0
E10g 2 -1.2470 -0.4450 1.8019 -1.8019 0.4450 1.2470 -2 1.2470 0.4450 -1.8019 1.8019 -0.4450 -1.2470 2 0 0 2 -1.2470 -0.4450 1.8019 -1.8019 0.4450 1.2470 -2 1.2470 0.4450 -1.8019 1.8019 -0.4450 -1.2470 2 0 0
E11g 2 -1.5637 0.4450 0.8678 -1.8019 1.9499 -1.2470 0 1.2470 -1.9499 1.8019 -0.8678 -0.4450 1.5637 -2 0 0 2 -1.5637 0.4450 0.8678 -1.8019 1.9499 -1.2470 0 1.2470 -1.9499 1.8019 -0.8678 -0.4450 1.5637 -2 0 0
E12g 2 -1.8019 1.2470 -0.4450 -0.4450 1.2470 -1.8019 2 -1.8019 1.2470 -0.4450 -0.4450 1.2470 -1.8019 2 0 0 2 -1.8019 1.2470 -0.4450 -0.4450 1.2470 -1.8019 2 -1.8019 1.2470 -0.4450 -0.4450 1.2470 -1.8019 2 0 0
E13g 2 -1.9499 1.8019 -1.5637 1.2470 -0.8678 0.4450 0 -0.4450 0.8678 -1.2470 1.5637 -1.8019 1.9499 -2 0 0 2 -1.9499 1.8019 -1.5637 1.2470 -0.8678 0.4450 0 -0.4450 0.8678 -1.2470 1.5637 -1.8019 1.9499 -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 -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 -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 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 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1
E1u 2 1.9499 1.8019 1.5637 1.2470 0.8678 0.4450 0 -0.4450 -0.8678 -1.2470 -1.5637 -1.8019 -1.9499 -2 0 0 -2 -1.9499 -1.8019 -1.5637 -1.2470 -0.8678 -0.4450 0 0.4450 0.8678 1.2470 1.5637 1.8019 1.9499 2 0 0
E2u 2 1.8019 1.2470 0.4450 -0.4450 -1.2470 -1.8019 -2 -1.8019 -1.2470 -0.4450 0.4450 1.2470 1.8019 2 0 0 -2 -1.8019 -1.2470 -0.4450 0.4450 1.2470 1.8019 2 1.8019 1.2470 0.4450 -0.4450 -1.2470 -1.8019 -2 0 0
E3u 2 1.5637 0.4450 -0.8678 -1.8019 -1.9499 -1.2470 0 1.2470 1.9499 1.8019 0.8678 -0.4450 -1.5637 -2 0 0 -2 -1.5637 -0.4450 0.8678 1.8019 1.9499 1.2470 0 -1.2470 -1.9499 -1.8019 -0.8678 0.4450 1.5637 2 0 0
E4u 2 1.2470 -0.4450 -1.8019 -1.8019 -0.4450 1.2470 2 1.2470 -0.4450 -1.8019 -1.8019 -0.4450 1.2470 2 0 0 -2 -1.2470 0.4450 1.8019 1.8019 0.4450 -1.2470 -2 -1.2470 0.4450 1.8019 1.8019 0.4450 -1.2470 -2 0 0
E5u 2 0.8678 -1.2470 -1.9499 -0.4450 1.5637 1.8019 0 -1.8019 -1.5637 0.4450 1.9499 1.2470 -0.8678 -2 0 0 -2 -0.8678 1.2470 1.9499 0.4450 -1.5637 -1.8019 0 1.8019 1.5637 -0.4450 -1.9499 -1.2470 0.8678 2 0 0
E6u 2 0.4450 -1.8019 -1.2470 1.2470 1.8019 -0.4450 -2 -0.4450 1.8019 1.2470 -1.2470 -1.8019 0.4450 2 0 0 -2 -0.4450 1.8019 1.2470 -1.2470 -1.8019 0.4450 2 0.4450 -1.8019 -1.2470 1.2470 1.8019 -0.4450 -2 0 0
E7u 2 0 -2 0 2 0 -2 0 2 0 -2 0 2 0 -2 0 0 -2 0 2 0 -2 0 2 0 -2 0 2 0 -2 0 2 0 0
E8u 2 -0.4450 -1.8019 1.2470 1.2470 -1.8019 -0.4450 2 -0.4450 -1.8019 1.2470 1.2470 -1.8019 -0.4450 2 0 0 -2 0.4450 1.8019 -1.2470 -1.2470 1.8019 0.4450 -2 0.4450 1.8019 -1.2470 -1.2470 1.8019 0.4450 -2 0 0
E9u 2 -0.8678 -1.2470 1.9499 -0.4450 -1.5637 1.8019 0 -1.8019 1.5637 0.4450 -1.9499 1.2470 0.8678 -2 0 0 -2 0.8678 1.2470 -1.9499 0.4450 1.5637 -1.8019 0 1.8019 -1.5637 -0.4450 1.9499 -1.2470 -0.8678 2 0 0
E10u 2 -1.2470 -0.4450 1.8019 -1.8019 0.4450 1.2470 -2 1.2470 0.4450 -1.8019 1.8019 -0.4450 -1.2470 2 0 0 -2 1.2470 0.4450 -1.8019 1.8019 -0.4450 -1.2470 2 -1.2470 -0.4450 1.8019 -1.8019 0.4450 1.2470 -2 0 0
E11u 2 -1.5637 0.4450 0.8678 -1.8019 1.9499 -1.2470 0 1.2470 -1.9499 1.8019 -0.8678 -0.4450 1.5637 -2 0 0 -2 1.5637 -0.4450 -0.8678 1.8019 -1.9499 1.2470 0 -1.2470 1.9499 -1.8019 0.8678 0.4450 -1.5637 2 0 0
E12u 2 -1.8019 1.2470 -0.4450 -0.4450 1.2470 -1.8019 2 -1.8019 1.2470 -0.4450 -0.4450 1.2470 -1.8019 2 0 0 -2 1.8019 -1.2470 0.4450 0.4450 -1.2470 1.8019 -2 1.8019 -1.2470 0.4450 0.4450 -1.2470 1.8019 -2 0 0
E13u 2 -1.9499 1.8019 -1.5637 1.2470 -0.8678 0.4450 0 -0.4450 0.8678 -1.2470 1.5637 -1.8019 1.9499 -2 0 0 -2 1.9499 -1.8019 1.5637 -1.2470 0.8678 -0.4450 0 0.4450 -0.8678 1.2470 -1.5637 1.8019 -1.9499 2 0 0
View A
View B
✅


Additional information

Number of symmetry elements h = 112
Number of classes, irreps n = 34
Abelian group no
Optical Isomerism (Chirality) no
Polar no
Parity yes


Reduce representation to irreducible representations


E 2C28 2C14 2(C28)3 2C7 2(C28)5 2(C14)3 2C4 2(C7)2 2(C28)9 2(C14)5 2(C28)11 2(C7)3 2(C28)13 C2 14C'2 14C''2 i 2(S28)13 2(S7)3 2(S28)11 2(S14)5 2(S28)9 2(S7)5 2S4 2(S14)3 2(S28)5 2S7 2(S28)3 2S14 2S28 σh 14σv 14σd



Genrate representation from irreducible representations


A1g A2g B1g B2g E1g E2g E3g E4g E5g E6g E7g E8g E9g E10g E11g E12g E13g A1u A2u B1u B2u E1u E2u E3u E4u E5u E6u E7u E8u E9u E10u E11u E12u E13u



Direct products of irreducible representations




Error: Reduction failed

Reduction to integer numbers for irreducible representations failed.
Error Code: 1

Binary products
⊙ A1g A2g B1g B2g E1g E2g E3g E4g E5g E6g E7g E8g E9g E10g E11g E12g E13g A1u A2u B1u B2u E1u E2u E3u E4u E5u E6u E7u E8u E9u E10u E11u E12u E13u
A1g
Characters of reducible representation
E 2C28 2C14 2(C28)3 2C7 2(C28)5 2(C14)3 2C4 2(C7)2 2(C28)9 2(C14)5 2(C28)11 2(C7)3 2(C28)13 C2 14C'2 14C''2 i 2(S28)13 2(S7)3 2(S28)11 2(S14)5 2(S28)9 2(S7)5 2S4 2(S14)3 2(S28)5 2S7 2(S28)3 2S14 2S28 σh 14σv 14σd
5 0.112 19.411 22.477 22.477 19.411 0.112 49 0.112 19.411 22.477 22.477 19.411 0.112 49 1 1 25 5.453 41.034 7.513 7.513 41.034 5.453 25 5.453 41.034 7.513 7.513 41.034 5.453 25 1 1