Point Group C28h



C28h 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 i 2(S28)13 2(S7)3 2(S28)11 2(S14)5 2(S28)9 2(S7)9 2S4 2(S14)3 2(S28)5 2S7 2(S28)3 2S14 2S28 σh
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 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 -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 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
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 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
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 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
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 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
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 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
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 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
E7g* 2 0 -2 0 2 0 -2 0 2 0 -2 0 2 0 -2 2 0 -2 0 2 0 -2 0 2 0 -2 0 2 0 -2
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 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
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 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
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 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
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 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
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 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
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 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
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 -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 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 -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
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 -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
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 -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
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 -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
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 -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
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 -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
E7u* 2 0 -2 0 2 0 -2 0 2 0 -2 0 2 0 -2 -2 0 2 0 -2 0 2 0 -2 0 2 0 -2 0 2
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 -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
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 -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
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 -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
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 -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
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 -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
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 -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
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Additional information

Number of symmetry elements h = 56
Number of classes, irreps n = 56
Number of real-valued irreducible representations n = 30
Abelian group yes
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 i 2(S28)13 2(S7)3 2(S28)11 2(S14)5 2(S28)9 2(S7)9 2S4 2(S14)3 2(S28)5 2S7 2(S28)3 2S14 2S28 σh



Genrate representation from irreducible representations


Ag Bg E1g* E2g* E3g* E4g* E5g* E6g* E7g* E8g* E9g* E10g* E11g* E12g* E13g* Au Bu 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
⊙ Ag Bg E1g* E2g* E3g* E4g* E5g* E6g* E7g* E8g* E9g* E10g* E11g* E12g* E13g* Au Bu E1u* E2u* E3u* E4u* E5u* E6u* E7u* E8u* E9u* E10u* E11u* E12u* E13u*
Ag
Characters of reducible representation
E C28 C14 (C28)3 C7 (C28)5 (C14)3 C4 (C7)2 (C28)9 (C14)5 (C28)11 (C7)3 (C28)13 C2 (C28)15 (C7)4 (C28)17 (C14)9 (C28)19 (C7)5 (C4)3 (C14)11 (C28)23 (C7)6 (C28)25 (C14)13 (C28)27 i (S28)15 (S7)11 (S28)17 (S14)9 (S28)19 (S7)5 (S4)3 (S14)11 (S28)23 (S7)13 (S28)25 (S14)13 (S28)27 σh S28 S14 (S28)3 S7 (S28)5 (S14)3 S4 (S7)9 (S28)9 (S14)5 (S28)11 (S7)3 (S28)13
6 -28.223 -12.995 -0.783 -0.783 -12.995 -28.223 49 -28.223 -12.995 -0.783 -0.783 -12.995 -28.223 49 19.411 22.477 0.112 0.112 22.477 19.411 49 19.411 22.477 0.112 0.112 22.477 19.411 25 41.034 7.513 5.453 5.453 7.513 41.034 25 41.034 7.513 5.453 5.453 7.513 41.034 25 41.034 7.513 5.453 5.453 7.513 41.034 25 41.034 7.513 5.453 5.453 7.513 41.034