Point Group C30h



C30h E 2C30 2C15 2C10 2(C15)2 2C6 2C5 2(C30)7 2(C15)4 2(C10)3 2C3 2(C30)11 2(C5)2 2(C30)13 2(C15)7 C2 i 2(S15)7 2(S30)13 2(S5)7 2(S30)11 2S3 2(S10)3 2(S15)19 2(S30)7 2S5 2S6 2(S15)17 2S10 2S15 2S30 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 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 1 -1
E1g* 2 1.9563 1.8271 1.6180 1.3383 1 0.6180 0.2091 -0.2091 -0.6180 -1 -1.3383 -1.6180 -1.8271 -1.9563 -2 2 1.9563 1.8271 1.6180 1.3383 1 0.6180 0.2091 -0.2091 -0.6180 -1 -1.3383 -1.6180 -1.8271 -1.9563 -2
E2g* 2 1.8271 1.3383 0.6180 -0.2091 -1 -1.6180 -1.9563 -1.9563 -1.6180 -1 -0.2091 0.6180 1.3383 1.8271 2 2 1.8271 1.3383 0.6180 -0.2091 -1 -1.6180 -1.9563 -1.9563 -1.6180 -1 -0.2091 0.6180 1.3383 1.8271 2
E3g* 2 1.6180 0.6180 -0.6180 -1.6180 -2 -1.6180 -0.6180 0.6180 1.6180 2 1.6180 0.6180 -0.6180 -1.6180 -2 2 1.6180 0.6180 -0.6180 -1.6180 -2 -1.6180 -0.6180 0.6180 1.6180 2 1.6180 0.6180 -0.6180 -1.6180 -2
E4g* 2 1.3383 -0.2091 -1.6180 -1.9563 -1 0.6180 1.8271 1.8271 0.6180 -1 -1.9563 -1.6180 -0.2091 1.3383 2 2 1.3383 -0.2091 -1.6180 -1.9563 -1 0.6180 1.8271 1.8271 0.6180 -1 -1.9563 -1.6180 -0.2091 1.3383 2
E5g* 2 1 -1 -2 -1 1 2 1 -1 -2 -1 1 2 1 -1 -2 2 1 -1 -2 -1 1 2 1 -1 -2 -1 1 2 1 -1 -2
E6g* 2 0.6180 -1.6180 -1.6180 0.6180 2 0.6180 -1.6180 -1.6180 0.6180 2 0.6180 -1.6180 -1.6180 0.6180 2 2 0.6180 -1.6180 -1.6180 0.6180 2 0.6180 -1.6180 -1.6180 0.6180 2 0.6180 -1.6180 -1.6180 0.6180 2
E7g* 2 0.2091 -1.9563 -0.6180 1.8271 1 -1.6180 -1.3383 1.3383 1.6180 -1 -1.8271 0.6180 1.9563 -0.2091 -2 2 0.2091 -1.9563 -0.6180 1.8271 1 -1.6180 -1.3383 1.3383 1.6180 -1 -1.8271 0.6180 1.9563 -0.2091 -2
E8g* 2 -0.2091 -1.9563 0.6180 1.8271 -1 -1.6180 1.3383 1.3383 -1.6180 -1 1.8271 0.6180 -1.9563 -0.2091 2 2 -0.2091 -1.9563 0.6180 1.8271 -1 -1.6180 1.3383 1.3383 -1.6180 -1 1.8271 0.6180 -1.9563 -0.2091 2
E9g* 2 -0.6180 -1.6180 1.6180 0.6180 -2 0.6180 1.6180 -1.6180 -0.6180 2 -0.6180 -1.6180 1.6180 0.6180 -2 2 -0.6180 -1.6180 1.6180 0.6180 -2 0.6180 1.6180 -1.6180 -0.6180 2 -0.6180 -1.6180 1.6180 0.6180 -2
E10g* 2 -1 -1 2 -1 -1 2 -1 -1 2 -1 -1 2 -1 -1 2 2 -1 -1 2 -1 -1 2 -1 -1 2 -1 -1 2 -1 -1 2
E11g* 2 -1.3383 -0.2091 1.6180 -1.9563 1 0.6180 -1.8271 1.8271 -0.6180 -1 1.9563 -1.6180 0.2091 1.3383 -2 2 -1.3383 -0.2091 1.6180 -1.9563 1 0.6180 -1.8271 1.8271 -0.6180 -1 1.9563 -1.6180 0.2091 1.3383 -2
E12g* 2 -1.6180 0.6180 0.6180 -1.6180 2 -1.6180 0.6180 0.6180 -1.6180 2 -1.6180 0.6180 0.6180 -1.6180 2 2 -1.6180 0.6180 0.6180 -1.6180 2 -1.6180 0.6180 0.6180 -1.6180 2 -1.6180 0.6180 0.6180 -1.6180 2
E13g* 2 -1.8271 1.3383 -0.6180 -0.2091 1 -1.6180 1.9563 -1.9563 1.6180 -1 0.2091 0.6180 -1.3383 1.8271 -2 2 -1.8271 1.3383 -0.6180 -0.2091 1 -1.6180 1.9563 -1.9563 1.6180 -1 0.2091 0.6180 -1.3383 1.8271 -2
E14g* 2 -1.9563 1.8271 -1.6180 1.3383 -1 0.6180 -0.2091 -0.2091 0.6180 -1 1.3383 -1.6180 1.8271 -1.9563 2 2 -1.9563 1.8271 -1.6180 1.3383 -1 0.6180 -0.2091 -0.2091 0.6180 -1 1.3383 -1.6180 1.8271 -1.9563 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 -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 -1 1
E1u* 2 1.9563 1.8271 1.6180 1.3383 1 0.6180 0.2091 -0.2091 -0.6180 -1 -1.3383 -1.6180 -1.8271 -1.9563 -2 -2 -1.9563 -1.8271 -1.6180 -1.3383 -1 -0.6180 -0.2091 0.2091 0.6180 1 1.3383 1.6180 1.8271 1.9563 2
E2u* 2 1.8271 1.3383 0.6180 -0.2091 -1 -1.6180 -1.9563 -1.9563 -1.6180 -1 -0.2091 0.6180 1.3383 1.8271 2 -2 -1.8271 -1.3383 -0.6180 0.2091 1 1.6180 1.9563 1.9563 1.6180 1 0.2091 -0.6180 -1.3383 -1.8271 -2
E3u* 2 1.6180 0.6180 -0.6180 -1.6180 -2 -1.6180 -0.6180 0.6180 1.6180 2 1.6180 0.6180 -0.6180 -1.6180 -2 -2 -1.6180 -0.6180 0.6180 1.6180 2 1.6180 0.6180 -0.6180 -1.6180 -2 -1.6180 -0.6180 0.6180 1.6180 2
E4u* 2 1.3383 -0.2091 -1.6180 -1.9563 -1 0.6180 1.8271 1.8271 0.6180 -1 -1.9563 -1.6180 -0.2091 1.3383 2 -2 -1.3383 0.2091 1.6180 1.9563 1 -0.6180 -1.8271 -1.8271 -0.6180 1 1.9563 1.6180 0.2091 -1.3383 -2
E5u* 2 1 -1 -2 -1 1 2 1 -1 -2 -1 1 2 1 -1 -2 -2 -1 1 2 1 -1 -2 -1 1 2 1 -1 -2 -1 1 2
E6u* 2 0.6180 -1.6180 -1.6180 0.6180 2 0.6180 -1.6180 -1.6180 0.6180 2 0.6180 -1.6180 -1.6180 0.6180 2 -2 -0.6180 1.6180 1.6180 -0.6180 -2 -0.6180 1.6180 1.6180 -0.6180 -2 -0.6180 1.6180 1.6180 -0.6180 -2
E7u* 2 0.2091 -1.9563 -0.6180 1.8271 1 -1.6180 -1.3383 1.3383 1.6180 -1 -1.8271 0.6180 1.9563 -0.2091 -2 -2 -0.2091 1.9563 0.6180 -1.8271 -1 1.6180 1.3383 -1.3383 -1.6180 1 1.8271 -0.6180 -1.9563 0.2091 2
E8u* 2 -0.2091 -1.9563 0.6180 1.8271 -1 -1.6180 1.3383 1.3383 -1.6180 -1 1.8271 0.6180 -1.9563 -0.2091 2 -2 0.2091 1.9563 -0.6180 -1.8271 1 1.6180 -1.3383 -1.3383 1.6180 1 -1.8271 -0.6180 1.9563 0.2091 -2
E9u* 2 -0.6180 -1.6180 1.6180 0.6180 -2 0.6180 1.6180 -1.6180 -0.6180 2 -0.6180 -1.6180 1.6180 0.6180 -2 -2 0.6180 1.6180 -1.6180 -0.6180 2 -0.6180 -1.6180 1.6180 0.6180 -2 0.6180 1.6180 -1.6180 -0.6180 2
E10u* 2 -1 -1 2 -1 -1 2 -1 -1 2 -1 -1 2 -1 -1 2 -2 1 1 -2 1 1 -2 1 1 -2 1 1 -2 1 1 -2
E11u* 2 -1.3383 -0.2091 1.6180 -1.9563 1 0.6180 -1.8271 1.8271 -0.6180 -1 1.9563 -1.6180 0.2091 1.3383 -2 -2 1.3383 0.2091 -1.6180 1.9563 -1 -0.6180 1.8271 -1.8271 0.6180 1 -1.9563 1.6180 -0.2091 -1.3383 2
E12u* 2 -1.6180 0.6180 0.6180 -1.6180 2 -1.6180 0.6180 0.6180 -1.6180 2 -1.6180 0.6180 0.6180 -1.6180 2 -2 1.6180 -0.6180 -0.6180 1.6180 -2 1.6180 -0.6180 -0.6180 1.6180 -2 1.6180 -0.6180 -0.6180 1.6180 -2
E13u* 2 -1.8271 1.3383 -0.6180 -0.2091 1 -1.6180 1.9563 -1.9563 1.6180 -1 0.2091 0.6180 -1.3383 1.8271 -2 -2 1.8271 -1.3383 0.6180 0.2091 -1 1.6180 -1.9563 1.9563 -1.6180 1 -0.2091 -0.6180 1.3383 -1.8271 2
E14u* 2 -1.9563 1.8271 -1.6180 1.3383 -1 0.6180 -0.2091 -0.2091 0.6180 -1 1.3383 -1.6180 1.8271 -1.9563 2 -2 1.9563 -1.8271 1.6180 -1.3383 1 -0.6180 0.2091 0.2091 -0.6180 1 -1.3383 1.6180 -1.8271 1.9563 -2
Math View
Phys View A
Phys View B
Chem View A
Chem View B
✅


Additional information

Number of symmetry elements h = 60
Number of classes, irreps n = 60
Number of real-valued irreducible representations n = 32
Abelian group yes
Optical Isomerism (Chirality) no
Polar no
Parity yes


Reduce representation to irreducible representations


E 2C30 2C15 2C10 2(C15)2 2C6 2C5 2(C30)7 2(C15)4 2(C10)3 2C3 2(C30)11 2(C5)2 2(C30)13 2(C15)7 C2 i 2(S15)7 2(S30)13 2(S5)7 2(S30)11 2S3 2(S10)3 2(S15)19 2(S30)7 2S5 2S6 2(S15)17 2S10 2S15 2S30 σh



Genrate representation from irreducible representations


Ag Bg E1g* E2g* E3g* E4g* E5g* E6g* E7g* E8g* E9g* E10g* E11g* E12g* E13g* E14g* Au Bu E1u* E2u* E3u* E4u* E5u* E6u* E7u* E8u* E9u* E10u* E11u* E12u* E13u* E14u*



Direct products of irreducible representations




Error: Reduction failed

Reduction to integer numbers for irreducible representations failed.
Error Code: 2

Binary products
⊙ Ag Bg E1g* E2g* E3g* E4g* E5g* E6g* E7g* E8g* E9g* E10g* E11g* E12g* E13g* E14g* Au Bu E1u* E2u* E3u* E4u* E5u* E6u* E7u* E8u* E9u* E10u* E11u* E12u* E13u* E14u*
Ag
Characters of reducible representation
E C30 C15 C10 (C15)2 C6 C5 (C30)7 (C15)4 (C10)3 C3 (C30)11 (C5)2 (C30)13 (C15)7 C2 (C15)8 (C30)17 (C5)3 (C30)19 (C3)2 (C10)7 (C15)11 (C30)23 (C5)4 (C6)5 (C15)13 (C10)9 (C15)14 (C30)29 i (S15)23 (S30)17 (S5)3 (S30)19 (S3)5 (S10)7 (S15)11 (S30)23 (S5)9 (S6)5 (S15)13 (S10)9 (S15)29 (S30)29 σh S30 S15 S10 (S15)17 S6 S5 (S30)7 (S15)19 (S10)3 S3 (S30)11 (S5)7 (S30)13 (S15)7
0 -1.124 -1.124 34.271 14.679 16 16.708 21.819 42.007 -2.438 4 44.519 3.292 2.648 34.446 25 8.160 8.160 14.854 47.182 4 0.729 42.007 20.082 8.146 16 23.706 34.271 0.139 9.089 25 25.148 2.648 14.854 47.182 4 0.729 42.007 20.082 8.146 16 23.706 34.271 0.139 9.089 49 9.089 0.139 34.271 23.706 16 8.146 20.082 42.007 0.729 4 47.182 14.854 2.648 25.148