Results for Point Group Ih



Symmetric powers of degenerate representation Gu
Vibrational overtones


Characters of symmetric powers
Power
To		 E 12C5 12(C5)2 20C3 15C2 i 12S10 12(S10)3 20S6 15σd
1 4 -1.000 -1.000 1 0 -4 1.000 1.000 -1 0
2 10 0.000 0.000 1 2 10 0.000 0.000 1 2
3 20 0.000 0.000 2 0 -20 0.000 0.000 -2 0
4 35 0.000 0.000 2 3 35 0.000 0.000 2 3
5 56 1.000 1.000 2 0 -56 -1.000 -1.000 -2 0
6 84 -1.000 -1.000 3 4 84 -1.000 -1.000 3 4
7 120 0.000 0.000 3 0 -120 0.000 0.000 -3 0
8 165 0.000 0.000 3 5 165 0.000 0.000 3 5
9 220 0.000 0.000 4 0 -220 0.000 0.000 -4 0
10 286 1.000 1.000 4 6 286 1.000 1.000 4 6
11 364 -1.000 -1.000 4 0 -364 1.000 1.000 -4 0
12 455 0.000 0.000 5 7 455 0.000 0.000 5 7
13 560 0.000 0.000 5 0 -560 0.000 0.000 -5 0
14 680 0.000 0.000 5 8 680 0.000 0.000 5 8
15 816 1.000 1.000 6 0 -816 -1.000 -1.000 -6 0
16 969 -1.000 -1.000 6 9 969 -1.000 -1.000 6 9
17 1.140 0.000 0.000 6 0 -1.140 0.000 0.000 -6 0
18 1.330 0.000 0.000 7 10 1.330 0.000 0.000 7 10
19 1.540 0.000 0.000 7 0 -1.540 0.000 0.000 -7 0
20 1.771 1.000 1.000 7 11 1.771 1.000 1.000 7 11


Decomposition to irreducible representations
Power
To		 Ag T1g T2g Gg Hg Au T1u T2u Gu Hu
1 0 0 0 0 0 0 0 0 1 0 Gu
2 1 0 0 1 1 0 0 0 0 0 Ag⊕Gg⊕Hg
3 0 0 0 0 0 1 1 1 2 1 Au⊕T1u⊕T2u⊕2Gu⊕Hu
4 2 1 1 3 3 0 0 0 0 0 2Ag⊕T1g⊕T2g⊕3Gg⊕3Hg
5 0 0 0 0 0 2 3 3 4 4 2Au⊕3T1u⊕3T2u⊕4Gu⊕4Hu
6 3 3 3 7 7 0 0 0 0 0 3Ag⊕3T1g⊕3T2g⊕7Gg⊕7Hg
7 0 0 0 0 0 3 6 6 9 9 3Au⊕6T1u⊕6T2u⊕9Gu⊕9Hu
8 5 7 7 12 14 0 0 0 0 0 5Ag⊕7T1g⊕7T2g⊕12Gg⊕14Hg
9 0 0 0 0 0 5 11 11 16 17 5Au⊕11T1u⊕11T2u⊕16Gu⊕17Hu
10 8 13 13 20 24 0 0 0 0 0 8Ag⊕13T1g⊕13T2g⊕20Gg⊕24Hg
11 0 0 0 0 0 7 18 18 26 29 7Au⊕18T1u⊕18T2u⊕26Gu⊕29Hu
12 11 21 21 32 38 0 0 0 0 0 11Ag⊕21T1g⊕21T2g⊕32Gg⊕38Hg
13 0 0 0 0 0 11 28 28 39 45 11Au⊕28T1u⊕28T2u⊕39Gu⊕45Hu
14 15 32 32 47 57 0 0 0 0 0 15Ag⊕32T1g⊕32T2g⊕47Gg⊕57Hg
15 0 0 0 0 0 16 41 41 56 66 16Au⊕41T1u⊕41T2u⊕56Gu⊕66Hu
16 20 46 46 67 81 0 0 0 0 0 20Ag⊕46T1g⊕46T2g⊕67Gg⊕81Hg
17 0 0 0 0 0 21 57 57 78 93 21Au⊕57T1u⊕57T2u⊕78Gu⊕93Hu
18 27 64 64 91 111 0 0 0 0 0 27Ag⊕64T1g⊕64T2g⊕91Gg⊕111Hg
19 0 0 0 0 0 28 77 77 105 126 28Au⊕77T1u⊕77T2u⊕105Gu⊕126Hu
20 35 86 86 120 148 0 0 0 0 0 35Ag⊕86T1g⊕86T2g⊕120Gg⊕148Hg


Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement