Results for Point Group Th



Symmetric powers of degenerate representation Tg
Vibrational overtones


Characters of symmetric powers
Power
To		 E 8C3 3C2 i 8S6 3σh
1 3 0 -1 3 0 -1
2 6 0 2 6 0 2
3 10 1 -2 10 1 -2
4 15 0 3 15 0 3
5 21 0 -3 21 0 -3
6 28 1 4 28 1 4
7 36 0 -4 36 0 -4
8 45 0 5 45 0 5
9 55 1 -5 55 1 -5
10 66 0 6 66 0 6
11 78 0 -6 78 0 -6
12 91 1 7 91 1 7
13 105 0 -7 105 0 -7
14 120 0 8 120 0 8
15 136 1 -8 136 1 -8
16 153 0 9 153 0 9
17 171 0 -9 171 0 -9
18 190 1 10 190 1 10
19 210 0 -10 210 0 -10
20 231 0 11 231 0 11


Decomposition to irreducible representations
Power
To		 Ag Eg* Tg Au Eu* Tu
1 0 0 1 0 0 0 Tg
2 1 1 1 0 0 0 Ag⊕Eg⊕Tg
3 1 0 3 0 0 0 Ag⊕3Tg
4 2 2 3 0 0 0 2Ag⊕2Eg⊕3Tg
5 1 1 6 0 0 0 Ag⊕Eg⊕6Tg
6 4 3 6 0 0 0 4Ag⊕3Eg⊕6Tg
7 2 2 10 0 0 0 2Ag⊕2Eg⊕10Tg
8 5 5 10 0 0 0 5Ag⊕5Eg⊕10Tg
9 4 3 15 0 0 0 4Ag⊕3Eg⊕15Tg
10 7 7 15 0 0 0 7Ag⊕7Eg⊕15Tg
11 5 5 21 0 0 0 5Ag⊕5Eg⊕21Tg
12 10 9 21 0 0 0 10Ag⊕9Eg⊕21Tg
13 7 7 28 0 0 0 7Ag⊕7Eg⊕28Tg
14 12 12 28 0 0 0 12Ag⊕12Eg⊕28Tg
15 10 9 36 0 0 0 10Ag⊕9Eg⊕36Tg
16 15 15 36 0 0 0 15Ag⊕15Eg⊕36Tg
17 12 12 45 0 0 0 12Ag⊕12Eg⊕45Tg
18 19 18 45 0 0 0 19Ag⊕18Eg⊕45Tg
19 15 15 55 0 0 0 15Ag⊕15Eg⊕55Tg
20 22 22 55 0 0 0 22Ag⊕22Eg⊕55Tg


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