Results for Point Group Th



Symmetric powers of degenerate representation Tu
Vibrational overtones


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


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


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