Results for Point Group Th



Symmetric powers of degenerate representation Eu
Vibrational overtones


Characters of symmetric powers
Power
To
E 4C3 4(C3)2 3C2 i 4(S6)5 4S6 h
1 2 -1 -1 2 -2 1 1 -2
2 3 0 0 3 3 0 0 3
3 4 1 1 4 -4 -1 -1 -4
4 5 -1 -1 5 5 -1 -1 5
5 6 0 0 6 -6 0 0 -6
6 7 1 1 7 7 1 1 7
7 8 -1 -1 8 -8 1 1 -8
8 9 0 0 9 9 0 0 9
9 10 1 1 10 -10 -1 -1 -10
10 11 -1 -1 11 11 -1 -1 11
11 12 0 0 12 -12 0 0 -12
12 13 1 1 13 13 1 1 13
13 14 -1 -1 14 -14 1 1 -14
14 15 0 0 15 15 0 0 15
15 16 1 1 16 -16 -1 -1 -16
16 17 -1 -1 17 17 -1 -1 17
17 18 0 0 18 -18 0 0 -18
18 19 1 1 19 19 1 1 19
19 20 -1 -1 20 -20 1 1 -20
20 21 0 0 21 21 0 0 21


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



Last update January, 3rd 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement