Results for Point Group S12



Symmetric powers of degenerate representation E4
Vibrational overtones


Characters of symmetric powers
Power
To
E S12 C6 S4 C3 (S12)5 C2 (S12)7 (C3)2 (S4)3 (C6)5 (S12)11
1 2 -1.000 -1 2 -1 -1.000 2 -1.000 -1 2 -1 -1.000
2 3 0.000 0 3 0 0.000 3 0.000 0 3 0 0.000
3 4 1.000 1 4 1 1.000 4 1.000 1 4 1 1.000
4 5 -1.000 -1 5 -1 -1.000 5 -1.000 -1 5 -1 -1.000
5 6 0.000 0 6 0 0.000 6 0.000 0 6 0 0.000
6 7 1.000 1 7 1 1.000 7 1.000 1 7 1 1.000
7 8 -1.000 -1 8 -1 -1.000 8 -1.000 -1 8 -1 -1.000
8 9 0.000 0 9 0 0.000 9 0.000 0 9 0 0.000
9 10 1.000 1 10 1 1.000 10 1.000 1 10 1 1.000
10 11 -1.000 -1 11 -1 -1.000 11 -1.000 -1 11 -1 -1.000
11 12 0.000 0 12 0 0.000 12 0.000 0 12 0 0.000
12 13 1.000 1 13 1 1.000 13 1.000 1 13 1 1.000
13 14 -1.000 -1 14 -1 -1.000 14 -1.000 -1 14 -1 -1.000
14 15 0.000 0 15 0 0.000 15 0.000 0 15 0 0.000
15 16 1.000 1 16 1 1.000 16 1.000 1 16 1 1.000
16 17 -1.000 -1 17 -1 -1.000 17 -1.000 -1 17 -1 -1.000
17 18 0.000 0 18 0 0.000 18 0.000 0 18 0 0.000
18 19 1.000 1 19 1 1.000 19 1.000 1 19 1 1.000
19 20 -1.000 -1 20 -1 -1.000 20 -1.000 -1 20 -1 -1.000
20 21 0.000 0 21 0 0.000 21 0.000 0 21 0 0.000


Decomposition to irreducible representations
Power
To
A B E1* E2* E3* E4* E5*
1 0 0 0 0 0 1 0 E4
2 1 0 0 0 0 1 0 A⊕E4
3 2 0 0 0 0 1 0 2A⊕E4
4 1 0 0 0 0 2 0 A⊕2E4
5 2 0 0 0 0 2 0 2A⊕2E4
6 3 0 0 0 0 2 0 3A⊕2E4
7 2 0 0 0 0 3 0 2A⊕3E4
8 3 0 0 0 0 3 0 3A⊕3E4
9 4 0 0 0 0 3 0 4A⊕3E4
10 3 0 0 0 0 4 0 3A⊕4E4
11 4 0 0 0 0 4 0 4A⊕4E4
12 5 0 0 0 0 4 0 5A⊕4E4
13 4 0 0 0 0 5 0 4A⊕5E4
14 5 0 0 0 0 5 0 5A⊕5E4
15 6 0 0 0 0 5 0 6A⊕5E4
16 5 0 0 0 0 6 0 5A⊕6E4
17 6 0 0 0 0 6 0 6A⊕6E4
18 7 0 0 0 0 6 0 7A⊕6E4
19 6 0 0 0 0 7 0 6A⊕7E4
20 7 0 0 0 0 7 0 7A⊕7E4



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