Results for Point Group S12



Symmetric powers of degenerate representation E1
Vibrational overtones


Characters of symmetric powers
Power
To
E 2S12 2C6 2S4 2C3 2(S12)5 C2
1 2 1.732 1 0 -1 -1.732 -2
2 3 2.000 0 -1 0 2.000 3
3 4 1.732 -1 0 1 -1.732 -4
4 5 1.000 -1 1 -1 1.000 5
5 6 0.000 0 0 0 0.000 -6
6 7 -1.000 1 -1 1 -1.000 7
7 8 -1.732 1 0 -1 1.732 -8
8 9 -2.000 0 1 0 -2.000 9
9 10 -1.732 -1 0 1 1.732 -10
10 11 -1.000 -1 -1 -1 -1.000 11
11 12 -0.000 0 0 0 -0.000 -12
12 13 1.000 1 1 1 1.000 13
13 14 1.732 1 0 -1 -1.732 -14
14 15 2.000 0 -1 0 2.000 15
15 16 1.732 -1 0 1 -1.732 -16
16 17 1.000 -1 1 -1 1.000 17
17 18 0.000 0 0 0 0.000 -18
18 19 -1.000 1 -1 1 -1.000 19
19 20 -1.732 1 0 -1 1.732 -20
20 21 -2.000 0 1 0 -2.000 21


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



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