Results for Point Group C12



Symmetric powers of degenerate representation E5
Vibrational overtones


Characters of symmetric powers
Power
To
E C12 C6 C4 C3 (C12)5 C2 (C12)7 (C3)2 (C4)3 (C6)5 (C12)11
1 2 -1.732 1 0 -1 1.732 -2 1.732 -1 0 1 -1.732
2 3 2.000 0 -1 0 2.000 3 2.000 0 -1 0 2.000
3 4 -1.732 -1 0 1 1.732 -4 1.732 1 0 -1 -1.732
4 5 1.000 -1 1 -1 1.000 5 1.000 -1 1 -1 1.000
5 6 -0.000 0 0 0 -0.000 -6 0.000 0 0 0 0.000
6 7 -1.000 1 -1 1 -1.000 7 -1.000 1 -1 1 -1.000
7 8 1.732 1 0 -1 -1.732 -8 -1.732 -1 0 1 1.732
8 9 -2.000 0 1 0 -2.000 9 -2.000 0 1 0 -2.000
9 10 1.732 -1 0 1 -1.732 -10 -1.732 1 0 -1 1.732
10 11 -1.000 -1 -1 -1 -1.000 11 -1.000 -1 -1 -1 -1.000
11 12 0.000 0 0 0 0.000 -12 -0.000 0 0 0 -0.000
12 13 1.000 1 1 1 1.000 13 1.000 1 1 1 1.000
13 14 -1.732 1 0 -1 1.732 -14 1.732 -1 0 1 -1.732
14 15 2.000 0 -1 0 2.000 15 2.000 0 -1 0 2.000
15 16 -1.732 -1 0 1 1.732 -16 1.732 1 0 -1 -1.732
16 17 1.000 -1 1 -1 1.000 17 1.000 -1 1 -1 1.000
17 18 -0.000 0 0 0 -0.000 -18 0.000 0 0 0 0.000
18 19 -1.000 1 -1 1 -1.000 19 -1.000 1 -1 1 -1.000
19 20 1.732 1 0 -1 -1.732 -20 -1.732 -1 0 1 1.732
20 21 -2.000 0 1 0 -2.000 21 -2.000 0 1 0 -2.000


Decomposition to irreducible representations
Power
To
A B E1* E2* E3* E4* E5*
1 0 0 0 0 0 0 1 E5
2 1 0 0 1 0 0 0 A⊕E2
3 0 0 0 0 1 0 1 E3⊕E5
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 2 0 1 0 1 2E1⊕E3⊕E5
8 1 2 0 1 0 2 0 A⊕2B⊕E2⊕2E4
9 0 0 2 0 2 0 1 2E1⊕2E3⊕E5
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 2 0 2 0 3 2E1⊕2E3⊕3E5
14 3 2 0 3 0 2 0 3A⊕2B⊕3E2⊕2E4
15 0 0 2 0 3 0 3 2E1⊕3E3⊕3E5
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 4 0 3 0 3 4E1⊕3E3⊕3E5
20 3 4 0 3 0 4 0 3A⊕4B⊕3E2⊕4E4



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