Results for Point Group D12



Symmetric powers of degenerate representation E5
Vibrational overtones


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


Decomposition to irreducible representations
Power
To
A1 A2 B1 B2 E1 E2 E3 E4 E5
1 0 0 0 0 0 0 0 0 1 E5
2 1 0 0 0 0 1 0 0 0 A1⊕E2
3 0 0 0 0 0 0 1 0 1 E3⊕E5
4 1 0 0 0 0 1 0 1 0 A1⊕E2⊕E4
5 0 0 0 0 1 0 1 0 1 E1⊕E3⊕E5
6 1 0 1 1 0 1 0 1 0 A1⊕B1⊕B2⊕E2⊕E4
7 0 0 0 0 2 0 1 0 1 2E1⊕E3⊕E5
8 1 0 1 1 0 1 0 2 0 A1⊕B1⊕B2⊕E2⊕2E4
9 0 0 0 0 2 0 2 0 1 2E1⊕2E3⊕E5
10 1 0 1 1 0 2 0 2 0 A1⊕B1⊕B2⊕2E2⊕2E4
11 0 0 0 0 2 0 2 0 2 2E1⊕2E3⊕2E5
12 2 1 1 1 0 2 0 2 0 2A1⊕A2⊕B1⊕B2⊕2E2⊕2E4
13 0 0 0 0 2 0 2 0 3 2E1⊕2E3⊕3E5
14 2 1 1 1 0 3 0 2 0 2A1⊕A2⊕B1⊕B2⊕3E2⊕2E4
15 0 0 0 0 2 0 3 0 3 2E1⊕3E3⊕3E5
16 2 1 1 1 0 3 0 3 0 2A1⊕A2⊕B1⊕B2⊕3E2⊕3E4
17 0 0 0 0 3 0 3 0 3 3E1⊕3E3⊕3E5
18 2 1 2 2 0 3 0 3 0 2A1⊕A2⊕2B1⊕2B2⊕3E2⊕3E4
19 0 0 0 0 4 0 3 0 3 4E1⊕3E3⊕3E5
20 2 1 2 2 0 3 0 4 0 2A1⊕A2⊕2B1⊕2B2⊕3E2⊕4E4



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