Results for Point Group D12



Symmetric powers of degenerate representation E2
Vibrational overtones


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


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


Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement