Results for Point Group D12



Symmetric powers of degenerate representation E3
Vibrational overtones


Characters of symmetric powers
Power
To		 E 2C12 2C6 2C4 2C3 2(C12)5 C2 6C'2 6C''2
1 2 0.000 -2 0 2 0.000 -2 0 0
2 3 -1.000 3 -1 3 -1.000 3 1 1
3 4 0.000 -4 0 4 0.000 -4 0 0
4 5 1.000 5 1 5 1.000 5 1 1
5 6 0.000 -6 0 6 0.000 -6 0 0
6 7 -1.000 7 -1 7 -1.000 7 1 1
7 8 0.000 -8 0 8 0.000 -8 0 0
8 9 1.000 9 1 9 1.000 9 1 1
9 10 0.000 -10 0 10 0.000 -10 0 0
10 11 -1.000 11 -1 11 -1.000 11 1 1
11 12 0.000 -12 0 12 0.000 -12 0 0
12 13 1.000 13 1 13 1.000 13 1 1
13 14 0.000 -14 0 14 0.000 -14 0 0
14 15 -1.000 15 -1 15 -1.000 15 1 1
15 16 0.000 -16 0 16 0.000 -16 0 0
16 17 1.000 17 1 17 1.000 17 1 1
17 18 0.000 -18 0 18 0.000 -18 0 0
18 19 -1.000 19 -1 19 -1.000 19 1 1
19 20 0.000 -20 0 20 0.000 -20 0 0
20 21 1.000 21 1 21 1.000 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 1 0 0 E3
2 1 0 1 1 0 0 0 0 0 A1⊕B1⊕B2
3 0 0 0 0 0 0 2 0 0 2E3
4 2 1 1 1 0 0 0 0 0 2A1⊕A2⊕B1⊕B2
5 0 0 0 0 0 0 3 0 0 3E3
6 2 1 2 2 0 0 0 0 0 2A1⊕A2⊕2B1⊕2B2
7 0 0 0 0 0 0 4 0 0 4E3
8 3 2 2 2 0 0 0 0 0 3A1⊕2A2⊕2B1⊕2B2
9 0 0 0 0 0 0 5 0 0 5E3
10 3 2 3 3 0 0 0 0 0 3A1⊕2A2⊕3B1⊕3B2
11 0 0 0 0 0 0 6 0 0 6E3
12 4 3 3 3 0 0 0 0 0 4A1⊕3A2⊕3B1⊕3B2
13 0 0 0 0 0 0 7 0 0 7E3
14 4 3 4 4 0 0 0 0 0 4A1⊕3A2⊕4B1⊕4B2
15 0 0 0 0 0 0 8 0 0 8E3
16 5 4 4 4 0 0 0 0 0 5A1⊕4A2⊕4B1⊕4B2
17 0 0 0 0 0 0 9 0 0 9E3
18 5 4 5 5 0 0 0 0 0 5A1⊕4A2⊕5B1⊕5B2
19 0 0 0 0 0 0 10 0 0 10E3
20 6 5 5 5 0 0 0 0 0 6A1⊕5A2⊕5B1⊕5B2


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