Results for Point Group D12d



Symmetric powers of degenerate representation E7
Vibrational overtones


Characters of symmetric powers
Power
To
E 2S24 2C12 2S8 2C6 2(S24)5 2C4 2(S24)7 2C3 2(S8)3 2(C12)5 2(S24)11 C2 12C'2 12σd
1 2 -0.518 -1.732 1.414 1 -1.932 0 1.932 -1 -1.414 1.732 0.518 -2 0 0
2 3 -0.732 2.000 1.000 0 2.732 -1 2.732 0 1.000 2.000 -0.732 3 1 1
3 4 0.897 -1.732 -0.000 -1 -3.346 0 3.346 1 0.000 1.732 -0.897 -4 0 0
4 5 0.268 1.000 -1.000 -1 3.732 1 3.732 -1 -1.000 1.000 0.268 5 1 1
5 6 -1.035 -0.000 -1.414 0 -3.864 0 3.864 0 1.414 -0.000 1.035 -6 0 0
6 7 0.268 -1.000 -1.000 1 3.732 -1 3.732 1 -1.000 -1.000 0.268 7 1 1
7 8 0.897 1.732 0.000 1 -3.346 0 3.346 -1 -0.000 -1.732 -0.897 -8 0 0
8 9 -0.732 -2.000 1.000 0 2.732 1 2.732 0 1.000 -2.000 -0.732 9 1 1
9 10 -0.518 1.732 1.414 -1 -1.932 0 1.932 1 -1.414 -1.732 0.518 -10 0 0
10 11 1.000 -1.000 1.000 -1 1.000 -1 1.000 -1 1.000 -1.000 1.000 11 1 1
11 12 0.000 0.000 -0.000 0 0.000 0 0.000 0 0.000 0.000 0.000 -12 0 0
12 13 -1.000 1.000 -1.000 1 -1.000 1 -1.000 1 -1.000 1.000 -1.000 13 1 1
13 14 0.518 -1.732 -1.414 1 1.932 0 -1.932 -1 1.414 1.732 -0.518 -14 0 0
14 15 0.732 2.000 -1.000 0 -2.732 -1 -2.732 0 -1.000 2.000 0.732 15 1 1
15 16 -0.897 -1.732 0.000 -1 3.346 0 -3.346 1 -0.000 1.732 0.897 -16 0 0
16 17 -0.268 1.000 1.000 -1 -3.732 1 -3.732 -1 1.000 1.000 -0.268 17 1 1
17 18 1.035 -0.000 1.414 0 3.864 0 -3.864 0 -1.414 -0.000 -1.035 -18 0 0
18 19 -0.268 -1.000 1.000 1 -3.732 -1 -3.732 1 1.000 -1.000 -0.268 19 1 1
19 20 -0.897 1.732 -0.000 1 3.346 0 -3.346 -1 0.000 -1.732 0.897 -20 0 0
20 21 0.732 -2.000 -1.000 0 -2.732 1 -2.732 0 -1.000 -2.000 0.732 21 1 1


Decomposition to irreducible representations
Power
To
A1 A2 B1 B2 E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11
1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 E7
2 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 A1⊕E10
3 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 E3⊕E7
4 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 A1⊕E4⊕E10
5 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 E3⊕E7⊕E11
6 1 0 0 0 0 0 0 1 0 1 0 0 0 1 0 A1⊕E4⊕E6⊕E10
7 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 E1⊕E3⊕E7⊕E11
8 1 0 0 0 0 0 0 1 0 1 0 1 0 1 0 A1⊕E4⊕E6⊕E8⊕E10
9 0 0 0 0 1 0 1 0 0 0 1 0 1 0 1 E1⊕E3⊕E7⊕E9⊕E11
10 1 0 0 0 0 1 0 1 0 1 0 1 0 1 0 A1⊕E2⊕E4⊕E6⊕E8⊕E10
11 0 0 0 0 1 0 1 0 1 0 1 0 1 0 1 E1⊕E3⊕E5⊕E7⊕E9⊕E11
12 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 A1⊕B1⊕B2⊕E2⊕E4⊕E6⊕E8⊕E10
13 0 0 0 0 1 0 1 0 2 0 1 0 1 0 1 E1⊕E3⊕2E5⊕E7⊕E9⊕E11
14 1 0 1 1 0 2 0 1 0 1 0 1 0 1 0 A1⊕B1⊕B2⊕2E2⊕E4⊕E6⊕E8⊕E10
15 0 0 0 0 1 0 1 0 2 0 1 0 2 0 1 E1⊕E3⊕2E5⊕E7⊕2E9⊕E11
16 1 0 1 1 0 2 0 1 0 1 0 2 0 1 0 A1⊕B1⊕B2⊕2E2⊕E4⊕E6⊕2E8⊕E10
17 0 0 0 0 2 0 1 0 2 0 1 0 2 0 1 2E1⊕E3⊕2E5⊕E7⊕2E9⊕E11
18 1 0 1 1 0 2 0 1 0 2 0 2 0 1 0 A1⊕B1⊕B2⊕2E2⊕E4⊕2E6⊕2E8⊕E10
19 0 0 0 0 2 0 1 0 2 0 1 0 2 0 2 2E1⊕E3⊕2E5⊕E7⊕2E9⊕2E11
20 1 0 1 1 0 2 0 2 0 2 0 2 0 1 0 A1⊕B1⊕B2⊕2E2⊕2E4⊕2E6⊕2E8⊕E10



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