Results for Point Group C18



Symmetric powers of degenerate representation E5
Vibrational overtones


Characters of symmetric powers
Power
To
E C18 C9 C6 (C9)2 (C18)5 C3 (C18)7 (C9)4 C2 (C9)5 (C18)11 (C3)2 (C18)13 (C9)7 (C6)5 (C9)8 (C18)17
1 2 -0.347 -1.879 1 1.532 -1.532 -1 1.879 0.347 -2 0.347 1.879 -1 -1.532 1.532 1 -1.879 -0.347
2 3 -0.879 2.532 0 1.347 1.347 0 2.532 -0.879 3 -0.879 2.532 0 1.347 1.347 0 2.532 -0.879
3 4 0.653 -2.879 -1 0.532 -0.532 1 2.879 -0.653 -4 -0.653 2.879 1 -0.532 0.532 -1 -2.879 0.653
4 5 0.653 2.879 -1 -0.532 -0.532 -1 2.879 0.653 5 0.653 2.879 -1 -0.532 -0.532 -1 2.879 0.653
5 6 -0.879 -2.532 0 -1.347 1.347 0 2.532 0.879 -6 0.879 2.532 0 1.347 -1.347 0 -2.532 -0.879
6 7 -0.347 1.879 1 -1.532 -1.532 1 1.879 -0.347 7 -0.347 1.879 1 -1.532 -1.532 1 1.879 -0.347
7 8 1.000 -1.000 1 -1.000 1.000 -1 1.000 -1.000 -8 -1.000 1.000 -1 1.000 -1.000 1 -1.000 1.000
8 9 0.000 -0.000 0 -0.000 -0.000 0 0.000 -0.000 9 -0.000 0.000 0 -0.000 -0.000 0 0.000 0.000
9 10 -1.000 1.000 -1 1.000 -1.000 1 -1.000 1.000 -10 1.000 -1.000 1 -1.000 1.000 -1 1.000 -1.000
10 11 0.347 -1.879 -1 1.532 1.532 -1 -1.879 0.347 11 0.347 -1.879 -1 1.532 1.532 -1 -1.879 0.347
11 12 0.879 2.532 0 1.347 -1.347 0 -2.532 -0.879 -12 -0.879 -2.532 0 -1.347 1.347 0 2.532 0.879
12 13 -0.653 -2.879 1 0.532 0.532 1 -2.879 -0.653 13 -0.653 -2.879 1 0.532 0.532 1 -2.879 -0.653
13 14 -0.653 2.879 1 -0.532 0.532 -1 -2.879 0.653 -14 0.653 -2.879 -1 0.532 -0.532 1 2.879 -0.653
14 15 0.879 -2.532 0 -1.347 -1.347 0 -2.532 0.879 15 0.879 -2.532 0 -1.347 -1.347 0 -2.532 0.879
15 16 0.347 1.879 -1 -1.532 1.532 1 -1.879 -0.347 -16 -0.347 -1.879 1 1.532 -1.532 -1 1.879 0.347
16 17 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000 17 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000
17 18 -0.000 -0.000 0 -0.000 0.000 0 -0.000 -0.000 -18 -0.000 -0.000 0 0.000 -0.000 0 0.000 -0.000
18 19 1.000 1.000 1 1.000 1.000 1 1.000 1.000 19 1.000 1.000 1 1.000 1.000 1 1.000 1.000
19 20 -0.347 -1.879 1 1.532 -1.532 -1 1.879 0.347 -20 0.347 1.879 -1 -1.532 1.532 1 -1.879 -0.347
20 21 -0.879 2.532 0 1.347 1.347 0 2.532 -0.879 21 -0.879 2.532 0 1.347 1.347 0 2.532 -0.879


Decomposition to irreducible representations
Power
To
A B E1* E2* E3* E4* E5* E6* E7* E8*
1 0 0 0 0 0 0 1 0 0 0 E5
2 1 0 0 0 0 0 0 0 0 1 A⊕E8
3 0 0 0 0 1 0 1 0 0 0 E3⊕E5
4 1 0 0 1 0 0 0 0 0 1 A⊕E2⊕E8
5 0 0 0 0 1 0 1 0 1 0 E3⊕E5⊕E7
6 1 0 0 1 0 0 0 1 0 1 A⊕E2⊕E6⊕E8
7 0 0 1 0 1 0 1 0 1 0 E1⊕E3⊕E5⊕E7
8 1 0 0 1 0 1 0 1 0 1 A⊕E2⊕E4⊕E6⊕E8
9 0 2 1 0 1 0 1 0 1 0 2B⊕E1⊕E3⊕E5⊕E7
10 1 0 0 1 0 2 0 1 0 1 A⊕E2⊕2E4⊕E6⊕E8
11 0 2 2 0 1 0 1 0 1 0 2B⊕2E1⊕E3⊕E5⊕E7
12 1 0 0 1 0 2 0 2 0 1 A⊕E2⊕2E4⊕2E6⊕E8
13 0 2 2 0 1 0 1 0 2 0 2B⊕2E1⊕E3⊕E5⊕2E7
14 1 0 0 2 0 2 0 2 0 1 A⊕2E2⊕2E4⊕2E6⊕E8
15 0 2 2 0 2 0 1 0 2 0 2B⊕2E1⊕2E3⊕E5⊕2E7
16 1 0 0 2 0 2 0 2 0 2 A⊕2E2⊕2E4⊕2E6⊕2E8
17 0 2 2 0 2 0 2 0 2 0 2B⊕2E1⊕2E3⊕2E5⊕2E7
18 3 0 0 2 0 2 0 2 0 2 3A⊕2E2⊕2E4⊕2E6⊕2E8
19 0 2 2 0 2 0 3 0 2 0 2B⊕2E1⊕2E3⊕3E5⊕2E7
20 3 0 0 2 0 2 0 2 0 3 3A⊕2E2⊕2E4⊕2E6⊕3E8



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