Results for Point Group C16



Symmetric powers of degenerate representation E7
Vibrational overtones


Characters of symmetric powers
Power
To
E C16 C8 (C16)3 C4 (C16)5 (C8)3 (C16)7 C2 (C16)9 (C8)5 (C16)11 (C4)3 (C16)13 (C8)7 (C16)15
1 2 -1.848 1.414 -0.765 0 0.765 -1.414 1.848 -2 1.848 -1.414 0.765 0 -0.765 1.414 -1.848
2 3 2.414 1.000 -0.414 -1 -0.414 1.000 2.414 3 2.414 1.000 -0.414 -1 -0.414 1.000 2.414
3 4 -2.613 -0.000 1.082 0 -1.082 0.000 2.613 -4 2.613 0.000 -1.082 0 1.082 0.000 -2.613
4 5 2.414 -1.000 -0.414 1 -0.414 -1.000 2.414 5 2.414 -1.000 -0.414 1 -0.414 -1.000 2.414
5 6 -1.848 -1.414 -0.765 0 0.765 1.414 1.848 -6 1.848 1.414 0.765 0 -0.765 -1.414 -1.848
6 7 1.000 -1.000 1.000 -1 1.000 -1.000 1.000 7 1.000 -1.000 1.000 -1 1.000 -1.000 1.000
7 8 0.000 0.000 -0.000 0 0.000 0.000 0.000 -8 -0.000 -0.000 -0.000 0 -0.000 -0.000 -0.000
8 9 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000 9 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000
9 10 1.848 1.414 0.765 0 -0.765 -1.414 -1.848 -10 -1.848 -1.414 -0.765 0 0.765 1.414 1.848
10 11 -2.414 1.000 0.414 -1 0.414 1.000 -2.414 11 -2.414 1.000 0.414 -1 0.414 1.000 -2.414
11 12 2.613 -0.000 -1.082 0 1.082 -0.000 -2.613 -12 -2.613 0.000 1.082 0 -1.082 0.000 2.613
12 13 -2.414 -1.000 0.414 1 0.414 -1.000 -2.414 13 -2.414 -1.000 0.414 1 0.414 -1.000 -2.414
13 14 1.848 -1.414 0.765 0 -0.765 1.414 -1.848 -14 -1.848 1.414 -0.765 0 0.765 -1.414 1.848
14 15 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000 15 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000
15 16 -0.000 0.000 -0.000 0 -0.000 0.000 -0.000 -16 0.000 -0.000 0.000 0 0.000 -0.000 0.000
16 17 1.000 1.000 1.000 1 1.000 1.000 1.000 17 1.000 1.000 1.000 1 1.000 1.000 1.000
17 18 -1.848 1.414 -0.765 0 0.765 -1.414 1.848 -18 1.848 -1.414 0.765 0 -0.765 1.414 -1.848
18 19 2.414 1.000 -0.414 -1 -0.414 1.000 2.414 19 2.414 1.000 -0.414 -1 -0.414 1.000 2.414
19 20 -2.613 -0.000 1.082 0 -1.082 -0.000 2.613 -20 2.613 0.000 -1.082 0 1.082 0.000 -2.613
20 21 2.414 -1.000 -0.414 1 -0.414 -1.000 2.414 21 2.414 -1.000 -0.414 1 -0.414 -1.000 2.414


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



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