Results for Point Group C6h



Symmetric powers of degenerate representation E2u
Vibrational overtones


Characters of symmetric powers
Power
To
E C6 C3 C2 (C3)2 (C6)5 i (S3)5 (S6)5 σh S6 S3
1 2 -1 -1 2 -1 -1 -2 1 1 -2 1 1
2 3 0 0 3 0 0 3 0 0 3 0 0
3 4 1 1 4 1 1 -4 -1 -1 -4 -1 -1
4 5 -1 -1 5 -1 -1 5 -1 -1 5 -1 -1
5 6 0 0 6 0 0 -6 0 0 -6 0 0
6 7 1 1 7 1 1 7 1 1 7 1 1
7 8 -1 -1 8 -1 -1 -8 1 1 -8 1 1
8 9 0 0 9 0 0 9 0 0 9 0 0
9 10 1 1 10 1 1 -10 -1 -1 -10 -1 -1
10 11 -1 -1 11 -1 -1 11 -1 -1 11 -1 -1
11 12 0 0 12 0 0 -12 0 0 -12 0 0
12 13 1 1 13 1 1 13 1 1 13 1 1
13 14 -1 -1 14 -1 -1 -14 1 1 -14 1 1
14 15 0 0 15 0 0 15 0 0 15 0 0
15 16 1 1 16 1 1 -16 -1 -1 -16 -1 -1
16 17 -1 -1 17 -1 -1 17 -1 -1 17 -1 -1
17 18 0 0 18 0 0 -18 0 0 -18 0 0
18 19 1 1 19 1 1 19 1 1 19 1 1
19 20 -1 -1 20 -1 -1 -20 1 1 -20 1 1
20 21 0 0 21 0 0 21 0 0 21 0 0


Decomposition to irreducible representations
Power
To
Ag Bg E1g* E2g* Au Bu E1u* E2u*
1 0 0 0 0 0 0 0 1 E2u
2 1 0 0 1 0 0 0 0 Ag⊕E2g
3 0 0 0 0 2 0 0 1 2Au⊕E2u
4 1 0 0 2 0 0 0 0 Ag⊕2E2g
5 0 0 0 0 2 0 0 2 2Au⊕2E2u
6 3 0 0 2 0 0 0 0 3Ag⊕2E2g
7 0 0 0 0 2 0 0 3 2Au⊕3E2u
8 3 0 0 3 0 0 0 0 3Ag⊕3E2g
9 0 0 0 0 4 0 0 3 4Au⊕3E2u
10 3 0 0 4 0 0 0 0 3Ag⊕4E2g
11 0 0 0 0 4 0 0 4 4Au⊕4E2u
12 5 0 0 4 0 0 0 0 5Ag⊕4E2g
13 0 0 0 0 4 0 0 5 4Au⊕5E2u
14 5 0 0 5 0 0 0 0 5Ag⊕5E2g
15 0 0 0 0 6 0 0 5 6Au⊕5E2u
16 5 0 0 6 0 0 0 0 5Ag⊕6E2g
17 0 0 0 0 6 0 0 6 6Au⊕6E2u
18 7 0 0 6 0 0 0 0 7Ag⊕6E2g
19 0 0 0 0 6 0 0 7 6Au⊕7E2u
20 7 0 0 7 0 0 0 0 7Ag⊕7E2g



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