Results for Point Group C15h



Symmetric powers of degenerate representation E''6
Vibrational overtones


Characters of symmetric powers
Power
To
E C15 (C15)2 C5 (C15)4 C3 (C5)2 (C15)7 (C15)8 (C5)3 (C3)2 (C15)11 (C5)4 (C15)13 (C15)14 σh S15 (S15)17 S5 (S15)19 S3 (S5)7 (S15)7 (S15)23 (S5)3 (S3)5 (S15)11 (S5)9 (S15)13 (S15)29
1 2 -1.618 0.618 0.618 -1.618 2 -1.618 0.618 0.618 -1.618 2 -1.618 0.618 0.618 -1.618 -2 1.618 -0.618 -0.618 1.618 -2 1.618 -0.618 -0.618 1.618 -2 1.618 -0.618 -0.618 1.618
2 3 1.618 -0.618 -0.618 1.618 3 1.618 -0.618 -0.618 1.618 3 1.618 -0.618 -0.618 1.618 3 1.618 -0.618 -0.618 1.618 3 1.618 -0.618 -0.618 1.618 3 1.618 -0.618 -0.618 1.618
3 4 -1.000 -1.000 -1.000 -1.000 4 -1.000 -1.000 -1.000 -1.000 4 -1.000 -1.000 -1.000 -1.000 -4 1.000 1.000 1.000 1.000 -4 1.000 1.000 1.000 1.000 -4 1.000 1.000 1.000 1.000
4 5 -0.000 0.000 -0.000 0.000 5 -0.000 0.000 -0.000 0.000 5 -0.000 0.000 -0.000 0.000 5 -0.000 0.000 -0.000 0.000 5 -0.000 0.000 -0.000 0.000 5 -0.000 0.000 -0.000 0.000
5 6 1.000 1.000 1.000 1.000 6 1.000 1.000 1.000 1.000 6 1.000 1.000 1.000 1.000 -6 -1.000 -1.000 -1.000 -1.000 -6 -1.000 -1.000 -1.000 -1.000 -6 -1.000 -1.000 -1.000 -1.000
6 7 -1.618 0.618 0.618 -1.618 7 -1.618 0.618 0.618 -1.618 7 -1.618 0.618 0.618 -1.618 7 -1.618 0.618 0.618 -1.618 7 -1.618 0.618 0.618 -1.618 7 -1.618 0.618 0.618 -1.618
7 8 1.618 -0.618 -0.618 1.618 8 1.618 -0.618 -0.618 1.618 8 1.618 -0.618 -0.618 1.618 -8 -1.618 0.618 0.618 -1.618 -8 -1.618 0.618 0.618 -1.618 -8 -1.618 0.618 0.618 -1.618
8 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000
9 10 -0.000 0.000 -0.000 0.000 10 -0.000 0.000 -0.000 0.000 10 -0.000 0.000 -0.000 0.000 -10 0.000 -0.000 0.000 -0.000 -10 0.000 -0.000 0.000 -0.000 -10 0.000 -0.000 0.000 -0.000
10 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000
11 12 -1.618 0.618 0.618 -1.618 12 -1.618 0.618 0.618 -1.618 12 -1.618 0.618 0.618 -1.618 -12 1.618 -0.618 -0.618 1.618 -12 1.618 -0.618 -0.618 1.618 -12 1.618 -0.618 -0.618 1.618
12 13 1.618 -0.618 -0.618 1.618 13 1.618 -0.618 -0.618 1.618 13 1.618 -0.618 -0.618 1.618 13 1.618 -0.618 -0.618 1.618 13 1.618 -0.618 -0.618 1.618 13 1.618 -0.618 -0.618 1.618
13 14 -1.000 -1.000 -1.000 -1.000 14 -1.000 -1.000 -1.000 -1.000 14 -1.000 -1.000 -1.000 -1.000 -14 1.000 1.000 1.000 1.000 -14 1.000 1.000 1.000 1.000 -14 1.000 1.000 1.000 1.000
14 15 -0.000 0.000 -0.000 0.000 15 -0.000 0.000 -0.000 0.000 15 -0.000 0.000 -0.000 0.000 15 -0.000 0.000 -0.000 0.000 15 -0.000 0.000 -0.000 0.000 15 -0.000 0.000 -0.000 0.000
15 16 1.000 1.000 1.000 1.000 16 1.000 1.000 1.000 1.000 16 1.000 1.000 1.000 1.000 -16 -1.000 -1.000 -1.000 -1.000 -16 -1.000 -1.000 -1.000 -1.000 -16 -1.000 -1.000 -1.000 -1.000
16 17 -1.618 0.618 0.618 -1.618 17 -1.618 0.618 0.618 -1.618 17 -1.618 0.618 0.618 -1.618 17 -1.618 0.618 0.618 -1.618 17 -1.618 0.618 0.618 -1.618 17 -1.618 0.618 0.618 -1.618
17 18 1.618 -0.618 -0.618 1.618 18 1.618 -0.618 -0.618 1.618 18 1.618 -0.618 -0.618 1.618 -18 -1.618 0.618 0.618 -1.618 -18 -1.618 0.618 0.618 -1.618 -18 -1.618 0.618 0.618 -1.618
18 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000
19 20 -0.000 0.000 -0.000 0.000 20 -0.000 0.000 -0.000 0.000 20 -0.000 0.000 -0.000 0.000 -20 0.000 -0.000 0.000 -0.000 -20 0.000 -0.000 0.000 -0.000 -20 0.000 -0.000 0.000 -0.000
20 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000


Decomposition to irreducible representations
Power
To
A' E'1* E'2* E'3* E'4* E'5* E'6* E'7* A'' E''1* E''2* E''3* E''4* E''5* E''6* E''7*
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 E''6
2 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'3
3 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 E''3⊕E''6
4 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 A'⊕E'3⊕E'6
5 0 0 0 0 0 0 0 0 2 0 0 1 0 0 1 0 2A''⊕E''3⊕E''6
6 1 0 0 1 0 0 2 0 0 0 0 0 0 0 0 0 A'⊕E'3⊕2E'6
7 0 0 0 0 0 0 0 0 2 0 0 2 0 0 1 0 2A''⊕2E''3⊕E''6
8 1 0 0 2 0 0 2 0 0 0 0 0 0 0 0 0 A'⊕2E'3⊕2E'6
9 0 0 0 0 0 0 0 0 2 0 0 2 0 0 2 0 2A''⊕2E''3⊕2E''6
10 3 0 0 2 0 0 2 0 0 0 0 0 0 0 0 0 3A'⊕2E'3⊕2E'6
11 0 0 0 0 0 0 0 0 2 0 0 2 0 0 3 0 2A''⊕2E''3⊕3E''6
12 3 0 0 3 0 0 2 0 0 0 0 0 0 0 0 0 3A'⊕3E'3⊕2E'6
13 0 0 0 0 0 0 0 0 2 0 0 3 0 0 3 0 2A''⊕3E''3⊕3E''6
14 3 0 0 3 0 0 3 0 0 0 0 0 0 0 0 0 3A'⊕3E'3⊕3E'6
15 0 0 0 0 0 0 0 0 4 0 0 3 0 0 3 0 4A''⊕3E''3⊕3E''6
16 3 0 0 3 0 0 4 0 0 0 0 0 0 0 0 0 3A'⊕3E'3⊕4E'6
17 0 0 0 0 0 0 0 0 4 0 0 4 0 0 3 0 4A''⊕4E''3⊕3E''6
18 3 0 0 4 0 0 4 0 0 0 0 0 0 0 0 0 3A'⊕4E'3⊕4E'6
19 0 0 0 0 0 0 0 0 4 0 0 4 0 0 4 0 4A''⊕4E''3⊕4E''6
20 5 0 0 4 0 0 4 0 0 0 0 0 0 0 0 0 5A'⊕4E'3⊕4E'6



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