Results for Point Group C15h



Symmetric powers of degenerate representation E'3
Vibrational overtones


Characters of symmetric powers
Power
To
E 2C15 2(C15)2 2C5 2(C15)4 2C3 2(C5)2 2(C15)7 σh 2S15 2(S15)13 2S5 2(S15)11 2S3 2(S5)3 2(S15)7
1 2 0.618 -1.618 -1.618 0.618 2 0.618 -1.618 2 0.618 -1.618 -1.618 0.618 2 0.618 -1.618
2 3 -0.618 1.618 1.618 -0.618 3 -0.618 1.618 3 -0.618 1.618 1.618 -0.618 3 -0.618 1.618
3 4 -1.000 -1.000 -1.000 -1.000 4 -1.000 -1.000 4 -1.000 -1.000 -1.000 -1.000 4 -1.000 -1.000
4 5 -0.000 -0.000 0.000 0.000 5 -0.000 -0.000 5 -0.000 -0.000 0.000 0.000 5 -0.000 -0.000
5 6 1.000 1.000 1.000 1.000 6 1.000 1.000 6 1.000 1.000 1.000 1.000 6 1.000 1.000
6 7 0.618 -1.618 -1.618 0.618 7 0.618 -1.618 7 0.618 -1.618 -1.618 0.618 7 0.618 -1.618
7 8 -0.618 1.618 1.618 -0.618 8 -0.618 1.618 8 -0.618 1.618 1.618 -0.618 8 -0.618 1.618
8 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000
9 10 -0.000 -0.000 0.000 0.000 10 -0.000 -0.000 10 -0.000 -0.000 0.000 0.000 10 -0.000 -0.000
10 11 1.000 1.000 1.000 1.000 11 1.000 1.000 11 1.000 1.000 1.000 1.000 11 1.000 1.000
11 12 0.618 -1.618 -1.618 0.618 12 0.618 -1.618 12 0.618 -1.618 -1.618 0.618 12 0.618 -1.618
12 13 -0.618 1.618 1.618 -0.618 13 -0.618 1.618 13 -0.618 1.618 1.618 -0.618 13 -0.618 1.618
13 14 -1.000 -1.000 -1.000 -1.000 14 -1.000 -1.000 14 -1.000 -1.000 -1.000 -1.000 14 -1.000 -1.000
14 15 -0.000 -0.000 0.000 0.000 15 -0.000 -0.000 15 -0.000 -0.000 0.000 0.000 15 -0.000 -0.000
15 16 1.000 1.000 1.000 1.000 16 1.000 1.000 16 1.000 1.000 1.000 1.000 16 1.000 1.000
16 17 0.618 -1.618 -1.618 0.618 17 0.618 -1.618 17 0.618 -1.618 -1.618 0.618 17 0.618 -1.618
17 18 -0.618 1.618 1.618 -0.618 18 -0.618 1.618 18 -0.618 1.618 1.618 -0.618 18 -0.618 1.618
18 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000
19 20 -0.000 -0.000 0.000 0.000 20 -0.000 -0.000 20 -0.000 -0.000 0.000 0.000 20 -0.000 -0.000
20 21 1.000 1.000 1.000 1.000 21 1.000 1.000 21 1.000 1.000 1.000 1.000 21 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 1 0 0 0 0 0 0 0 0 0 0 0 0 E'3
2 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 A'⊕E'6
3 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 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 2 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 2A'⊕E'3⊕E'6
6 1 0 0 2 0 0 1 0 0 0 0 0 0 0 0 0 A'⊕2E'3⊕E'6
7 2 0 0 1 0 0 2 0 0 0 0 0 0 0 0 0 2A'⊕E'3⊕2E'6
8 1 0 0 2 0 0 2 0 0 0 0 0 0 0 0 0 A'⊕2E'3⊕2E'6
9 2 0 0 2 0 0 2 0 0 0 0 0 0 0 0 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 2 0 0 3 0 0 2 0 0 0 0 0 0 0 0 0 2A'⊕3E'3⊕2E'6
12 3 0 0 2 0 0 3 0 0 0 0 0 0 0 0 0 3A'⊕2E'3⊕3E'6
13 2 0 0 3 0 0 3 0 0 0 0 0 0 0 0 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 4 0 0 3 0 0 3 0 0 0 0 0 0 0 0 0 4A'⊕3E'3⊕3E'6
16 3 0 0 4 0 0 3 0 0 0 0 0 0 0 0 0 3A'⊕4E'3⊕3E'6
17 4 0 0 3 0 0 4 0 0 0 0 0 0 0 0 0 4A'⊕3E'3⊕4E'6
18 3 0 0 4 0 0 4 0 0 0 0 0 0 0 0 0 3A'⊕4E'3⊕4E'6
19 4 0 0 4 0 0 4 0 0 0 0 0 0 0 0 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