Results for Point Group C15h



Symmetric powers of degenerate representation E'2
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 1.338 -0.209 -1.618 -1.956 -1 0.618 1.827 2 1.338 -0.209 -1.618 -1.956 -1 0.618 1.827
2 3 0.791 -0.956 1.618 2.827 0 -0.618 2.338 3 0.791 -0.956 1.618 2.827 0 -0.618 2.338
3 4 -0.280 0.409 -1.000 -3.574 1 -1.000 2.445 4 -0.280 0.409 -1.000 -3.574 1 -1.000 2.445
4 5 -1.165 0.871 -0.000 4.165 -1 0.000 2.129 5 -1.165 0.871 -0.000 4.165 -1 0.000 2.129
5 6 -1.280 -0.591 1.000 -4.574 0 1.000 1.445 6 -1.280 -0.591 1.000 -4.574 0 1.000 1.445
6 7 -0.547 -0.747 -1.618 4.783 1 0.618 0.511 7 -0.547 -0.747 -1.618 4.783 1 0.618 0.511
7 8 0.547 0.747 1.618 -4.783 -1 -0.618 -0.511 8 0.547 0.747 1.618 -4.783 -1 -0.618 -0.511
8 9 1.280 0.591 -1.000 4.574 0 -1.000 -1.445 9 1.280 0.591 -1.000 4.574 0 -1.000 -1.445
9 10 1.165 -0.871 -0.000 -4.165 1 0.000 -2.129 10 1.165 -0.871 -0.000 -4.165 1 0.000 -2.129
10 11 0.280 -0.409 1.000 3.574 -1 1.000 -2.445 11 0.280 -0.409 1.000 3.574 -1 1.000 -2.445
11 12 -0.791 0.956 -1.618 -2.827 0 0.618 -2.338 12 -0.791 0.956 -1.618 -2.827 0 0.618 -2.338
12 13 -1.338 0.209 1.618 1.956 1 -0.618 -1.827 13 -1.338 0.209 1.618 1.956 1 -0.618 -1.827
13 14 -1.000 -1.000 -1.000 -1.000 -1 -1.000 -1.000 14 -1.000 -1.000 -1.000 -1.000 -1 -1.000 -1.000
14 15 -0.000 -0.000 -0.000 0.000 0 0.000 -0.000 15 -0.000 -0.000 -0.000 0.000 0 0.000 0.000
15 16 1.000 1.000 1.000 1.000 1 1.000 1.000 16 1.000 1.000 1.000 1.000 1 1.000 1.000
16 17 1.338 -0.209 -1.618 -1.956 -1 0.618 1.827 17 1.338 -0.209 -1.618 -1.956 -1 0.618 1.827
17 18 0.791 -0.956 1.618 2.827 0 -0.618 2.338 18 0.791 -0.956 1.618 2.827 0 -0.618 2.338
18 19 -0.280 0.409 -1.000 -3.574 1 -1.000 2.445 19 -0.280 0.409 -1.000 -3.574 1 -1.000 2.445
19 20 -1.165 0.871 -0.000 4.165 -1 0.000 2.129 20 -1.165 0.871 -0.000 4.165 -1 0.000 2.129
20 21 -1.280 -0.591 1.000 -4.574 0 1.000 1.445 21 -1.280 -0.591 1.000 -4.574 0 1.000 1.445


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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 E'2
2 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'4
3 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 E'2⊕E'6
4 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 A'⊕E'4⊕E'7
5 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 E'2⊕E'5⊕E'6
6 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 A'⊕E'3⊕E'4⊕E'7
7 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 E'1⊕E'2⊕E'5⊕E'6
8 1 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'3⊕E'4⊕E'7
9 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 E'1⊕E'2⊕E'3⊕E'5⊕E'6
10 1 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'3⊕E'4⊕E'5⊕E'7
11 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 E'1⊕E'2⊕E'3⊕E'5⊕E'6⊕E'7
12 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'3⊕E'4⊕E'5⊕E'6⊕E'7
13 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6⊕E'7
14 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6⊕E'7
15 2 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 2A'⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6⊕E'7
16 1 1 2 1 1 1 1 1 0 0 0 0 0 0 0 0 A'⊕E'1⊕2E'2⊕E'3⊕E'4⊕E'5⊕E'6⊕E'7
17 2 1 1 1 2 1 1 1 0 0 0 0 0 0 0 0 2A'⊕E'1⊕E'2⊕E'3⊕2E'4⊕E'5⊕E'6⊕E'7
18 1 1 2 1 1 1 2 1 0 0 0 0 0 0 0 0 A'⊕E'1⊕2E'2⊕E'3⊕E'4⊕E'5⊕2E'6⊕E'7
19 2 1 1 1 2 1 1 2 0 0 0 0 0 0 0 0 2A'⊕E'1⊕E'2⊕E'3⊕2E'4⊕E'5⊕E'6⊕2E'7
20 1 1 2 1 1 2 2 1 0 0 0 0 0 0 0 0 A'⊕E'1⊕2E'2⊕E'3⊕E'4⊕2E'5⊕2E'6⊕E'7



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