Results for Point Group C15h



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



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