Results for Point Group C15h



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


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 1 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 0 0 0 0 0 0 0 0 1 0 0 0 1 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 0 0 0 0 0 0 0 0 1 0 0 1 1 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 0 0 0 0 0 0 0 0 1 1 0 0 1 1 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 0 0 0 0 0 0 0 0 1 1 1 0 1 1 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 0 0 0 0 0 0 0 0 1 1 1 0 1 1 1 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 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 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 0 0 0 0 0 0 0 0 2 1 1 1 2 1 1 1 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 0 0 0 0 0 0 0 0 2 1 1 1 2 1 1 2 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 November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement