Results for Point Group C15h



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


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


Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement