Results for Point Group C15h



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


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


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