Results for Point Group C11h



Symmetric powers of degenerate representation E'1
Vibrational overtones


Characters of symmetric powers
Power
To		 E C11 (C11)2 (C11)3 (C11)4 (C11)5 (C11)6 (C11)7 (C11)8 (C11)9 (C11)10 σh S11 (S11)13 (S11)3 (S11)15 (S11)5 (S11)17 (S11)7 (S11)19 (S11)9 (S11)21
1 2 1.683 0.831 -0.285 -1.310 -1.919 -1.919 -1.310 -0.285 0.831 1.683 2 1.683 0.831 -0.285 -1.310 -1.919 -1.919 -1.310 -0.285 0.831 1.683
2 3 1.831 -0.310 -0.919 0.715 2.683 2.683 0.715 -0.919 -0.310 1.831 3 1.831 -0.310 -0.919 0.715 2.683 2.683 0.715 -0.919 -0.310 1.831
3 4 1.398 -1.088 0.546 0.373 -3.229 -3.229 0.373 0.546 -1.088 1.398 4 1.398 -1.088 0.546 0.373 -3.229 -3.229 0.373 0.546 -1.088 1.398
4 5 0.521 -0.594 0.764 -1.204 3.513 3.513 -1.204 0.764 -0.594 0.521 5 0.521 -0.594 0.764 -1.204 3.513 3.513 -1.204 0.764 -0.594 0.521
5 6 -0.521 0.594 -0.764 1.204 -3.513 -3.513 1.204 -0.764 0.594 -0.521 6 -0.521 0.594 -0.764 1.204 -3.513 -3.513 1.204 -0.764 0.594 -0.521
6 7 -1.398 1.088 -0.546 -0.373 3.229 3.229 -0.373 -0.546 1.088 -1.398 7 -1.398 1.088 -0.546 -0.373 3.229 3.229 -0.373 -0.546 1.088 -1.398
7 8 -1.831 0.310 0.919 -0.715 -2.683 -2.683 -0.715 0.919 0.310 -1.831 8 -1.831 0.310 0.919 -0.715 -2.683 -2.683 -0.715 0.919 0.310 -1.831
8 9 -1.683 -0.831 0.285 1.310 1.919 1.919 1.310 0.285 -0.831 -1.683 9 -1.683 -0.831 0.285 1.310 1.919 1.919 1.310 0.285 -0.831 -1.683
9 10 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 10 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000
10 11 -0.000 -0.000 -0.000 -0.000 -0.000 0.000 0.000 0.000 0.000 0.000 11 -0.000 -0.000 -0.000 -0.000 -0.000 0.000 0.000 0.000 0.000 0.000
11 12 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 12 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
12 13 1.683 0.831 -0.285 -1.310 -1.919 -1.919 -1.310 -0.285 0.831 1.683 13 1.683 0.831 -0.285 -1.310 -1.919 -1.919 -1.310 -0.285 0.831 1.683
13 14 1.831 -0.310 -0.919 0.715 2.683 2.683 0.715 -0.919 -0.310 1.831 14 1.831 -0.310 -0.919 0.715 2.683 2.683 0.715 -0.919 -0.310 1.831
14 15 1.398 -1.088 0.546 0.373 -3.229 -3.229 0.373 0.546 -1.088 1.398 15 1.398 -1.088 0.546 0.373 -3.229 -3.229 0.373 0.546 -1.088 1.398
15 16 0.521 -0.594 0.764 -1.204 3.513 3.513 -1.204 0.764 -0.594 0.521 16 0.521 -0.594 0.764 -1.204 3.513 3.513 -1.204 0.764 -0.594 0.521
16 17 -0.521 0.594 -0.764 1.204 -3.513 -3.513 1.204 -0.764 0.594 -0.521 17 -0.521 0.594 -0.764 1.204 -3.513 -3.513 1.204 -0.764 0.594 -0.521
17 18 -1.398 1.088 -0.546 -0.373 3.229 3.229 -0.373 -0.546 1.088 -1.398 18 -1.398 1.088 -0.546 -0.373 3.229 3.229 -0.373 -0.546 1.088 -1.398
18 19 -1.831 0.310 0.919 -0.715 -2.683 -2.683 -0.715 0.919 0.310 -1.831 19 -1.831 0.310 0.919 -0.715 -2.683 -2.683 -0.715 0.919 0.310 -1.831
19 20 -1.683 -0.831 0.285 1.310 1.919 1.919 1.310 0.285 -0.831 -1.683 20 -1.683 -0.831 0.285 1.310 1.919 1.919 1.310 0.285 -0.831 -1.683
20 21 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 21 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000


Decomposition to irreducible representations
Power
To		 A' E'1* E'2* E'3* E'4* E'5* A'' E''1* E''2* E''3* E''4* E''5*
1 0 1 0 0 0 0 0 0 0 0 0 0 E'1
2 1 0 1 0 0 0 0 0 0 0 0 0 A'⊕E'2
3 0 1 0 1 0 0 0 0 0 0 0 0 E'1⊕E'3
4 1 0 1 0 1 0 0 0 0 0 0 0 A'⊕E'2⊕E'4
5 0 1 0 1 0 1 0 0 0 0 0 0 E'1⊕E'3⊕E'5
6 1 0 1 0 1 1 0 0 0 0 0 0 A'⊕E'2⊕E'4⊕E'5
7 0 1 0 1 1 1 0 0 0 0 0 0 E'1⊕E'3⊕E'4⊕E'5
8 1 0 1 1 1 1 0 0 0 0 0 0 A'⊕E'2⊕E'3⊕E'4⊕E'5
9 0 1 1 1 1 1 0 0 0 0 0 0 E'1⊕E'2⊕E'3⊕E'4⊕E'5
10 1 1 1 1 1 1 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5
11 2 1 1 1 1 1 0 0 0 0 0 0 2A'⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5
12 1 2 1 1 1 1 0 0 0 0 0 0 A'⊕2E'1⊕E'2⊕E'3⊕E'4⊕E'5
13 2 1 2 1 1 1 0 0 0 0 0 0 2A'⊕E'1⊕2E'2⊕E'3⊕E'4⊕E'5
14 1 2 1 2 1 1 0 0 0 0 0 0 A'⊕2E'1⊕E'2⊕2E'3⊕E'4⊕E'5
15 2 1 2 1 2 1 0 0 0 0 0 0 2A'⊕E'1⊕2E'2⊕E'3⊕2E'4⊕E'5
16 1 2 1 2 1 2 0 0 0 0 0 0 A'⊕2E'1⊕E'2⊕2E'3⊕E'4⊕2E'5
17 2 1 2 1 2 2 0 0 0 0 0 0 2A'⊕E'1⊕2E'2⊕E'3⊕2E'4⊕2E'5
18 1 2 1 2 2 2 0 0 0 0 0 0 A'⊕2E'1⊕E'2⊕2E'3⊕2E'4⊕2E'5
19 2 1 2 2 2 2 0 0 0 0 0 0 2A'⊕E'1⊕2E'2⊕2E'3⊕2E'4⊕2E'5
20 1 2 2 2 2 2 0 0 0 0 0 0 A'⊕2E'1⊕2E'2⊕2E'3⊕2E'4⊕2E'5


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