Results for Point Group C13



Symmetric powers of degenerate representation E1
Vibrational overtones


Characters of symmetric powers
Power
To		 E C13 (C13)2 (C13)3 (C13)4 (C13)5 (C13)6 (C13)7 (C13)8 (C13)9 (C13)10 (C13)11 (C13)12
1 2 1.771 1.136 0.241 -0.709 -1.497 -1.942 -1.942 -1.497 -0.709 0.241 1.136 1.771
2 3 2.136 0.291 -0.942 -0.497 1.241 2.771 2.771 1.241 -0.497 -0.942 0.291 2.136
3 4 2.012 -0.806 -0.468 1.062 -0.361 -3.439 -3.439 -0.361 1.062 -0.468 -0.806 2.012
4 5 1.427 -1.206 0.829 -0.256 -0.701 3.907 3.907 -0.701 -0.256 0.829 -1.206 1.427
5 6 0.515 -0.565 0.668 -0.880 1.410 -4.148 -4.148 1.410 -0.880 0.668 -0.565 0.515
6 7 -0.515 0.565 -0.668 0.880 -1.410 4.148 4.148 -1.410 0.880 -0.668 0.565 -0.515
7 8 -1.427 1.206 -0.829 0.256 0.701 -3.907 -3.907 0.701 0.256 -0.829 1.206 -1.427
8 9 -2.012 0.806 0.468 -1.062 0.361 3.439 3.439 0.361 -1.062 0.468 0.806 -2.012
9 10 -2.136 -0.291 0.942 0.497 -1.241 -2.771 -2.771 -1.241 0.497 0.942 -0.291 -2.136
10 11 -1.771 -1.136 -0.241 0.709 1.497 1.942 1.942 1.497 0.709 -0.241 -1.136 -1.771
11 12 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000
12 13 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 0.000 0.000 0.000 0.000 0.000 0.000
13 14 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
14 15 1.771 1.136 0.241 -0.709 -1.497 -1.942 -1.942 -1.497 -0.709 0.241 1.136 1.771
15 16 2.136 0.291 -0.942 -0.497 1.241 2.771 2.771 1.241 -0.497 -0.942 0.291 2.136
16 17 2.012 -0.806 -0.468 1.062 -0.361 -3.439 -3.439 -0.361 1.062 -0.468 -0.806 2.012
17 18 1.427 -1.206 0.829 -0.256 -0.701 3.907 3.907 -0.701 -0.256 0.829 -1.206 1.427
18 19 0.515 -0.565 0.668 -0.880 1.410 -4.148 -4.148 1.410 -0.880 0.668 -0.565 0.515
19 20 -0.515 0.565 -0.668 0.880 -1.410 4.148 4.148 -1.410 0.880 -0.668 0.565 -0.515
20 21 -1.427 1.206 -0.829 0.256 0.701 -3.907 -3.907 0.701 0.256 -0.829 1.206 -1.427


Decomposition to irreducible representations
Power
To		 A E1* E2* E3* E4* E5* E6*
1 0 1 0 0 0 0 0 E1
2 1 0 1 0 0 0 0 A⊕E2
3 0 1 0 1 0 0 0 E1⊕E3
4 1 0 1 0 1 0 0 A⊕E2⊕E4
5 0 1 0 1 0 1 0 E1⊕E3⊕E5
6 1 0 1 0 1 0 1 A⊕E2⊕E4⊕E6
7 0 1 0 1 0 1 1 E1⊕E3⊕E5⊕E6
8 1 0 1 0 1 1 1 A⊕E2⊕E4⊕E5⊕E6
9 0 1 0 1 1 1 1 E1⊕E3⊕E4⊕E5⊕E6
10 1 0 1 1 1 1 1 A⊕E2⊕E3⊕E4⊕E5⊕E6
11 0 1 1 1 1 1 1 E1⊕E2⊕E3⊕E4⊕E5⊕E6
12 1 1 1 1 1 1 1 A⊕E1⊕E2⊕E3⊕E4⊕E5⊕E6
13 2 1 1 1 1 1 1 2A⊕E1⊕E2⊕E3⊕E4⊕E5⊕E6
14 1 2 1 1 1 1 1 A⊕2E1⊕E2⊕E3⊕E4⊕E5⊕E6
15 2 1 2 1 1 1 1 2A⊕E1⊕2E2⊕E3⊕E4⊕E5⊕E6
16 1 2 1 2 1 1 1 A⊕2E1⊕E2⊕2E3⊕E4⊕E5⊕E6
17 2 1 2 1 2 1 1 2A⊕E1⊕2E2⊕E3⊕2E4⊕E5⊕E6
18 1 2 1 2 1 2 1 A⊕2E1⊕E2⊕2E3⊕E4⊕2E5⊕E6
19 2 1 2 1 2 1 2 2A⊕E1⊕2E2⊕E3⊕2E4⊕E5⊕2E6
20 1 2 1 2 1 2 2 A⊕2E1⊕E2⊕2E3⊕E4⊕2E5⊕2E6


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