Results for Point Group C17



Symmetric powers of degenerate representation E1
Vibrational overtones


Characters of symmetric powers
Power
To
E C17 (C17)2 (C17)3 (C17)4 (C17)5 (C17)6 (C17)7 (C17)8 (C17)9 (C17)10 (C17)11 (C17)12 (C17)13 (C17)14 (C17)15 (C17)16
1 2 1.865 1.478 0.891 0.185 -0.547 -1.205 -1.700 -1.966 -1.966 -1.700 -1.205 -0.547 0.185 0.891 1.478 1.865
2 3 2.478 1.185 -0.205 -0.966 -0.700 0.453 1.891 2.865 2.865 1.891 0.453 -0.700 -0.966 -0.205 1.185 2.478
3 4 2.756 0.273 -1.074 -0.363 0.931 0.660 -1.516 -3.666 -3.666 -1.516 0.660 0.931 -0.363 -1.074 0.273 2.756
4 5 2.663 -0.781 -0.753 0.899 0.191 -1.248 0.686 4.343 4.343 0.686 -1.248 0.191 0.899 -0.753 -0.781 2.663
5 6 2.209 -1.428 0.404 0.529 -1.035 0.844 0.349 -4.872 -4.872 0.349 0.844 -1.035 0.529 0.404 -1.428 2.209
6 7 1.457 -1.329 1.112 -0.801 0.376 0.230 -1.280 5.234 5.234 -1.280 0.230 0.376 -0.801 1.112 -1.329 1.457
7 8 0.509 -0.536 0.588 -0.677 0.830 -1.122 1.827 -5.419 -5.419 1.827 -1.122 0.830 -0.677 0.588 -0.536 0.509
8 9 -0.509 0.536 -0.588 0.677 -0.830 1.122 -1.827 5.419 5.419 -1.827 1.122 -0.830 0.677 -0.588 0.536 -0.509
9 10 -1.457 1.329 -1.112 0.801 -0.376 -0.230 1.280 -5.234 -5.234 1.280 -0.230 -0.376 0.801 -1.112 1.329 -1.457
10 11 -2.209 1.428 -0.404 -0.529 1.035 -0.844 -0.349 4.872 4.872 -0.349 -0.844 1.035 -0.529 -0.404 1.428 -2.209
11 12 -2.663 0.781 0.753 -0.899 -0.191 1.248 -0.686 -4.343 -4.343 -0.686 1.248 -0.191 -0.899 0.753 0.781 -2.663
12 13 -2.756 -0.273 1.074 0.363 -0.931 -0.660 1.516 3.666 3.666 1.516 -0.660 -0.931 0.363 1.074 -0.273 -2.756
13 14 -2.478 -1.185 0.205 0.966 0.700 -0.453 -1.891 -2.865 -2.865 -1.891 -0.453 0.700 0.966 0.205 -1.185 -2.478
14 15 -1.865 -1.478 -0.891 -0.185 0.547 1.205 1.700 1.966 1.966 1.700 1.205 0.547 -0.185 -0.891 -1.478 -1.865
15 16 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000
16 17 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 0.000 0.000 0.000 0.000 -0.000 0.000 0.000 0.000
17 18 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
18 19 1.865 1.478 0.891 0.185 -0.547 -1.205 -1.700 -1.966 -1.966 -1.700 -1.205 -0.547 0.185 0.891 1.478 1.865
19 20 2.478 1.185 -0.205 -0.966 -0.700 0.453 1.891 2.865 2.865 1.891 0.453 -0.700 -0.966 -0.205 1.185 2.478
20 21 2.756 0.273 -1.074 -0.363 0.931 0.660 -1.516 -3.666 -3.666 -1.516 0.660 0.931 -0.363 -1.074 0.273 2.756


Decomposition to irreducible representations
Power
To
A E1* E2* E3* E4* E5* E6* E7* E8*
1 0 1 0 0 0 0 0 0 0 E1
2 1 0 1 0 0 0 0 0 0 A⊕E2
3 0 1 0 1 0 0 0 0 0 E1⊕E3
4 1 0 1 0 1 0 0 0 0 A⊕E2⊕E4
5 0 1 0 1 0 1 0 0 0 E1⊕E3⊕E5
6 1 0 1 0 1 0 1 0 0 A⊕E2⊕E4⊕E6
7 0 1 0 1 0 1 0 1 0 E1⊕E3⊕E5⊕E7
8 1 0 1 0 1 0 1 0 1 A⊕E2⊕E4⊕E6⊕E8
9 0 1 0 1 0 1 0 1 1 E1⊕E3⊕E5⊕E7⊕E8
10 1 0 1 0 1 0 1 1 1 A⊕E2⊕E4⊕E6⊕E7⊕E8
11 0 1 0 1 0 1 1 1 1 E1⊕E3⊕E5⊕E6⊕E7⊕E8
12 1 0 1 0 1 1 1 1 1 A⊕E2⊕E4⊕E5⊕E6⊕E7⊕E8
13 0 1 0 1 1 1 1 1 1 E1⊕E3⊕E4⊕E5⊕E6⊕E7⊕E8
14 1 0 1 1 1 1 1 1 1 A⊕E2⊕E3⊕E4⊕E5⊕E6⊕E7⊕E8
15 0 1 1 1 1 1 1 1 1 E1⊕E2⊕E3⊕E4⊕E5⊕E6⊕E7⊕E8
16 1 1 1 1 1 1 1 1 1 A⊕E1⊕E2⊕E3⊕E4⊕E5⊕E6⊕E7⊕E8
17 2 1 1 1 1 1 1 1 1 2A⊕E1⊕E2⊕E3⊕E4⊕E5⊕E6⊕E7⊕E8
18 1 2 1 1 1 1 1 1 1 A⊕2E1⊕E2⊕E3⊕E4⊕E5⊕E6⊕E7⊕E8
19 2 1 2 1 1 1 1 1 1 2A⊕E1⊕2E2⊕E3⊕E4⊕E5⊕E6⊕E7⊕E8
20 1 2 1 2 1 1 1 1 1 A⊕2E1⊕E2⊕2E3⊕E4⊕E5⊕E6⊕E7⊕E8



Last update January, 3rd 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement