Results for Point Group C17



Symmetric powers of degenerate representation E6
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 -1.205 -0.547 1.865 -1.700 0.185 1.478 -1.966 0.891 0.891 -1.966 1.478 0.185 -1.700 1.865 -0.547 -1.205
2 3 0.453 -0.700 2.478 1.891 -0.966 1.185 2.865 -0.205 -0.205 2.865 1.185 -0.966 1.891 2.478 -0.700 0.453
3 4 0.660 0.931 2.756 -1.516 -0.363 0.273 -3.666 -1.074 -1.074 -3.666 0.273 -0.363 -1.516 2.756 0.931 0.660
4 5 -1.248 0.191 2.663 0.686 0.899 -0.781 4.343 -0.753 -0.753 4.343 -0.781 0.899 0.686 2.663 0.191 -1.248
5 6 0.844 -1.035 2.209 0.349 0.529 -1.428 -4.872 0.404 0.404 -4.872 -1.428 0.529 0.349 2.209 -1.035 0.844
6 7 0.230 0.376 1.457 -1.280 -0.801 -1.329 5.234 1.112 1.112 5.234 -1.329 -0.801 -1.280 1.457 0.376 0.230
7 8 -1.122 0.830 0.509 1.827 -0.677 -0.536 -5.419 0.588 0.588 -5.419 -0.536 -0.677 1.827 0.509 0.830 -1.122
8 9 1.122 -0.830 -0.509 -1.827 0.677 0.536 5.419 -0.588 -0.588 5.419 0.536 0.677 -1.827 -0.509 -0.830 1.122
9 10 -0.230 -0.376 -1.457 1.280 0.801 1.329 -5.234 -1.112 -1.112 -5.234 1.329 0.801 1.280 -1.457 -0.376 -0.230
10 11 -0.844 1.035 -2.209 -0.349 -0.529 1.428 4.872 -0.404 -0.404 4.872 1.428 -0.529 -0.349 -2.209 1.035 -0.844
11 12 1.248 -0.191 -2.663 -0.686 -0.899 0.781 -4.343 0.753 0.753 -4.343 0.781 -0.899 -0.686 -2.663 -0.191 1.248
12 13 -0.660 -0.931 -2.756 1.516 0.363 -0.273 3.666 1.074 1.074 3.666 -0.273 0.363 1.516 -2.756 -0.931 -0.660
13 14 -0.453 0.700 -2.478 -1.891 0.966 -1.185 -2.865 0.205 0.205 -2.865 -1.185 0.966 -1.891 -2.478 0.700 -0.453
14 15 1.205 0.547 -1.865 1.700 -0.185 -1.478 1.966 -0.891 -0.891 1.966 -1.478 -0.185 1.700 -1.865 0.547 1.205
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 -1.205 -0.547 1.865 -1.700 0.185 1.478 -1.966 0.891 0.891 -1.966 1.478 0.185 -1.700 1.865 -0.547 -1.205
19 20 0.453 -0.700 2.478 1.891 -0.966 1.185 2.865 -0.205 -0.205 2.865 1.185 -0.966 1.891 2.478 -0.700 0.453
20 21 0.660 0.931 2.756 -1.516 -0.363 0.273 -3.666 -1.074 -1.074 -3.666 0.273 -0.363 -1.516 2.756 0.931 0.660


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


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