Results for Point Group C17h



Symmetric powers of degenerate representation E''7
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 σh S17 (S17)19 (S17)3 (S17)21 (S17)5 (S17)23 (S17)7 (S17)25 (S17)9 (S17)27 (S17)11 (S17)29 (S17)13 (S17)31 (S17)15 (S17)33
1 2 -1.700 0.891 0.185 -1.205 1.865 -1.966 1.478 -0.547 -0.547 1.478 -1.966 1.865 -1.205 0.185 0.891 -1.700 -2 1.700 -0.891 -0.185 1.205 -1.865 1.966 -1.478 0.547 0.547 -1.478 1.966 -1.865 1.205 -0.185 -0.891 1.700
2 3 1.891 -0.205 -0.966 0.453 2.478 2.865 1.185 -0.700 -0.700 1.185 2.865 2.478 0.453 -0.966 -0.205 1.891 3 1.891 -0.205 -0.966 0.453 2.478 2.865 1.185 -0.700 -0.700 1.185 2.865 2.478 0.453 -0.966 -0.205 1.891
3 4 -1.516 -1.074 -0.363 0.660 2.756 -3.666 0.273 0.931 0.931 0.273 -3.666 2.756 0.660 -0.363 -1.074 -1.516 -4 1.516 1.074 0.363 -0.660 -2.756 3.666 -0.273 -0.931 -0.931 -0.273 3.666 -2.756 -0.660 0.363 1.074 1.516
4 5 0.686 -0.753 0.899 -1.248 2.663 4.343 -0.781 0.191 0.191 -0.781 4.343 2.663 -1.248 0.899 -0.753 0.686 5 0.686 -0.753 0.899 -1.248 2.663 4.343 -0.781 0.191 0.191 -0.781 4.343 2.663 -1.248 0.899 -0.753 0.686
5 6 0.349 0.404 0.529 0.844 2.209 -4.872 -1.428 -1.035 -1.035 -1.428 -4.872 2.209 0.844 0.529 0.404 0.349 -6 -0.349 -0.404 -0.529 -0.844 -2.209 4.872 1.428 1.035 1.035 1.428 4.872 -2.209 -0.844 -0.529 -0.404 -0.349
6 7 -1.280 1.112 -0.801 0.230 1.457 5.234 -1.329 0.376 0.376 -1.329 5.234 1.457 0.230 -0.801 1.112 -1.280 7 -1.280 1.112 -0.801 0.230 1.457 5.234 -1.329 0.376 0.376 -1.329 5.234 1.457 0.230 -0.801 1.112 -1.280
7 8 1.827 0.588 -0.677 -1.122 0.509 -5.419 -0.536 0.830 0.830 -0.536 -5.419 0.509 -1.122 -0.677 0.588 1.827 -8 -1.827 -0.588 0.677 1.122 -0.509 5.419 0.536 -0.830 -0.830 0.536 5.419 -0.509 1.122 0.677 -0.588 -1.827
8 9 -1.827 -0.588 0.677 1.122 -0.509 5.419 0.536 -0.830 -0.830 0.536 5.419 -0.509 1.122 0.677 -0.588 -1.827 9 -1.827 -0.588 0.677 1.122 -0.509 5.419 0.536 -0.830 -0.830 0.536 5.419 -0.509 1.122 0.677 -0.588 -1.827
9 10 1.280 -1.112 0.801 -0.230 -1.457 -5.234 1.329 -0.376 -0.376 1.329 -5.234 -1.457 -0.230 0.801 -1.112 1.280 -10 -1.280 1.112 -0.801 0.230 1.457 5.234 -1.329 0.376 0.376 -1.329 5.234 1.457 0.230 -0.801 1.112 -1.280
10 11 -0.349 -0.404 -0.529 -0.844 -2.209 4.872 1.428 1.035 1.035 1.428 4.872 -2.209 -0.844 -0.529 -0.404 -0.349 11 -0.349 -0.404 -0.529 -0.844 -2.209 4.872 1.428 1.035 1.035 1.428 4.872 -2.209 -0.844 -0.529 -0.404 -0.349
11 12 -0.686 0.753 -0.899 1.248 -2.663 -4.343 0.781 -0.191 -0.191 0.781 -4.343 -2.663 1.248 -0.899 0.753 -0.686 -12 0.686 -0.753 0.899 -1.248 2.663 4.343 -0.781 0.191 0.191 -0.781 4.343 2.663 -1.248 0.899 -0.753 0.686
12 13 1.516 1.074 0.363 -0.660 -2.756 3.666 -0.273 -0.931 -0.931 -0.273 3.666 -2.756 -0.660 0.363 1.074 1.516 13 1.516 1.074 0.363 -0.660 -2.756 3.666 -0.273 -0.931 -0.931 -0.273 3.666 -2.756 -0.660 0.363 1.074 1.516
13 14 -1.891 0.205 0.966 -0.453 -2.478 -2.865 -1.185 0.700 0.700 -1.185 -2.865 -2.478 -0.453 0.966 0.205 -1.891 -14 1.891 -0.205 -0.966 0.453 2.478 2.865 1.185 -0.700 -0.700 1.185 2.865 2.478 0.453 -0.966 -0.205 1.891
14 15 1.700 -0.891 -0.185 1.205 -1.865 1.966 -1.478 0.547 0.547 -1.478 1.966 -1.865 1.205 -0.185 -0.891 1.700 15 1.700 -0.891 -0.185 1.205 -1.865 1.966 -1.478 0.547 0.547 -1.478 1.966 -1.865 1.205 -0.185 -0.891 1.700
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 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 -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 -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 -1.700 0.891 0.185 -1.205 1.865 -1.966 1.478 -0.547 -0.547 1.478 -1.966 1.865 -1.205 0.185 0.891 -1.700 19 -1.700 0.891 0.185 -1.205 1.865 -1.966 1.478 -0.547 -0.547 1.478 -1.966 1.865 -1.205 0.185 0.891 -1.700
19 20 1.891 -0.205 -0.966 0.453 2.478 2.865 1.185 -0.700 -0.700 1.185 2.865 2.478 0.453 -0.966 -0.205 1.891 -20 -1.891 0.205 0.966 -0.453 -2.478 -2.865 -1.185 0.700 0.700 -1.185 -2.865 -2.478 -0.453 0.966 0.205 -1.891
20 21 -1.516 -1.074 -0.363 0.660 2.756 -3.666 0.273 0.931 0.931 0.273 -3.666 2.756 0.660 -0.363 -1.074 -1.516 21 -1.516 -1.074 -0.363 0.660 2.756 -3.666 0.273 0.931 0.931 0.273 -3.666 2.756 0.660 -0.363 -1.074 -1.516


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



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