Results for Point Group C17h



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


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 1 0 0 0 0 0 E''3
2 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'6
3 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 E''3⊕E''8
4 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'5⊕E'6
5 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 E''2⊕E''3⊕E''8
6 1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'5⊕E'6
7 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 E''2⊕E''3⊕E''4⊕E''8
8 1 1 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'5⊕E'6⊕E'7
9 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 E''2⊕E''3⊕E''4⊕E''7⊕E''8
10 1 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'4⊕E'5⊕E'6⊕E'7
11 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 E''1⊕E''2⊕E''3⊕E''4⊕E''7⊕E''8
12 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'4⊕E'5⊕E'6⊕E'7
13 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 E''1⊕E''2⊕E''3⊕E''4⊕E''5⊕E''7⊕E''8
14 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'4⊕E'5⊕E'6⊕E'7⊕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 2 1 1 1 1 1 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕2E'3⊕E'4⊕E'5⊕E'6⊕E'7⊕E'8
19 0 0 0 0 0 0 0 0 0 2 1 1 1 1 1 2 1 1 2A''⊕E''1⊕E''2⊕E''3⊕E''4⊕E''5⊕2E''6⊕E''7⊕E''8
20 1 1 1 2 1 1 1 1 2 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕2E'3⊕E'4⊕E'5⊕E'6⊕E'7⊕2E'8


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