Results for Point Group C17h



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


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


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