Results for Point Group C17h



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


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


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