Results for Point Group C17h



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


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


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