Results for Point Group C17h



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


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 1 0 0 0 0 0 0 0 0 0 0 0 0 E'5
2 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'7
3 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 E'2⊕E'5
4 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'3⊕E'7
5 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 E'2⊕E'5⊕E'8
6 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'3⊕E'4⊕E'7
7 0 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 E'1⊕E'2⊕E'5⊕E'8
8 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'3⊕E'4⊕E'6⊕E'7
9 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 E'1⊕E'2⊕E'5⊕E'6⊕E'8
10 1 1 0 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'3⊕E'4⊕E'6⊕E'7
11 0 1 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 E'1⊕E'2⊕E'4⊕E'5⊕E'6⊕E'8
12 1 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'3⊕E'4⊕E'6⊕E'7⊕E'8
13 0 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6⊕E'8
14 1 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'3⊕E'4⊕E'6⊕E'7⊕E'8
15 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 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 2 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 2A'⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6⊕E'7⊕E'8
18 1 1 1 1 1 2 1 1 1 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'3⊕E'4⊕2E'5⊕E'6⊕E'7⊕E'8
19 2 1 1 1 1 1 1 2 1 0 0 0 0 0 0 0 0 0 2A'⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕E'6⊕2E'7⊕E'8
20 1 1 2 1 1 2 1 1 1 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕2E'2⊕E'3⊕E'4⊕2E'5⊕E'6⊕E'7⊕E'8



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