Results for Point Group C19h



Symmetric powers of degenerate representation E''6
Vibrational overtones


Characters of symmetric powers
Power
To
E C19 (C19)2 (C19)3 (C19)4 (C19)5 (C19)6 (C19)7 (C19)8 (C19)9 (C19)10 (C19)11 (C19)12 (C19)13 (C19)14 (C19)15 (C19)16 (C19)17 (C19)18 σh S19 (S19)21 (S19)3 (S19)23 (S19)5 (S19)25 (S19)7 (S19)27 (S19)9 (S19)29 (S19)11 (S19)31 (S19)13 (S19)33 (S19)15 (S19)35 (S19)17 (S19)37
1 2 -0.803 -1.355 1.892 -0.165 -1.759 1.578 0.491 -1.973 1.094 1.094 -1.973 0.491 1.578 -1.759 -0.165 1.892 -1.355 -0.803 -2 0.803 1.355 -1.892 0.165 1.759 -1.578 -0.491 1.973 -1.094 -1.094 1.973 -0.491 -1.578 1.759 0.165 -1.892 1.355 0.803
2 3 -0.355 0.835 2.578 -0.973 2.094 1.491 -0.759 2.892 0.197 0.197 2.892 -0.759 1.491 2.094 -0.973 2.578 0.835 -0.355 3 -0.355 0.835 2.578 -0.973 2.094 1.491 -0.759 2.892 0.197 0.197 2.892 -0.759 1.491 2.094 -0.973 2.578 0.835 -0.355
3 4 1.088 0.224 2.986 0.326 -1.924 0.775 -0.864 -3.732 -0.879 -0.879 -3.732 -0.864 0.775 -1.924 0.326 2.986 0.224 1.088 -4 -1.088 -0.224 -2.986 -0.326 1.924 -0.775 0.864 3.732 0.879 0.879 3.732 0.864 -0.775 1.924 -0.326 -2.986 -0.224 -1.088
4 5 -0.520 -1.138 3.069 0.919 1.291 -0.268 0.335 4.470 -1.158 -1.158 4.470 0.335 -0.268 1.291 0.919 3.069 -1.138 -0.520 5 -0.520 -1.138 3.069 0.919 1.291 -0.268 0.335 4.470 -1.158 -1.158 4.470 0.335 -0.268 1.291 0.919 3.069 -1.138 -0.520
5 6 -0.671 1.318 2.820 -0.478 -0.346 -1.198 1.028 -5.086 -0.388 -0.388 -5.086 1.028 -1.198 -0.346 -0.478 2.820 1.318 -0.671 -6 0.671 -1.318 -2.820 0.478 0.346 1.198 -1.028 5.086 0.388 0.388 5.086 -1.028 1.198 0.346 0.478 -2.820 -1.318 0.671
6 7 1.059 -0.647 2.266 -0.840 -0.682 -1.623 0.170 5.564 0.734 0.734 5.564 0.170 -1.623 -0.682 -0.840 2.266 -0.647 1.059 7 1.059 -0.647 2.266 -0.840 -0.682 -1.623 0.170 5.564 0.734 0.734 5.564 0.170 -1.623 -0.682 -0.840 2.266 -0.647 1.059
7 8 -0.180 -0.441 1.466 0.616 1.546 -1.363 -0.945 -5.890 1.190 1.190 -5.890 -0.945 -1.363 1.546 0.616 1.466 -0.441 -0.180 -8 0.180 0.441 -1.466 -0.616 -1.546 1.363 0.945 5.890 -1.190 -1.190 5.890 0.945 1.363 -1.546 -0.616 -1.466 0.441 0.180
8 9 -0.914 1.245 0.507 0.738 -2.037 -0.529 -0.634 6.055 0.569 0.569 6.055 -0.634 -0.529 -2.037 0.738 0.507 1.245 -0.914 9 -0.914 1.245 0.507 0.738 -2.037 -0.529 -0.634 6.055 0.569 0.569 6.055 -0.634 -0.529 -2.037 0.738 0.507 1.245 -0.914
9 10 0.914 -1.245 -0.507 -0.738 2.037 0.529 0.634 -6.055 -0.569 -0.569 -6.055 0.634 0.529 2.037 -0.738 -0.507 -1.245 0.914 -10 -0.914 1.245 0.507 0.738 -2.037 -0.529 -0.634 6.055 0.569 0.569 6.055 -0.634 -0.529 -2.037 0.738 0.507 1.245 -0.914
10 11 0.180 0.441 -1.466 -0.616 -1.546 1.363 0.945 5.890 -1.190 -1.190 5.890 0.945 1.363 -1.546 -0.616 -1.466 0.441 0.180 11 0.180 0.441 -1.466 -0.616 -1.546 1.363 0.945 5.890 -1.190 -1.190 5.890 0.945 1.363 -1.546 -0.616 -1.466 0.441 0.180
11 12 -1.059 0.647 -2.266 0.840 0.682 1.623 -0.170 -5.564 -0.734 -0.734 -5.564 -0.170 1.623 0.682 0.840 -2.266 0.647 -1.059 -12 1.059 -0.647 2.266 -0.840 -0.682 -1.623 0.170 5.564 0.734 0.734 5.564 0.170 -1.623 -0.682 -0.840 2.266 -0.647 1.059
12 13 0.671 -1.318 -2.820 0.478 0.346 1.198 -1.028 5.086 0.388 0.388 5.086 -1.028 1.198 0.346 0.478 -2.820 -1.318 0.671 13 0.671 -1.318 -2.820 0.478 0.346 1.198 -1.028 5.086 0.388 0.388 5.086 -1.028 1.198 0.346 0.478 -2.820 -1.318 0.671
13 14 0.520 1.138 -3.069 -0.919 -1.291 0.268 -0.335 -4.470 1.158 1.158 -4.470 -0.335 0.268 -1.291 -0.919 -3.069 1.138 0.520 -14 -0.520 -1.138 3.069 0.919 1.291 -0.268 0.335 4.470 -1.158 -1.158 4.470 0.335 -0.268 1.291 0.919 3.069 -1.138 -0.520
14 15 -1.088 -0.224 -2.986 -0.326 1.924 -0.775 0.864 3.732 0.879 0.879 3.732 0.864 -0.775 1.924 -0.326 -2.986 -0.224 -1.088 15 -1.088 -0.224 -2.986 -0.326 1.924 -0.775 0.864 3.732 0.879 0.879 3.732 0.864 -0.775 1.924 -0.326 -2.986 -0.224 -1.088
15 16 0.355 -0.835 -2.578 0.973 -2.094 -1.491 0.759 -2.892 -0.197 -0.197 -2.892 0.759 -1.491 -2.094 0.973 -2.578 -0.835 0.355 -16 -0.355 0.835 2.578 -0.973 2.094 1.491 -0.759 2.892 0.197 0.197 2.892 -0.759 1.491 2.094 -0.973 2.578 0.835 -0.355
16 17 0.803 1.355 -1.892 0.165 1.759 -1.578 -0.491 1.973 -1.094 -1.094 1.973 -0.491 -1.578 1.759 0.165 -1.892 1.355 0.803 17 0.803 1.355 -1.892 0.165 1.759 -1.578 -0.491 1.973 -1.094 -1.094 1.973 -0.491 -1.578 1.759 0.165 -1.892 1.355 0.803
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 -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 1.000 1.000
18 19 -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 -0.000 0.000 19 -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 -0.000 0.000
19 20 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 1.000 1.000 -20 -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 -1.000 -1.000
20 21 -0.803 -1.355 1.892 -0.165 -1.759 1.578 0.491 -1.973 1.094 1.094 -1.973 0.491 1.578 -1.759 -0.165 1.892 -1.355 -0.803 21 -0.803 -1.355 1.892 -0.165 -1.759 1.578 0.491 -1.973 1.094 1.094 -1.973 0.491 1.578 -1.759 -0.165 1.892 -1.355 -0.803


Decomposition to irreducible representations
Power
To
A' E'1* E'2* E'3* E'4* E'5* E'6* E'7* E'8* E'9* A'' E''1* E''2* E''3* E''4* E''5* E''6* E''7* E''8* E''9*
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 E''6
2 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'7
3 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 E''1⊕E''6
4 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'5⊕E'7
5 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 0 E''1⊕E''6⊕E''8
6 1 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'2⊕E'5⊕E'7
7 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 E''1⊕E''4⊕E''6⊕E''8
8 1 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'2⊕E'5⊕E'7⊕E'9
9 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 E''1⊕E''3⊕E''4⊕E''6⊕E''8
10 1 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'2⊕E'3⊕E'5⊕E'7⊕E'9
11 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 1 E''1⊕E''3⊕E''4⊕E''6⊕E''8⊕E''9
12 1 0 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'2⊕E'3⊕E'4⊕E'5⊕E'7⊕E'9
13 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 E''1⊕E''2⊕E''3⊕E''4⊕E''6⊕E''8⊕E''9
14 1 0 1 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'2⊕E'3⊕E'4⊕E'5⊕E'7⊕E'8⊕E'9
15 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 E''1⊕E''2⊕E''3⊕E''4⊕E''5⊕E''6⊕E''8⊕E''9
16 1 1 1 1 1 1 0 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'7⊕E'8⊕E'9
17 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 E''1⊕E''2⊕E''3⊕E''4⊕E''5⊕E''6⊕E''7⊕E''8⊕E''9
18 1 1 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⊕E'8⊕E'9
19 0 0 0 0 0 0 0 0 0 0 2 1 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⊕E''9
20 1 1 1 1 1 1 2 1 1 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'2⊕E'3⊕E'4⊕E'5⊕2E'6⊕E'7⊕E'8⊕E'9



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