Results for Point Group C19h



Symmetric powers of degenerate representation E''2
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 1.578 0.491 -0.803 -1.759 -1.973 -1.355 -0.165 1.094 1.892 1.892 1.094 -0.165 -1.355 -1.973 -1.759 -0.803 0.491 1.578 -2 -1.578 -0.491 0.803 1.759 1.973 1.355 0.165 -1.094 -1.892 -1.892 -1.094 0.165 1.355 1.973 1.759 0.803 -0.491 -1.578
2 3 1.491 -0.759 -0.355 2.094 2.892 0.835 -0.973 0.197 2.578 2.578 0.197 -0.973 0.835 2.892 2.094 -0.355 -0.759 1.491 3 1.491 -0.759 -0.355 2.094 2.892 0.835 -0.973 0.197 2.578 2.578 0.197 -0.973 0.835 2.892 2.094 -0.355 -0.759 1.491
3 4 0.775 -0.864 1.088 -1.924 -3.732 0.224 0.326 -0.879 2.986 2.986 -0.879 0.326 0.224 -3.732 -1.924 1.088 -0.864 0.775 -4 -0.775 0.864 -1.088 1.924 3.732 -0.224 -0.326 0.879 -2.986 -2.986 0.879 -0.326 -0.224 3.732 1.924 -1.088 0.864 -0.775
4 5 -0.268 0.335 -0.520 1.291 4.470 -1.138 0.919 -1.158 3.069 3.069 -1.158 0.919 -1.138 4.470 1.291 -0.520 0.335 -0.268 5 -0.268 0.335 -0.520 1.291 4.470 -1.138 0.919 -1.158 3.069 3.069 -1.158 0.919 -1.138 4.470 1.291 -0.520 0.335 -0.268
5 6 -1.198 1.028 -0.671 -0.346 -5.086 1.318 -0.478 -0.388 2.820 2.820 -0.388 -0.478 1.318 -5.086 -0.346 -0.671 1.028 -1.198 -6 1.198 -1.028 0.671 0.346 5.086 -1.318 0.478 0.388 -2.820 -2.820 0.388 0.478 -1.318 5.086 0.346 0.671 -1.028 1.198
6 7 -1.623 0.170 1.059 -0.682 5.564 -0.647 -0.840 0.734 2.266 2.266 0.734 -0.840 -0.647 5.564 -0.682 1.059 0.170 -1.623 7 -1.623 0.170 1.059 -0.682 5.564 -0.647 -0.840 0.734 2.266 2.266 0.734 -0.840 -0.647 5.564 -0.682 1.059 0.170 -1.623
7 8 -1.363 -0.945 -0.180 1.546 -5.890 -0.441 0.616 1.190 1.466 1.466 1.190 0.616 -0.441 -5.890 1.546 -0.180 -0.945 -1.363 -8 1.363 0.945 0.180 -1.546 5.890 0.441 -0.616 -1.190 -1.466 -1.466 -1.190 -0.616 0.441 5.890 -1.546 0.180 0.945 1.363
8 9 -0.529 -0.634 -0.914 -2.037 6.055 1.245 0.738 0.569 0.507 0.507 0.569 0.738 1.245 6.055 -2.037 -0.914 -0.634 -0.529 9 -0.529 -0.634 -0.914 -2.037 6.055 1.245 0.738 0.569 0.507 0.507 0.569 0.738 1.245 6.055 -2.037 -0.914 -0.634 -0.529
9 10 0.529 0.634 0.914 2.037 -6.055 -1.245 -0.738 -0.569 -0.507 -0.507 -0.569 -0.738 -1.245 -6.055 2.037 0.914 0.634 0.529 -10 -0.529 -0.634 -0.914 -2.037 6.055 1.245 0.738 0.569 0.507 0.507 0.569 0.738 1.245 6.055 -2.037 -0.914 -0.634 -0.529
10 11 1.363 0.945 0.180 -1.546 5.890 0.441 -0.616 -1.190 -1.466 -1.466 -1.190 -0.616 0.441 5.890 -1.546 0.180 0.945 1.363 11 1.363 0.945 0.180 -1.546 5.890 0.441 -0.616 -1.190 -1.466 -1.466 -1.190 -0.616 0.441 5.890 -1.546 0.180 0.945 1.363
11 12 1.623 -0.170 -1.059 0.682 -5.564 0.647 0.840 -0.734 -2.266 -2.266 -0.734 0.840 0.647 -5.564 0.682 -1.059 -0.170 1.623 -12 -1.623 0.170 1.059 -0.682 5.564 -0.647 -0.840 0.734 2.266 2.266 0.734 -0.840 -0.647 5.564 -0.682 1.059 0.170 -1.623
12 13 1.198 -1.028 0.671 0.346 5.086 -1.318 0.478 0.388 -2.820 -2.820 0.388 0.478 -1.318 5.086 0.346 0.671 -1.028 1.198 13 1.198 -1.028 0.671 0.346 5.086 -1.318 0.478 0.388 -2.820 -2.820 0.388 0.478 -1.318 5.086 0.346 0.671 -1.028 1.198
13 14 0.268 -0.335 0.520 -1.291 -4.470 1.138 -0.919 1.158 -3.069 -3.069 1.158 -0.919 1.138 -4.470 -1.291 0.520 -0.335 0.268 -14 -0.268 0.335 -0.520 1.291 4.470 -1.138 0.919 -1.158 3.069 3.069 -1.158 0.919 -1.138 4.470 1.291 -0.520 0.335 -0.268
14 15 -0.775 0.864 -1.088 1.924 3.732 -0.224 -0.326 0.879 -2.986 -2.986 0.879 -0.326 -0.224 3.732 1.924 -1.088 0.864 -0.775 15 -0.775 0.864 -1.088 1.924 3.732 -0.224 -0.326 0.879 -2.986 -2.986 0.879 -0.326 -0.224 3.732 1.924 -1.088 0.864 -0.775
15 16 -1.491 0.759 0.355 -2.094 -2.892 -0.835 0.973 -0.197 -2.578 -2.578 -0.197 0.973 -0.835 -2.892 -2.094 0.355 0.759 -1.491 -16 1.491 -0.759 -0.355 2.094 2.892 0.835 -0.973 0.197 2.578 2.578 0.197 -0.973 0.835 2.892 2.094 -0.355 -0.759 1.491
16 17 -1.578 -0.491 0.803 1.759 1.973 1.355 0.165 -1.094 -1.892 -1.892 -1.094 0.165 1.355 1.973 1.759 0.803 -0.491 -1.578 17 -1.578 -0.491 0.803 1.759 1.973 1.355 0.165 -1.094 -1.892 -1.892 -1.094 0.165 1.355 1.973 1.759 0.803 -0.491 -1.578
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 1.578 0.491 -0.803 -1.759 -1.973 -1.355 -0.165 1.094 1.892 1.892 1.094 -0.165 -1.355 -1.973 -1.759 -0.803 0.491 1.578 21 1.578 0.491 -0.803 -1.759 -1.973 -1.355 -0.165 1.094 1.892 1.892 1.094 -0.165 -1.355 -1.973 -1.759 -0.803 0.491 1.578


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 1 0 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 0 0 A'⊕E'4
3 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 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 0 0 A'⊕E'4⊕E'8
5 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 E''2⊕E''6⊕E''9
6 1 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'4⊕E'7⊕E'8
7 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 E''2⊕E''5⊕E''6⊕E''9
8 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'3⊕E'4⊕E'7⊕E'8
9 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 E''1⊕E''2⊕E''5⊕E''6⊕E''9
10 1 1 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'3⊕E'4⊕E'7⊕E'8
11 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 1 0 0 1 E''1⊕E''2⊕E''3⊕E''5⊕E''6⊕E''9
12 1 1 0 1 1 1 0 1 1 0 0 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 0 1 1 1 0 1 1 1 0 1 E''1⊕E''2⊕E''3⊕E''5⊕E''6⊕E''7⊕E''9
14 1 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕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 0 1 1 1 1 1 E''1⊕E''2⊕E''3⊕E''5⊕E''6⊕E''7⊕E''8⊕E''9
16 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 A'⊕E'1⊕E'3⊕E'4⊕E'5⊕E'6⊕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 2 1 1 1 1 1 1 1 0 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⊕E'9


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