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Ih Punktgruppe
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nicht abelsch, 10(32) irreduzible Darstellungen | Charaktertafel der Ih Punktgruppe
|
E |
12C5 |
12(C5)2 |
20C3 |
15C2 |
i |
12S10 |
12(S10)3 |
20S6 |
15σ |
linear, rotations |
quadratic |
Ag |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
|
x2+y2+z2 |
T1g |
3 |
-2cos(4π/5) |
-2cos(2π/5) |
0 |
-1 |
3 |
-2cos(2π/5) |
-2cos(4π/5) |
0 |
-1 |
(Rx, Ry, Rz) |
|
T2g |
3 |
-2cos(2π/5) |
-2cos(4π/5) |
0 |
-1 |
3 |
-2cos(4π/5) |
-2cos(2π/5) |
0 |
-1 |
|
|
Gg |
4 |
-1 |
-1 |
1 |
0 |
4 |
-1 |
-1 |
1 |
0 |
|
|
Hg |
5 |
0 |
0 |
-1 |
1 |
5 |
0 |
0 |
-1 |
1 |
|
[2z2-x2-y2, x2-y2, xy, xz, yz] |
Au |
1 |
1 |
1 |
1 |
1 |
-1 |
-1 |
-1 |
-1 |
-1 |
|
|
T1u |
3 |
-2cos(4π/5) |
-2cos(2π/5) |
0 |
-1 |
-3 |
2cos(2π/5) |
2cos(4π/5) |
0 |
1 |
(x, y, z) |
|
T2u |
3 |
-2cos(2π/5) |
-2cos(4π/5) |
0 |
-1 |
-3 |
2cos(4π/5) |
2cos(2π/5) |
0 |
1 |
|
|
Gu |
4 |
-1 |
-1 |
1 |
0 |
-4 |
1 |
1 |
-1 |
0 |
|
|
Hu |
5 |
0 |
0 |
-1 |
1 |
-5 |
0 |
0 |
1 |
-1 |
|
|
Multiplikationstabelle der Ih Punktgruppe | Ag | T1g | T2g | Gg | Hg | Au | T1u | T2u | Gu | Hu |
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Ag | Ag | T1g | T2g | Gg | Hg | Au | T1u | T2u | Gu | Hu |
---|
T1g | T1g | Ag+T1g+Hg | Gg+Hg | T2g+Gg+Hg | T1g+T2g+Gg+Hg | T1u | Au+T1u+Hu | Gu+Hu | T2u+Gu+Hu | T1u+T2u+Gu+Hu |
---|
T2g | T2g | Gg+Hg | Ag+T2g+Hg | T1g+Gg+Hg | T1g+T2g+Gg+Hg | T2u | Gu+Hu | Au+T2u+Hu | T1u+Gu+Hu | T1u+T2u+Gu+Hu |
---|
Gg | Gg | T2g+Gg+Hg | T1g+Gg+Hg | Ag+T1g+T2g+Gg+Hg | T1g+T2g+Gg+2Hg | Gu | T2u+Gu+Hu | T1u+Gu+Hu | Au+T1u+T2u+Gu+Hu | T1u+T2u+Gu+2Hu |
---|
Hg | Hg | T1g+T2g+Gg+Hg | T1g+T2g+Gg+Hg | T1g+T2g+Gg+2Hg | Ag+T1g+T2g+2Gg+2Hg | Hu | T1u+T2u+Gu+Hu | T1u+T2u+Gu+Hu | T1u+T2u+Gu+2Hu | Au+T1u+T2u+2Gu+2Hu |
---|
Au | Au | T1u | T2u | Gu | Hu | Ag | T1g | T2g | Gg | Hg |
---|
T1u | T1u | Au+T1u+Hu | Gu+Hu | T2u+Gu+Hu | T1u+T2u+Gu+Hu | T1g | Ag+T1g+Hg | Gg+Hg | T2g+Gg+Hg | T1g+T2g+Gg+Hg |
---|
T2u | T2u | Gu+Hu | Au+T2u+Hu | T1u+Gu+Hu | T1u+T2u+Gu+Hu | T2g | Gg+Hg | Ag+T2g+Hg | T1g+Gg+Hg | T1g+T2g+Gg+Hg |
---|
Gu | Gu | T2u+Gu+Hu | T1u+Gu+Hu | Au+T1u+T2u+Gu+Hu | T1u+T2u+Gu+2Hu | Gg | T2g+Gg+Hg | T1g+Gg+Hg | Ag+T1g+T2g+Gg+Hg | T1g+T2g+Gg+2Hg |
---|
Hu | Hu | T1u+T2u+Gu+Hu | T1u+T2u+Gu+Hu | T1u+T2u+Gu+2Hu | Au+T1u+T2u+2Gu+2Hu | Hg | T1g+T2g+Gg+Hg | T1g+T2g+Gg+Hg | T1g+T2g+Gg+2Hg | Ag+T1g+T2g+2Gg+2Hg |
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