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D5h Point Group
|
| Abelian, 8(12) irreducible representations | |
Subgroups of D5h point group: Cs, C2, C5, D5, C2v, C5v, C5h |
Character table for D5h point group
|
E |
2C5 |
2(C5)2 |
5C'2 |
h |
2S5 |
2(S5)3 |
5σv |
linear,
rotations |
quadratic |
| A'1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
|
x2+y2, z2 |
| A'2 |
1 |
1 |
1 |
-1 |
1 |
1 |
1 |
-1 |
Rz |
|
| E'1 |
2 |
2cos(2π/5) |
2cos(4π/5) |
0 |
2 |
2cos(2π/5) |
2cos(4π/5) |
0 |
(x, y) |
|
| E'2 |
2 |
2cos(4π/5) |
2cos(2π/5) |
0 |
2 |
2cos(4π/5) |
2cos(2π/5) |
0 |
|
(x2-y2, xy) |
| A''1 |
1 |
1 |
1 |
1 |
-1 |
-1 |
-1 |
-1 |
|
|
| A''2 |
1 |
1 |
1 |
-1 |
-1 |
-1 |
-1 |
1 |
z |
|
| E''1 |
2 |
2cos(2π/5) |
2cos(4π/5) |
0 |
-2 |
-2cos(2π/5) |
-2cos(4π/5) |
0 |
(Rx, Ry) |
(xz, yz) |
| E''2 |
2 |
2cos(4π>/5) |
2cos(2π/5) |
0 |
-2 |
-2cos(4π/5) |
-2cos(2π/5) |
0 |
|
|
Product table for D5h point group| | A'1 | A'2 | E'1 | E'2 | A''1 | A''2 | E''1 | E''2 |
|---|
| A'1 | A'1 | A'2 | E'1 | E'2 | A''1 | A''2 | E''1 | E''2 |
|---|
| A'2 | A'2 | A'1 | E'1 | E'2 | A''2 | A''1 | E''1 | E''2 |
|---|
| E'1 | E'1 | E'1 | A'1+A'2+E'2 | E'1+E'2 | E''1 | E''1 | A''1+A''2+E''2 | E''1+E''2 |
|---|
| E'2 | E'2 | E'2 | E'1+E'2 | A'1+A'2+E'2 | E''2 | E''2 | E''1+E''2 | A''1+A''2+E''2 |
|---|
| A''1 | A''1 | A''2 | E''1 | E''2 | A'1 | A'2 | E'1 | E'2 |
|---|
| A''2 | A''2 | A''1 | E''1 | E''2 | A'2 | A'1 | E'1 | E'2 |
|---|
| E''1 | E''1 | E''1 | A''1+A''2+E''2 | E''1+E''2 | E'1 | E'1 | A'1+A'2+E'2 | E'1+E'2 |
|---|
| E''2 | E''2 | E''2 | E''1+E''2 | A''1+A''2+E''2 | E'2 | E'2 | E'1+E'2 | A'1+A'2+E'2 |
|---|
|
