The Cn Groups
C2
| |
E |
C2 |
|
|
| A |
1 |
1 |
z, Rz |
x2, y2, z2, xy |
| B |
1 |
-1 |
x, y, Rx, Ry |
yz, xz |
C3
| |
E |
C3 |
C32 |
|
e = exp(2p
i/3) |
| A |
1 |
1 |
1 |
z, Rz |
x2 + y2, z2 |
| E |
1 |
e |
e* |
(x,y)(Rx, Ry) |
(x2 - y2, xy)(yz, xz) |
| 1 |
e* |
e |
C4
| |
E |
C4 |
C2 |
C43 |
|
|
| A |
1 |
1 |
1 |
1 |
z, Rz |
x2 + y2, z2 |
| B |
1 |
-1 |
1 |
-1 |
|
x2 - y2, xy |
| E |
1 |
i |
-1 |
-i |
(x, y)(Rx, Ry) |
(yz, xz) |
| 1 |
-i |
-1 |
i |
C5
| |
E |
C5 |
C52 |
C53 |
C54 |
|
e = exp(2p
i/5) |
| A |
1 |
1 |
1 |
1 |
1 |
z, Rz |
x2 + y2, z2 |
| E1 |
1 |
e |
e2 |
e2* |
e* |
(x, y) (Rx, Ry) |
(yz, xz) |
| 1 |
e* |
e2* |
e2 |
e |
| E2 |
1 |
e2 |
e* |
e |
e2* |
|
(x2 - y2, xy)
|
| 1 |
e2* |
e |
e* |
e2 |
C6
| |
E |
C6 |
C3 |
C2 |
C32 |
C65 |
|
e = exp(2p
i/6) |
| A |
1 |
1 |
1 |
1 |
1 |
1 |
z, Rz |
x2 + y2, z2 |
| B |
1 |
-1 |
1 |
-1 |
1 |
-1 |
|
|
| E1 |
1 |
e |
-e* |
-1 |
-e |
e* |
(x, y) (Rx, Ry) |
(xz, yz) |
| 1 |
e* |
-e |
-1 |
-e* |
e |
| E2 |
1 |
-e* |
-e |
1 |
-e* |
-e |
|
(x2 - y2, xy) |
| 1 |
-e |
-e* |
1 |
-e |
-e* |