S8 - POINT GROUP SYMMETRY CHARACTER TABLES |
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S8 Point Group |
| Abelian, 5(8) irreducible representations |
| Subgroups of S8 point group: C2, C4 |
| E | S8 | C4 (z) | (S8)3 | C2 | (S8)5 | (C4)3 | (S8)7 | linear, rotations |
quadratic | |
|---|---|---|---|---|---|---|---|---|---|---|
| A | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | Rz | x2+y2, z2 |
| B | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -1 | z | |
| E1 | 1 1 |
e e* | i -i | -e* -e | -1 -1 | -e -e* | -i i | e* e | x+iy x-iy |
|
| E2 | 1 1 |
i -i | -1 -1 | -i i | 1 1 | i -i | -1 -1 | -i i | (x2-y2, xy) | |
| E3 | 1 1 |
-e -e* | i -i | e* e | -1 -1 | e e* | -i i | -e* -e | Rx+iRy Rx-iRy |
(xz, yz) |
| A | B | E1 | E2 | E3 | |
|---|---|---|---|---|---|
| A | A | B | E1 | E2 | E3 |
| B | B | A | E3 | E2 | E1 |
| E1 | E1 | E3 | 2A+E2 | E1+E3 | 2B+E2 |
| E2 | E2 | E2 | E1+E3 | 2A+2B | E1+E3 |
| E3 | E3 | E1 | 2A+B | E1+E3 | 2A+E2 |
| Printable: character table for S8 product table for S8 S8 point group |