## Charakterentabelle für Punktgruppe S8

=exp(2i/8)

S8 | E | S8 | C4 (z) | (S8)3 | C2 | (S8)5 | (C4)3 | (S8)7 | h = 8, lineare Fkt., Rotation | quadratische Fkt. | kubische Fkt.
A | +1 | +1 | +1 | +1 | +1 | +1 | +1 | +1 | Rz | x2+y2, z2 | -
B | +1 | -1 | +1 | -1 | +1 | -1 | +1 | -1 | z | - | z3, z(x2+y2)
E1 | +1 +1 | + +* | +i -i | -* - | -1 -1 | - -* | -i +i | +* + | x+iy x-iy | - | (xz2, yz2) [x(x2+y2), y(x2+y2)]
E2 | +1 +1 | +i -i | -1 -1 | -i +i | +1 +1 | +i -i | -1 -1 | -i +i | - | (x2-y2, xy) | [xyz, z(x2-y2)]
E3 | +1 +1 | - -* | +i -i | +* + | -1 -1 | + +* | -i +i | -* - | Rx+iRy Rx-iRy | (xz, yz) | [y(3x2-y2), x(x2-3y2)]

Anzahl der Symmetrieelemente | h = 8
Anzahl der irreduziblen Darstellungen | n = 8
Anzahl der reellen irreduziblen Darstellungen | n = 5
abelsche Gruppe ? | ja
Untergruppen | C2 , C4
chiral ? | nein