Charakterentabelle für Punktgruppe S12

=exp(2i/12)
S12 E S12 C6 S4 C3 (S12)5 C2 (S12)7 (C3)2 (S4)3 (C6)5 (S12)11
h = 12, lineare Fkt.,
Rotation
quadratische
Fkt.
kubische Fkt.
A +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 +1 Rz z2, x2+y2 -
B +1 -1 +1 -1 +1 -1 +1 -1 +1 -1 +1 -1 z - z3, z(x2+y2)
E1 +1
+1		 +
+*		+2
+2*		+i
-i		-2*
-2		-*
-		-1
-1		-
-*		 -2
-2*		 -i
+i		 +2*
+2		 +*
+		 x+iy
x-iy		 - (xz2, yz2) [x(x2+y2), y(x2+y2)]
E2 +1
+1		 +2
+2*		-2*
+2		-1
-1		-2
-2*		+2*
+2		+1
+1		+2
+2*		 -2*
-2		 -1
-1		 -2
-2*		 +2*
+2		 - (x2-y2, xy) -
E3 +1
+1		 +i
-i		-1
-1		-i
+i		+1
+1		+i
-i		-1
-1		-i
+i		 +1
+1		 +i
-i		 -1
-1		 -i
+i		 - - [x(x2-3y2), y(3x2-y2)]
E4 +1
+1		 -2*
-2		-2
-2*		+1
+1		-2*
-2		-2
-2*		+1
+1		-2*
-2		 -2
-2*		 +1
+1		 -2*
-2		 -2
-2*		 - - [xyz, z(x2-y2)]
E5 +1
+1		 -*
+		+2*
+2		+i
-i		-2
+2*		+
+*		-1
-1		+*
+		 -2*
-2		 -i
+i		 +2
+2*		 -
-*		 Rx-iRy
Rx+iRy		 (xz, yz) -


Anzahl der Symmetrielemente h = 12
Anzahl der irreduziblen Darstellungen n = 12
Anzahl der reellen irreduziblen Darstellungen n = 7
abelsche Gruppe ? ja
Untergruppen C2 , C3 , C6 , S4
chiral ? nein



Auf diesem Webangebot gilt die Datenschutzerklärung der TU Braunschweig mit Ausnahme der Abschnitte VI, VII und VIII.