Wired Chemist

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		ε = exp(2π/3)
A	1	1	1	z, Rz	x2 + y2, z2
E	{ 1     ε     ε+ }    1     ε+    ε			(x, y)(Rx, Ry)	(x2 - y2, xy)(yz, xz)

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 }    1   -i     -1     i				(x, y)(Rz, Ry)	(yz, xz)

C5	E	C5	C52	C53	C54		ε = exp (2π/5)
A	1	1	1	1	1	z, Rz	x2 + y2, z2
E1	{ 1   ε     ε2      ε2+     ε+ }    1   ε+    ε2+    ε2       ε					(x, y)(Rz, Ry)	(yz, xz)
E2	{ 1   ε2     ε+     ε      ε2+ }    1   ε2+    ε      ε+     ε2						(x2 - y2, xy)

C6	E	C6	C3	C2	C32	C65		ε = exp(2π/6)
A	1	1	1	1	1	1	z, Rz	x2 + y2, z2
B	1	-1	1	-1	1	-1
E1	{ 1   ε    -ε+    -1    -ε     ε+ }    1   ε+   -ε     -1   -ε+ε						(x, y) (Rz, Ry)	(xz, yz)
E2	{ 1   -ε+   -ε     1    -ε+    -ε }    1   -ε     -ε+   1    -ε     -ε+							(x2 - y2, xy)

Reference: F.A. Cotton, "Chemical Applications of Group Theory," 3rd ed., Wiley-Interscience, NY, 1990.