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Groups

C2v	E	C2	σv(xz)	σv(yz)
A1	1	1	1	1	z	x2, y2, z2
A2	1	1	-1	-1	Rz	xy
B1	1	-1	1	-1	x, Ry	xz
B2	1	-1	-1	1	y, Rx	yz

C3v	E	2C3	3σv
A1	1	1	1	z	x2 + y2, z2
A2	1	1	-1	Rz
E	2	-1	0	(x, y)(Rx, Ry)	(x2 - y2, xy)(xz, yz)

C4v	E	2C4	C2	2σv	2σd
A1	1	1	1	1	1	z	x2 + y2, z2
A2	1	1	1	-1	-1	Rz
B1	1	-1	1	1	-1		x2 - y2
B2	1	-1	1	-1	1		xy
E	2	0	-2	0	0	(x, y)(Rx, Ry)	(xz, yz)

C5v	E	2C/5	2C52	5σv
A1	1	1	1	1	z	x2 + y2, z2
A2	1	1	1	-1	Rz
E1	2	2cos72°	2cos144°	0	(x, y)(Rx, Ry)	(xz, yz
E2	2	2cos144°	2cos72°	0		(x2 - y2, xy)

C6v	E	2C/6	2C3	C2	3σv	3σd
A1	1	1	1	1	1	1	z	x2 + y2, z2
A2	1	1	1	1	-1	-1	Rz
B1	-1	1	1	-1	1	-1
B2	1	-1	1	-1	-1	1
E1	2	1	-1	-2	0	0	(x, y)(Rx, Ry)	(xz, yz)
E2	2	-1	-1	2	0	0		(x2 - y2, xy)

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