This document is provided by the Chemical Portal www.webqc.org D5h point group

Abelian, 8(12) irreducible representations

Subgroups: Cs, C2, C5, D5, C2v, C5v, C5h

Character table

	E	2C5	2(C5)2	5C'2	h	2S5	2(S5)3	5σv	linear, rotations	quadratic
A'1	1	1	1	1	1	1	1	1		x2+y2, z2
A'2	1	1	1	-1	1	1	1	-1	Rz
E'1	2	2cos(2π/5)	2cos(4π/5)	0	2	2cos(2π/5)	2cos(4π/5)	0	(x, y)
E'2	2	2cos(4π/5)	2cos(2π/5)	0	2	2cos(4π/5)	2cos(2π/5)	0		(x2-y2, xy)
A''1	1	1	1	1	-1	-1	-1	-1
A''2	1	1	1	-1	-1	-1	-1	1	z
E''1	2	2cos(2π/5)	2cos(4π/5)	0	-2	-2cos(2π/5)	-2cos(4π/5)	0	(Rx, Ry)	(xz, yz)
E''2	2	2cos(4π>/5)	2cos(2π/5)	0	-2	-2cos(4π/5)	-2cos(2π/5)	0

Product table

	A'1	A'2	E'1	E'2	A''1	A''2	E''1	E''2
A'1	A'1	A'2	E'1	E'2	A''1	A''2	E''1	E''2
A'2	A'2	A'1	E'1	E'2	A''2	A''1	E''1	E''2
E'1	E'1	E'1	A'1+A'2+E'2	E'1+E'2	E''1	E''1	A''1+A''2+E''2	E''1+E''2
E'2	E'2	E'2	E'1+E'2	A'1+A'2+E'2	E''2	E''2	E''1+E''2	A''1+A''2+E''2
A''1	A''1	A''2	E''1	E''2	A'1	A'2	E'1	E'2
A''2	A''2	A''1	E''1	E''2	A'2	A'1	E'1	E'2
E''1	E''1	E''1	A''1+A''2+E''2	E''1+E''2	E'1	E'1	A'1+A'2+E'2	E'1+E'2
E''2	E''2	E''2	E''1+E''2	A''1+A''2+E''2	E'2	E'2	E'1+E'2	A'1+A'2+E'2

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