c5h - Point Group Symmetry Character Tables - Chemistry Online Education

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Linear
C_∞v
D_∞h

C_5h Point Group

Abelian, 6(10) irreducible representations

Subgroups of C_5h point group: C_s, C₅

Character table for C_5h point group

	E	C₅	(C₅)²	(C₅)³	(C₅)⁴	σ_h	S₅	(S₅)⁷	(S₅)³	(S₅)⁹	linear, rotations	quadratic
A'	1	1	1	1	1	1	1	1	1	1	R_z	x²+y², z²
E'₁	1 1	e e^*	e² e^2*	e^2* e²	e^* e	1 1	e e^*	e² e^2*	e^2* e²	e^* e	x+iy x-iy
E'₂	1 1	e² e^2*	e^* e	e e^*	e^2* e²	1 1	e² e^2*	e^* e	e e^*	e^2* e²		(x²-y², xy)
A''	1	1	1	1	1	-1	-1	-1	-1	-1	z
E''₁	1 1	e e^*	e² e^2*	e^2* e²	e^* e	-1 -1	-e -e^*	-e² -e^2*	-e^2* -e²	-e^* -e	R_x+iR_y R_x-iR_y	(xz, yz)
E''₂	1 1	e² e^2*	e^* e	e e^*	e^2* e²	-1 -1	-e² -e^2*	-e^* -e	-e -e^*	-e^2* -e²

Product table for C_5h point group

	A'	E_1'	E_2'	A''	E_1''	E_2''
A'	A'	E_1'	E_2'	A''	E_1''	E_2''
E_1'	E_1'	2A'+E_2'	E_1'+E_2'	E_1''	2A''+E_2''	E_1''+E_2''
E_2'	E_2'	E_1'+E_2'	2A'+E_1'	E_2''	E_1''+E_2''	2A''+E_1''
A''	A''	E_1''	E_2''	A'	E_1'	E_2'
E_1''	E_1''	2A''+E_2''	E_1''+E_2''	E_1'	2A'+E_2'	E_1'+E_2'
E_2''	E_2''	E_1''+E_2''	2A''+E_1''	E_2'	E_1'+E_2'	2A'+E_1'

Printable: character table for C_5h product table for C_5h C_5h point group