This document is provided by the Chemical Portal www.webqc.org C_{5h} point group 
Abelian, 6(10) irreducible representations 
Subgroups: C_{s}, C_{5} 
E  C_{5}  (C_{5})^{2}  (C_{5})^{3}  (C_{5})^{4}  σ_{h}  S_{5}  (S_{5})^{7}  (S_{5})^{3}  (S_{5})^{9}  linear, rotations 
quadratic  

A'  1  1  1  1  1  1  1  1  1  1  R_{z}  x^{2}+y^{2}, z^{2} 
E'_{1}  1 1 
e e^{*} 
e^{2} e^{2*} 
e^{2*} e^{2} 
e^{*} e 
1 1 
e e^{*}  e^{2} e^{2*}  e^{2*} e^{2}  e^{*} e  x+iy xiy 

E'_{2}  1 1 
e^{2} e^{2*} 
e^{*} e 
e e^{*} 
e^{2*} e^{2} 
1 1 
e^{2} e^{2*}  e^{*} e  e e^{*}  e^{2*} e^{2}  (x^{2}y^{2}, xy)  
A''  1  1  1  1  1  1  1  1  1  1  z  
E''_{1}  1 1 
e e^{*} 
e^{2} e^{2*} 
e^{2*} e^{2} 
e^{*} e 
1 1 
e e^{*}  e^{2} e^{2*}  e^{2*} e^{2}  e^{*} e  R_{x}+iR_{y} R_{x}iR_{y} 
(xz, yz) 
E''_{2}  1 1 
e^{2} e^{2*} 
e^{*} e 
e e^{*} 
e^{2*} e^{2} 
1 1 
e^{2} e^{2*}  e^{*} e  e e^{*}  e^{2*} e^{2} 
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'} 