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

A_{g}  1  1  1  1  1  1  1  1  1  1  R_{z}  z^{2}, x^{2}+y^{2} 
E_{1g}  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_{2g}  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_{u}  1  1  1  1  1  1  1  1  1  1  z  
E_{1u}  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_{2u}  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} 