This document is provided by the Chemical Portal www.webqc.org S_{8} point group 
Abelian, 5(8) irreducible representations 
Subgroups: C_{2}, C_{4} 
E  S_{8}  C_{4} (z)  (S_{8})^{3}  C_{2}  (S_{8})^{5}  (C_{4})^{3}  (S_{8})^{7}  linear, rotations 
quadratic  

A  1  1  1  1  1  1  1  1  R_{z}  x^{2}+y^{2}, z^{2} 
B  1  1  1  1  1  1  1  1  z  
E_{1}  1 1 
e e^{*}  i i  e^{*} e  1 1  e e^{*}  i i  e^{*} e  x+iy xiy 

E_{2}  1 1 
i i  1 1  i i  1 1  i i  1 1  i i  (x^{2}y^{2}, xy)  
E_{3}  1 1 
e e^{*}  i i  e^{*} e  1 1  e e^{*}  i i  e^{*} e  R_{x}+iR_{y} R_{x}iR_{y} 
(xz, yz) 
A_{}  B_{}  E_{1}  E_{2}  E_{3}  

A_{}  A_{}  B_{}  E_{1}  E_{2}  E_{3} 
B_{}  B_{}  A_{}  E_{3}  E_{2}  E_{1} 
E_{1}  E_{1}  E_{3}  2A_{}+E_{2}  E_{1}+E_{3}  2B_{}+E_{2} 
E_{2}  E_{2}  E_{2}  E_{1}+E_{3}  2A_{}+2B_{}  E_{1}+E_{3} 
E_{3}  E_{3}  E_{1}  2B_{}+E_{2}  E_{1}+E_{3}  2A_{}+E_{2} 