This document is provided by the Chemical Portal www.webqc.org D_{4} point group 
not Abelian, 5(6) irreducible representations 
Subgroups: C_{2}, C_{4}, D_{2} 
E  2C_{4} (z)  C_{2} (z)  2C'_{2}  2C''_{2}  rotations 
functions 


A_{1}  1  1  1  1  1  x^{2}+y^{2}, z^{2}  
A_{2}  1  1  1  1  1  z, R_{z}  
B_{1}  1  1  1  1  1  x^{2}y^{2}  
B_{2}  1  1  1  1  1  xy  
E  2  0  2  0  0  (x, y) (R_{x}, R_{y})  (xz, yz) 
A_{1}  A_{2}  B_{1}  B_{2}  E_{}  

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