The Cnv Groups

C2v

  E C2 sv(xz) sv(yz)    
A1 1 1 1 1 z x2, y2, z2
A2 1 1 -1 -1 Rz xy
B1 1 -1 1 -1 x, Ry xz
B2 1 -1 -1 1 y, Rx yz

C3v

  E 2C3 3sv    
A1 1 1 1 z x2 + y2, z2
A2 1 1 -1 Rz  
E 2 -1 0 (x, y) (Rx, Ry) (x2 - y2, xy) (xz, yz)

C4v

  E 2C4 C2 2sv 2sd    
A1 1 1 1 1 1 z x2 + y2, z2
A2 1 1 1 -1 -1 Rz  
B1 1 -1 1 1 -1   x2 - y2
B2 1 -1 1 -1 1   xy
E 2 0 -2 0 0 (x, y) (Rx, Ry) (xz, yz)

C5v

  E 2C5 2C52 5sv    
A1 1 1 1 1 z x2 + y2, z2
A2 1 1 1 -1 Rz  
E1 2 2 cos 72* 2 cos 144* 0 (x,y) (Rx, Ry) (xy, yz)
E2 2 2 cos 144* 2 cos 72* 0   (x2 - y2, xy)

C6v

  E 2C6 2C3 C2 3sv 3sd    
A1 1 1 1 1 1 1 z x2 + y2, z2
A2 1 1 1 1 -1 -1 Rz  
B1 1 -1 1 -1 1 -1    
B2 1 -1 1 -1 -1 1    
E1 2 1 -1 -2 0 0 (x,y) (Rx, Ry) (xz, yz)
E2 2 -1 -1 2 0 0   (x2 - y2, xy)