The Dn Groups

D2

  E C2(z) C2(y) C2(x)    
A 1 1 1 1   x2, y2, z2
B1 1 1 -1 -1 z, Rz xy
B2 1 -1 1 -1 y, Ry xz
B3 1 -1 -1 1 x, Rx yz

D3

  E 2C3 3C2    
A1 1 1 1   x2 + y2, z2
A2 1 1 -1 z, Rz  
E 2 -1 0 (x, y) (Rx, Ry) (x2 - y2, xy)(xz, yz)

D4

  E 2C4 C2(=C42) 2C'2 2C''2    
A1 1 1 1 1 1   x2 + y2, z2
A2 1 1 1 -1 -1 z, 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)

D5

  E 2C5 2C52 5C2    
A1 1 1 1 1   x2 + y2, z2
A2 1 1 1 -1 z, Rz  
E1 2 2 cos 72 2 cos 144 0 (x, y)(Rx, Ry) (xz, yz)
E2 2 2 cos 144 2 cos 72 0   (x2 - y2, xy)

D6

  E 2C6 2C3 C2 3C'2 3C''2    
A1 1 1 1 1 1 1   x2 + y2, z2
A2 1 1 1 1 -1 -1 z, 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)