Character Tables for Common Symmetry Groups - The Cn

Groups

C2EC2  
A11z, Rzx2, y2, z2, xy
B1-1x, y, Rx, Ryyz, xz

C3 EC3C32 ε = exp(2π/3)
A111z, Rzx2 + y2, z2
E{ 1     ε     ε+ }
   1     ε+    ε
(x, y)(Rx, Ry)(x2 - y2, xy)(yz, xz)

C4EC4C2C43  
A1111z, Rzx2 + y2, z2
B1-11-1 x2 - y2, xy
E{ 1   i     -1     -i }
   1   -i     -1     i
(x, y)(Rz, Ry)(yz, xz)

C5EC5C52C53C54 ε = exp (2π/5)
A11111z, Rzx2 + y2, z2
E1{ 1   ε     ε2      ε2+     ε+ }
   1   ε+    ε2+    ε2       ε
(x, y)(Rz, Ry)(yz, xz)
E2{ 1   ε2     ε+     ε      ε2+ }
   1   ε2+    ε      ε+     ε2
 (x2 - y2, xy)

C6EC6C3C2C32C65 ε = exp(2π/6)
A111111z, Rzx2 + y2, z2
B1-11-11-1  
E1{ 1   ε    -ε+    -1    -ε     ε+ }
   1   ε+   -ε     -1   -ε+ε
(x, y)
(Rz, Ry)
(xz, yz)
E2{ 1   -ε+   -ε     1    -ε+    -ε }
   1   -ε     -ε+   1    -ε     -ε+
 (x2 - y2, xy)

Reference: F.A. Cotton, "Chemical Applications of Group Theory," 3rd ed., Wiley-Interscience, NY, 1990.