Character Tables for Common Symmetry Groups - The Cnv

Groups

C2vEC2σv(xz)σv(yz)  
A11111zx2, y2, z2
A211-1-1Rzxy
B11-11-1x, Ryxz
B21-1-11y, Rxyz

C3vE2C3v  
A1111zx2 + y2, z2
A211-1Rz 
E2-10(x, y)(Rx, Ry)(x2 - y2, xy)(xz, yz)

C4vE2C4C2vd  
A111111zx2 + y2, z2
A2111-1-1Rz 
B11-111-1 x2 - y2
B21-11-11 xy
E20-200(x, y)(Rx, Ry)(xz, yz)

C5vE2C/52C52v  
A11111zx2 + y2, z2
A2111-1Rz 
E122cos72°2cos144°0(x, y)(Rx, Ry)(xz, yz
E222cos144°2cos72°0 (x2 - y2, xy)

C6vE2C/62C3C2vd  
A1111111zx2 + y2, z2
A21111-1-1Rz 
B1-111-11-1  
B21-11-1-11  
E121-1-200(x, y)(Rx, Ry)(xz, yz)
E22-1-1200 (x2 - y2, xy)

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