Symmetry operations for the point group C6h (6/m)

1 : x,y,z           => 1                   

[[ 1.  0.  0.]
 [ 0.  1.  0.]
 [ 0.  0.  1.]]

2 : -y,x-y,z        => 3+ [ 0 0 1 ]        

[[ 0. -1.  0.]
 [ 1. -1.  0.]
 [ 0.  0.  1.]]

3 : -x+y,-x,z       => 3- [ 0 0 1 ]        

[[-1.  1.  0.]
 [-1.  0.  0.]
 [ 0.  0.  1.]]

4 : -x,-y,z         => 2 [ 0 0 1 ]         

[[-1.  0.  0.]
 [ 0. -1.  0.]
 [ 0.  0.  1.]]

5 : y,-x+y,z        => 6- [ 0 0 1 ]        

[[ 0.  1.  0.]
 [-1.  1.  0.]
 [ 0.  0.  1.]]

6 : x-y,x,z         => 6+ [ 0 0 1 ]        

[[ 1. -1.  0.]
 [ 1.  0.  0.]
 [ 0.  0.  1.]]

7 : -x,-y,-z        => -1                  

[[-1.  0.  0.]
 [ 0. -1.  0.]
 [ 0.  0. -1.]]

8 : y,-x+y,-z       => -3+ [ 0 0 1 ]       

[[ 0.  1.  0.]
 [-1.  1.  0.]
 [ 0.  0. -1.]]

9 : x-y,x,-z        => -3- [ 0 0 1 ]       

[[ 1. -1.  0.]
 [ 1.  0.  0.]
 [ 0.  0. -1.]]

10: x,y,-z          => m [ 0 0 1 ]         

[[ 1.  0.  0.]
 [ 0.  1.  0.]
 [ 0.  0. -1.]]

11: -y,x-y,-z       => -6- [ 0 0 1 ]       

[[ 0. -1.  0.]
 [ 1. -1.  0.]
 [ 0.  0. -1.]]

12: -x+y,-x,-z      => -6+ [ 0 0 1 ]       

[[-1.  1.  0.]
 [-1.  0.  0.]
 [ 0.  0. -1.]]

Irreducible representations for the point group C6h  (6/m)
Irrep Ag ( dimension  1 )
1 : 1.0                 

2 : 1.0                 

3 : 1.0                 

4 : 1.0                 

5 : 1.0                 

6 : 1.0                 

7 : 1.0                 

8 : 1.0                 

9 : 1.0                 

10: 1.0                 

11: 1.0                 

12: 1.0                 

Irrep Au ( dimension  1 )
1 : 1.0                 

2 : 1.0                 

3 : 1.0                 

4 : 1.0                 

5 : 1.0                 

6 : 1.0                 

7 : -1.0                

8 : -1.0                

9 : -1.0                

10: -1.0                

11: -1.0                

12: -1.0                

Irrep Bg ( dimension  1 )
1 : 1.0                 

2 : 1.0                 

3 : 1.0                 

4 : -1.0                

5 : -1.0                

6 : -1.0                

7 : 1.0                 

8 : 1.0                 

9 : 1.0                 

10: -1.0                

11: -1.0                

12: -1.0                

Irrep Bu ( dimension  1 )
1 : 1.0                 

2 : 1.0                 

3 : 1.0                 

4 : -1.0                

5 : -1.0                

6 : -1.0                

7 : -1.0                

8 : -1.0                

9 : -1.0                

10: 1.0                 

11: 1.0                 

12: 1.0                 

Irrep E2g2 ( dimension  1 )
1 : 1.0                 

2 : (-0.5+0.86603j)     

3 : (-0.5-0.86603j)     

4 : 1.0                 

5 : (-0.5+0.86603j)     

6 : (-0.5-0.86603j)     

7 : 1.0                 

8 : (-0.5+0.86603j)     

9 : (-0.5-0.86603j)     

10: 1.0                 

11: (-0.5+0.86603j)     

12: (-0.5-0.86603j)     

Irrep E2u2 ( dimension  1 )
1 : 1.0                 

2 : (-0.5+0.86603j)     

3 : (-0.5-0.86603j)     

4 : 1.0                 

5 : (-0.5+0.86603j)     

6 : (-0.5-0.86603j)     

7 : -1.0                

8 : (0.5-0.86603j)      

9 : (0.5+0.86603j)      

10: -1.0                

11: (0.5-0.86603j)      

12: (0.5+0.86603j)      

Irrep E1g1 ( dimension  1 )
1 : 1.0                 

2 : (-0.5+0.86603j)     

3 : (-0.5-0.86603j)     

4 : -1.0                

5 : (0.5-0.86603j)      

6 : (0.5+0.86603j)      

7 : 1.0                 

8 : (-0.5+0.86603j)     

9 : (-0.5-0.86603j)     

10: -1.0                

11: (0.5-0.86603j)      

12: (0.5+0.86603j)      

Irrep E1u1 ( dimension  1 )
1 : 1.0                 

2 : (-0.5+0.86603j)     

3 : (-0.5-0.86603j)     

4 : -1.0                

5 : (0.5-0.86603j)      

6 : (0.5+0.86603j)      

7 : -1.0                

8 : (0.5-0.86603j)      

9 : (0.5+0.86603j)      

10: 1.0                 

11: (-0.5+0.86603j)     

12: (-0.5-0.86603j)     

Irrep E2g1 ( dimension  1 )
1 : 1.0                 

2 : (-0.5-0.86603j)     

3 : (-0.5+0.86603j)     

4 : 1.0                 

5 : (-0.5-0.86603j)     

6 : (-0.5+0.86603j)     

7 : 1.0                 

8 : (-0.5-0.86603j)     

9 : (-0.5+0.86603j)     

10: 1.0                 

11: (-0.5-0.86603j)     

12: (-0.5+0.86603j)     

Irrep E2u1 ( dimension  1 )
1 : 1.0                 

2 : (-0.5-0.86603j)     

3 : (-0.5+0.86603j)     

4 : 1.0                 

5 : (-0.5-0.86603j)     

6 : (-0.5+0.86603j)     

7 : -1.0                

8 : (0.5+0.86603j)      

9 : (0.5-0.86603j)      

10: -1.0                

11: (0.5+0.86603j)      

12: (0.5-0.86603j)      

Irrep E1g2 ( dimension  1 )
1 : 1.0                 

2 : (-0.5-0.86603j)     

3 : (-0.5+0.86603j)     

4 : -1.0                

5 : (0.5+0.86603j)      

6 : (0.5-0.86603j)      

7 : 1.0                 

8 : (-0.5-0.86603j)     

9 : (-0.5+0.86603j)     

10: -1.0                

11: (0.5+0.86603j)      

12: (0.5-0.86603j)      

Irrep E1u2 ( dimension  1 )
1 : 1.0                 

2 : (-0.5-0.86603j)     

3 : (-0.5+0.86603j)     

4 : -1.0                

5 : (0.5+0.86603j)      

6 : (0.5-0.86603j)      

7 : -1.0                

8 : (0.5+0.86603j)      

9 : (0.5-0.86603j)      

10: 1.0                 

11: (-0.5-0.86603j)     

12: (-0.5+0.86603j)     

