Symmetry operations for the point group D6h (6/mmm)
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 : y,x,-z          => 2 [ 1 1 0 ]         

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

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

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

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

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

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

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

11: -x+y,y,-z       => 2 [ 0.5 1 0 ]       

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

12: x,x-y,-z        => 2 [ 1 0.5 0 ]       

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

23: x-y,-y,z        => m [ 0.5 1 0 ]       

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

24: -x,-x+y,z       => m [ 1 0.5 0 ]       

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

Irreducible representations for the point group D6h (6/mmm)
Irrep A1g ( 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                 

13: 1.0                 

14: 1.0                 

15: 1.0                 

16: 1.0                 

17: 1.0                 

18: 1.0                 

19: 1.0                 

20: 1.0                 

21: 1.0                 

22: 1.0                 

23: 1.0                 

24: 1.0                 

Irrep A1u ( 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                 

13: -1.0                

14: -1.0                

15: -1.0                

16: -1.0                

17: -1.0                

18: -1.0                

19: -1.0                

20: -1.0                

21: -1.0                

22: -1.0                

23: -1.0                

24: -1.0                

Irrep A2g ( 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                

13: 1.0                 

14: 1.0                 

15: 1.0                 

16: 1.0                 

17: 1.0                 

18: 1.0                 

19: -1.0                

20: -1.0                

21: -1.0                

22: -1.0                

23: -1.0                

24: -1.0                

Irrep A2u ( 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                

13: -1.0                

14: -1.0                

15: -1.0                

16: -1.0                

17: -1.0                

18: -1.0                

19: 1.0                 

20: 1.0                 

21: 1.0                 

22: 1.0                 

23: 1.0                 

24: 1.0                 

Irrep B1g ( 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                

13: 1.0                 

14: 1.0                 

15: 1.0                 

16: -1.0                

17: -1.0                

18: -1.0                

19: 1.0                 

20: 1.0                 

21: 1.0                 

22: -1.0                

23: -1.0                

24: -1.0                

Irrep B1u ( 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                

13: -1.0                

14: -1.0                

15: -1.0                

16: 1.0                 

17: 1.0                 

18: 1.0                 

19: -1.0                

20: -1.0                

21: -1.0                

22: 1.0                 

23: 1.0                 

24: 1.0                 

Irrep B2g ( 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                 

13: 1.0                 

14: 1.0                 

15: 1.0                 

16: -1.0                

17: -1.0                

18: -1.0                

19: -1.0                

20: -1.0                

21: -1.0                

22: 1.0                 

23: 1.0                 

24: 1.0                 

Irrep B2u ( 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                 

13: -1.0                

14: -1.0                

15: -1.0                

16: 1.0                 

17: 1.0                 

18: 1.0                 

19: 1.0                 

20: 1.0                 

21: 1.0                 

22: -1.0                

23: -1.0                

24: -1.0                

Irrep E2u ( dimension  2 )
1 :
[[ 1.  0.]
 [ 0.  1.]]

2 :
[[-0.5+0.86603j  0. +0.j     ]
 [ 0. +0.j      -0.5-0.86603j]]

3 :
[[-0.5-0.86603j  0. +0.j     ]
 [ 0. +0.j      -0.5+0.86603j]]

4 :
[[ 1.  0.]
 [ 0.  1.]]

5 :
[[-0.5+0.86603j  0. +0.j     ]
 [ 0. +0.j      -0.5-0.86603j]]

6 :
[[-0.5-0.86603j  0. +0.j     ]
 [ 0. +0.j      -0.5+0.86603j]]

7 :
[[ 0.  1.]
 [ 1.  0.]]

8 :
[[ 0. +0.j      -0.5-0.86603j]
 [-0.5+0.86603j  0. +0.j     ]]

9 :
[[ 0. +0.j      -0.5+0.86603j]
 [-0.5-0.86603j  0. +0.j     ]]

10:
[[ 0.  1.]
 [ 1.  0.]]

11:
[[ 0. +0.j      -0.5-0.86603j]
 [-0.5+0.86603j  0. +0.j     ]]

12:
[[ 0. +0.j      -0.5+0.86603j]
 [-0.5-0.86603j  0. +0.j     ]]

13:
[[-1.  0.]
 [ 0. -1.]]

14:
[[ 0.5-0.86603j  0. +0.j     ]
 [ 0. +0.j       0.5+0.86603j]]

15:
[[ 0.5+0.86603j  0. +0.j     ]
 [ 0. +0.j       0.5-0.86603j]]

16:
[[-1.  0.]
 [ 0. -1.]]

17:
[[ 0.5-0.86603j  0. +0.j     ]
 [ 0. +0.j       0.5+0.86603j]]

18:
[[ 0.5+0.86603j  0. +0.j     ]
 [ 0. +0.j       0.5-0.86603j]]

19:
[[ 0. -1.]
 [-1.  0.]]

20:
[[ 0. +0.j       0.5+0.86603j]
 [ 0.5-0.86603j  0. +0.j     ]]

21:
[[ 0. +0.j       0.5-0.86603j]
 [ 0.5+0.86603j  0. +0.j     ]]

22:
[[ 0. -1.]
 [-1.  0.]]

23:
[[ 0. +0.j       0.5+0.86603j]
 [ 0.5-0.86603j  0. +0.j     ]]

24:
[[ 0. +0.j       0.5-0.86603j]
 [ 0.5+0.86603j  0. +0.j     ]]

Irrep E2g ( dimension  2 )
1 :
[[ 1.  0.]
 [ 0.  1.]]

2 :
[[-0.5+0.86603j  0. +0.j     ]
 [ 0. +0.j      -0.5-0.86603j]]

3 :
[[-0.5-0.86603j  0. +0.j     ]
 [ 0. +0.j      -0.5+0.86603j]]

4 :
[[ 1.  0.]
 [ 0.  1.]]

5 :
[[-0.5+0.86603j  0. +0.j     ]
 [ 0. +0.j      -0.5-0.86603j]]

6 :
[[-0.5-0.86603j  0. +0.j     ]
 [ 0. +0.j      -0.5+0.86603j]]

7 :
[[ 0.  1.]
 [ 1.  0.]]

8 :
[[ 0. +0.j      -0.5-0.86603j]
 [-0.5+0.86603j  0. +0.j     ]]

9 :
[[ 0. +0.j      -0.5+0.86603j]
 [-0.5-0.86603j  0. +0.j     ]]

10:
[[ 0.  1.]
 [ 1.  0.]]

11:
[[ 0. +0.j      -0.5-0.86603j]
 [-0.5+0.86603j  0. +0.j     ]]

12:
[[ 0. +0.j      -0.5+0.86603j]
 [-0.5-0.86603j  0. +0.j     ]]

13:
[[ 1.  0.]
 [ 0.  1.]]

14:
[[-0.5+0.86603j  0. +0.j     ]
 [ 0. +0.j      -0.5-0.86603j]]

15:
[[-0.5-0.86603j  0. +0.j     ]
 [ 0. +0.j      -0.5+0.86603j]]

16:
[[ 1.  0.]
 [ 0.  1.]]

17:
[[-0.5+0.86603j  0. +0.j     ]
 [ 0. +0.j      -0.5-0.86603j]]

18:
[[-0.5-0.86603j  0. +0.j     ]
 [ 0. +0.j      -0.5+0.86603j]]

19:
[[ 0.  1.]
 [ 1.  0.]]

20:
[[ 0. +0.j      -0.5-0.86603j]
 [-0.5+0.86603j  0. +0.j     ]]

21:
[[ 0. +0.j      -0.5+0.86603j]
 [-0.5-0.86603j  0. +0.j     ]]

22:
[[ 0.  1.]
 [ 1.  0.]]

23:
[[ 0. +0.j      -0.5-0.86603j]
 [-0.5+0.86603j  0. +0.j     ]]

24:
[[ 0. +0.j      -0.5+0.86603j]
 [-0.5-0.86603j  0. +0.j     ]]

Irrep E1u ( dimension  2 )
1 :
[[ 1.  0.]
 [ 0.  1.]]

2 :
[[-0.5+0.86603j  0. +0.j     ]
 [ 0. +0.j      -0.5-0.86603j]]

3 :
[[-0.5-0.86603j  0. +0.j     ]
 [ 0. +0.j      -0.5+0.86603j]]

4 :
[[-1.  0.]
 [ 0. -1.]]

5 :
[[ 0.5-0.86603j  0. +0.j     ]
 [ 0. +0.j       0.5+0.86603j]]

6 :
[[ 0.5+0.86603j  0. +0.j     ]
 [ 0. +0.j       0.5-0.86603j]]

7 :
[[ 0.  1.]
 [ 1.  0.]]

8 :
[[ 0. +0.j      -0.5-0.86603j]
 [-0.5+0.86603j  0. +0.j     ]]

9 :
[[ 0. +0.j      -0.5+0.86603j]
 [-0.5-0.86603j  0. +0.j     ]]

10:
[[ 0. -1.]
 [-1.  0.]]

11:
[[ 0. +0.j       0.5+0.86603j]
 [ 0.5-0.86603j  0. +0.j     ]]

12:
[[ 0. +0.j       0.5-0.86603j]
 [ 0.5+0.86603j  0. +0.j     ]]

13:
[[-1.  0.]
 [ 0. -1.]]

14:
[[ 0.5-0.86603j  0. +0.j     ]
 [ 0. +0.j       0.5+0.86603j]]

15:
[[ 0.5+0.86603j  0. +0.j     ]
 [ 0. +0.j       0.5-0.86603j]]

16:
[[ 1.  0.]
 [ 0.  1.]]

17:
[[-0.5+0.86603j  0. +0.j     ]
 [ 0. +0.j      -0.5-0.86603j]]

18:
[[-0.5-0.86603j  0. +0.j     ]
 [ 0. +0.j      -0.5+0.86603j]]

19:
[[ 0. -1.]
 [-1.  0.]]

20:
[[ 0. +0.j       0.5+0.86603j]
 [ 0.5-0.86603j  0. +0.j     ]]

21:
[[ 0. +0.j       0.5-0.86603j]
 [ 0.5+0.86603j  0. +0.j     ]]

22:
[[ 0.  1.]
 [ 1.  0.]]

23:
[[ 0. +0.j      -0.5-0.86603j]
 [-0.5+0.86603j  0. +0.j     ]]

24:
[[ 0. +0.j      -0.5+0.86603j]
 [-0.5-0.86603j  0. +0.j     ]]

Irrep E1g ( dimension  2 )
1 :
[[ 1.  0.]
 [ 0.  1.]]

2 :
[[-0.5+0.86603j  0. +0.j     ]
 [ 0. +0.j      -0.5-0.86603j]]

3 :
[[-0.5-0.86603j  0. +0.j     ]
 [ 0. +0.j      -0.5+0.86603j]]

4 :
[[-1.  0.]
 [ 0. -1.]]

5 :
[[ 0.5-0.86603j  0. +0.j     ]
 [ 0. +0.j       0.5+0.86603j]]

6 :
[[ 0.5+0.86603j  0. +0.j     ]
 [ 0. +0.j       0.5-0.86603j]]

7 :
[[ 0.  1.]
 [ 1.  0.]]

8 :
[[ 0. +0.j      -0.5-0.86603j]
 [-0.5+0.86603j  0. +0.j     ]]

9 :
[[ 0. +0.j      -0.5+0.86603j]
 [-0.5-0.86603j  0. +0.j     ]]

10:
[[ 0. -1.]
 [-1.  0.]]

11:
[[ 0. +0.j       0.5+0.86603j]
 [ 0.5-0.86603j  0. +0.j     ]]

12:
[[ 0. +0.j       0.5-0.86603j]
 [ 0.5+0.86603j  0. +0.j     ]]

13:
[[ 1.  0.]
 [ 0.  1.]]

14:
[[-0.5+0.86603j  0. +0.j     ]
 [ 0. +0.j      -0.5-0.86603j]]

15:
[[-0.5-0.86603j  0. +0.j     ]
 [ 0. +0.j      -0.5+0.86603j]]

16:
[[-1.  0.]
 [ 0. -1.]]

17:
[[ 0.5-0.86603j  0. +0.j     ]
 [ 0. +0.j       0.5+0.86603j]]

18:
[[ 0.5+0.86603j  0. +0.j     ]
 [ 0. +0.j       0.5-0.86603j]]

19:
[[ 0.  1.]
 [ 1.  0.]]

20:
[[ 0. +0.j      -0.5-0.86603j]
 [-0.5+0.86603j  0. +0.j     ]]

21:
[[ 0. +0.j      -0.5+0.86603j]
 [-0.5-0.86603j  0. +0.j     ]]

22:
[[ 0. -1.]
 [-1.  0.]]

23:
[[ 0. +0.j       0.5+0.86603j]
 [ 0.5-0.86603j  0. +0.j     ]]

24:
[[ 0. +0.j       0.5-0.86603j]
 [ 0.5+0.86603j  0. +0.j     ]]

