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Magnetic Point Group Tables of 6'/mmm' (#27.4.103)


Useful data about magnetic point group 6'/mmm'


Number of elements of the group (order): 24
This group is centrosymmetric
This group is not polar
This group is not compatible with ferromagnetism


Symmetry operations of the group


N (x,y,z) form matrix form Seitz symbol
1 x,y,z, +1
mx,my,mz
(
  1  0  0  
  0  1  0  
  0  0  1
)
 1
2 -y,x-y,z, +1
-my,mx-my,mz
(
  0  -1  0  
  1  -1  0  
  0  0  1
)
 3z
3 -x+y,-x,z, +1
-mx+my,-mx,mz
(
  -1  1  0  
  -1  0  0  
  0  0  1
)
 3z-1
4 x,x-y,-z, +1
mx,mx-my,-mz
(
  1  0  0  
  1  -1  0  
  0  0  -1
)
 21
5 -x+y,y,-z, +1
-mx+my,my,-mz
(
  -1  1  0  
  0  1  0  
  0  0  -1
)
 22
6 -y,-x,-z, +1
-my,-mx,-mz
(
  0  -1  0  
  -1  0  0  
  0  0  -1
)
 23
7 -x+y,-x,-z, +1
mx-my, mx, mz
(
  -1  1  0  
  -1  0  0  
  0  0  -1
)
 -6z
8 x,y,-z, +1
-mx, -my, mz
(
  1  0  0  
  0  1  0  
  0  0  -1
)
 mz
9 -y,x-y,-z, +1
my, -mx+my, mz
(
  0  -1  0  
  1  -1  0  
  0  0  -1
)
 -6z-1
10 -x+y,y,z, +1
mx-my, -my, -mz
(
  -1  1  0  
  0  1  0  
  0  0  1
)
 mx
11 -y,-x,z, +1
my, mx, -mz
(
  0  -1  0  
  -1  0  0  
  0  0  1
)
 mxy
12 x,x-y,z, +1
-mx, -mx+my, -mz
(
  1  0  0  
  1  -1  0  
  0  0  1
)
 my
13 x-y,x,z, -1
-mx+my, -mx, -mz
(
  1  -1  0  
  1  0  0  
  0  0  1
)'
 6z'
14 -x,-y,z, -1
mx, my, -mz
(
  -1  0  0  
  0  -1  0  
  0  0  1
)'
 2z'
15 y,-x+y,z, -1
-my, mx-my, -mz
(
  0  1  0  
  -1  1  0  
  0  0  1
)'
 6z-1'
16 x-y,-y,-z, -1
-mx+my, my, mz
(
  1  -1  0  
  0  -1  0  
  0  0  -1
)'
 2x'
17 y,x,-z, -1
-my, -mx, mz
(
  0  1  0  
  1  0  0  
  0  0  -1
)'
 2xy'
18 -x,-x+y,-z, -1
mx, mx-my, mz
(
  -1  0  0  
  -1  1  0  
  0  0  -1
)'
 2y'
19 -x,-y,-z, -1
-mx,-my,-mz
(
  -1  0  0  
  0  -1  0  
  0  0  -1
)'
 -1'
20 y,-x+y,-z, -1
my,-mx+my,-mz
(
  0  1  0  
  -1  1  0  
  0  0  -1
)'
 -3z'
21 x-y,x,-z, -1
mx-my,mx,-mz
(
  1  -1  0  
  1  0  0  
  0  0  -1
)'
 -3z-1'
22 -x,-x+y,z, -1
-mx,-mx+my,mz
(
  -1  0  0  
  -1  1  0  
  0  0  1
)'
 m1'
23 x-y,-y,z, -1
mx-my,-my,mz
(
  1  -1  0  
  0  -1  0  
  0  0  1
)'
 m2'
24 y,x,z, -1
my,mx,mz
(
  0  1  0  
  1  0  0  
  0  0  1
)'
 m3'

Subgroups Table

Symmetry-adapted form of material tensors for the magnetic point group 6'/mmm' (#27.4.103) via MTENSOR


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