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Magnetic Point Group Tables of 6/mm'm' (#27.6.105)


Useful data about magnetic point group 6/mm'm'


Number of elements of the group (order): 24
This group is centrosymmetric
This group is not polar
This group is 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 x-y,x,z, +1
mx-my,mx,mz
(
  1  -1  0  
  1  0  0  
  0  0  1
)
 6z
3 -y,x-y,z, +1
-my,mx-my,mz
(
  0  -1  0  
  1  -1  0  
  0  0  1
)
 3z
4 -x,-y,z, +1
-mx,-my,mz
(
  -1  0  0  
  0  -1  0  
  0  0  1
)
 2z
5 -x+y,-x,z, +1
-mx+my,-mx,mz
(
  -1  1  0  
  -1  0  0  
  0  0  1
)
 3z-1
6 y,-x+y,z, +1
my,-mx+my,mz
(
  0  1  0  
  -1  1  0  
  0  0  1
)
 6z-1
7 -x,-y,-z, +1
mx, my, mz
(
  -1  0  0  
  0  -1  0  
  0  0  -1
)
 -1
8 -x+y,-x,-z, +1
mx-my, mx, mz
(
  -1  1  0  
  -1  0  0  
  0  0  -1
)
 -6z
9 y,-x+y,-z, +1
-my, mx-my, mz
(
  0  1  0  
  -1  1  0  
  0  0  -1
)
 -3z
10 x,y,-z, +1
-mx, -my, mz
(
  1  0  0  
  0  1  0  
  0  0  -1
)
 mz
11 x-y,x,-z, +1
-mx+my, -mx, mz
(
  1  -1  0  
  1  0  0  
  0  0  -1
)
 -3z-1
12 -y,x-y,-z, +1
my, -mx+my, mz
(
  0  -1  0  
  1  -1  0  
  0  0  -1
)
 -6z-1
13 x-y,-y,-z, -1
-mx+my, my, mz
(
  1  -1  0  
  0  -1  0  
  0  0  -1
)'
 2x'
14 x,x-y,-z, -1
-mx, -mx+my, mz
(
  1  0  0  
  1  -1  0  
  0  0  -1
)'
 21'
15 y,x,-z, -1
-my, -mx, mz
(
  0  1  0  
  1  0  0  
  0  0  -1
)'
 2xy'
16 -x+y,y,-z, -1
mx-my, -my, mz
(
  -1  1  0  
  0  1  0  
  0  0  -1
)'
 22'
17 -x,-x+y,-z, -1
mx, mx-my, mz
(
  -1  0  0  
  -1  1  0  
  0  0  -1
)'
 2y'
18 -y,-x,-z, -1
my, mx, mz
(
  0  -1  0  
  -1  0  0  
  0  0  -1
)'
 23'
19 -x+y,y,z, -1
-mx+my,my,mz
(
  -1  1  0  
  0  1  0  
  0  0  1
)'
 mx'
20 -x,-x+y,z, -1
-mx,-mx+my,mz
(
  -1  0  0  
  -1  1  0  
  0  0  1
)'
 m1'
21 -y,-x,z, -1
-my,-mx,mz
(
  0  -1  0  
  -1  0  0  
  0  0  1
)'
 mxy'
22 x-y,-y,z, -1
mx-my,-my,mz
(
  1  -1  0  
  0  -1  0  
  0  0  1
)'
 m2'
23 x,x-y,z, -1
mx,mx-my,mz
(
  1  0  0  
  1  -1  0  
  0  0  1
)'
 my'
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/mm'm' (#27.6.105) via MTENSOR


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