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Magnetic Point Group Tables of 4/mmm1' (#15.2.54)


Useful data about magnetic point group 4/mmm1'


Number of elements of the group (order): 32
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 x,-y,-z, +1
mx,-my,-mz
(
  1  0  0  
  0  -1  0  
  0  0  -1  
)
2x
3 -x,y,-z, +1
-mx,my,-mz
(
  -1  0  0  
  0  1  0  
  0  0  -1  
)
2y
4 -x,-y,z, +1
-mx,-my,mz
(
  -1  0  0  
  0  -1  0  
  0  0  1  
)
2z
5 -y,-x,-z, +1
-my,-mx,-mz
(
  0  -1  0  
  -1  0  0  
  0  0  -1  
)
2-xy
6 -y,x,z, +1
-my,mx,mz
(
  0  -1  0  
  1  0  0  
  0  0  1  
)
4z
7 y,-x,z, +1
my,-mx,mz
(
  0  1  0  
  -1  0  0  
  0  0  1  
)
4z-1
8 y,x,-z, +1
my,mx,-mz
(
  0  1  0  
  1  0  0  
  0  0  -1  
)
2xy
9 -x,-y,-z, +1
mx, my, mz
(
  -1  0  0  
  0  -1  0  
  0  0  -1  
)
-1
10 -x,y,z, +1
mx, -my, -mz
(
  -1  0  0  
  0  1  0  
  0  0  1  
)
mx
11 x,-y,z, +1
-mx, my, -mz
(
  1  0  0  
  0  -1  0  
  0  0  1  
)
my
12 x,y,-z, +1
-mx, -my, mz
(
  1  0  0  
  0  1  0  
  0  0  -1  
)
mz
13 y,x,z, +1
-my, -mx, -mz
(
  0  1  0  
  1  0  0  
  0  0  1  
)
m-xy
14 y,-x,-z, +1
-my, mx, mz
(
  0  1  0  
  -1  0  0  
  0  0  -1  
)
-4z
15 -y,x,-z, +1
my, -mx, mz
(
  0  -1  0  
  1  0  0  
  0  0  -1  
)
-4z-1
16 -y,-x,z, +1
my, mx, -mz
(
  0  -1  0  
  -1  0  0  
  0  0  1  
)
mxy
17 x,y,z, -1
-mx, -my, -mz
(
  1  0  0  
  0  1  0  
  0  0  1  
)'
1'
18 x,-y,-z, -1
-mx, my, mz
(
  1  0  0  
  0  -1  0  
  0  0  -1  
)'
2x'
19 -x,y,-z, -1
mx, -my, mz
(
  -1  0  0  
  0  1  0  
  0  0  -1  
)'
2y'
20 -x,-y,z, -1
mx, my, -mz
(
  -1  0  0  
  0  -1  0  
  0  0  1  
)'
2z'
21 -y,-x,-z, -1
my, mx, mz
(
  0  -1  0  
  -1  0  0  
  0  0  -1  
)'
2-xy'
22 -y,x,z, -1
my, -mx, -mz
(
  0  -1  0  
  1  0  0  
  0  0  1  
)'
4z'
23 y,-x,z, -1
-my, mx, -mz
(
  0  1  0  
  -1  0  0  
  0  0  1  
)'
4z-1'
24 y,x,-z, -1
-my, -mx, mz
(
  0  1  0  
  1  0  0  
  0  0  -1  
)'
2xy'
25 -x,-y,-z, -1
-mx,-my,-mz
(
  -1  0  0  
  0  -1  0  
  0  0  -1  
)'
-1'
26 -x,y,z, -1
-mx,my,mz
(
  -1  0  0  
  0  1  0  
  0  0  1  
)'
mx'
27 x,-y,z, -1
mx,-my,mz
(
  1  0  0  
  0  -1  0  
  0  0  1  
)'
my'
28 x,y,-z, -1
mx,my,-mz
(
  1  0  0  
  0  1  0  
  0  0  -1  
)'
mz'
29 y,x,z, -1
my,mx,mz
(
  0  1  0  
  1  0  0  
  0  0  1  
)'
m-xy'
30 y,-x,-z, -1
my,-mx,-mz
(
  0  1  0  
  -1  0  0  
  0  0  -1  
)'
-4z'
31 -y,x,-z, -1
-my,mx,-mz
(
  0  -1  0  
  1  0  0  
  0  0  -1  
)'
-4z-1'
32 -y,-x,z, -1
-my,-mx,mz
(
  0  -1  0  
  -1  0  0  
  0  0  1  
)'
mxy'

Subgroups Table

Symmetry-adapted form of material tensors for the magnetic point group 4/mmm1' (#15.2.54) via MTENSOR


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