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Magnetic Point Group Tables of m-3m' (#32.4.121)


Useful data about magnetic point group m-3m'


Number of elements of the group (order): 48
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,z,x, +1
my,mz,mx
(
  0  1  0  
  0  0  1  
  1  0  0
)
 3xyz-1
6 y,-z,-x, +1
my,-mz,-mx
(
  0  1  0  
  0  0  -1  
  -1  0  0
)
 3xy-z
7 -y,z,-x, +1
-my,mz,-mx
(
  0  -1  0  
  0  0  1  
  -1  0  0
)
 3-xyz
8 -y,-z,x, +1
-my,-mz,mx
(
  0  -1  0  
  0  0  -1  
  1  0  0
)
 3x-yz
9 z,x,y, +1
mz,mx,my
(
  0  0  1  
  1  0  0  
  0  1  0
)
 3xyz
10 z,-x,-y, +1
mz,-mx,-my
(
  0  0  1  
  -1  0  0  
  0  -1  0
)
 3x-yz-1
11 -z,x,-y, +1
-mz,mx,-my
(
  0  0  -1  
  1  0  0  
  0  -1  0
)
 3xy-z-1
12 -z,-x,y, +1
-mz,-mx,my
(
  0  0  -1  
  -1  0  0  
  0  1  0
)
 3-xyz-1
13 -x,-y,-z, +1
mx, my, mz
(
  -1  0  0  
  0  -1  0  
  0  0  -1
)
 -1
14 -x,y,z, +1
mx, -my, -mz
(
  -1  0  0  
  0  1  0  
  0  0  1
)
 mx
15 x,-y,z, +1
-mx, my, -mz
(
  1  0  0  
  0  -1  0  
  0  0  1
)
 my
16 x,y,-z, +1
-mx, -my, mz
(
  1  0  0  
  0  1  0  
  0  0  -1
)
 mz
17 -y,-z,-x, +1
my, mz, mx
(
  0  -1  0  
  0  0  -1  
  -1  0  0
)
 -3xyz-1
18 -y,z,x, +1
my, -mz, -mx
(
  0  -1  0  
  0  0  1  
  1  0  0
)
 -3xy-z
19 y,-z,x, +1
-my, mz, -mx
(
  0  1  0  
  0  0  -1  
  1  0  0
)
 -3-xyz
20 y,z,-x, +1
-my, -mz, mx
(
  0  1  0  
  0  0  1  
  -1  0  0
)
 -3x-yz
21 -z,-x,-y, +1
mz, mx, my
(
  0  0  -1  
  -1  0  0  
  0  -1  0
)
 -3xyz
22 -z,x,y, +1
mz, -mx, -my
(
  0  0  -1  
  1  0  0  
  0  1  0
)
 -3x-yz-1
23 z,-x,y, +1
-mz, mx, -my
(
  0  0  1  
  -1  0  0  
  0  1  0
)
 -3xy-z-1
24 z,x,-y, +1
-mz, -mx, my
(
  0  0  1  
  1  0  0  
  0  -1  0
)
 -3-xyz-1
25 -y,-x,-z, -1
my, mx, mz
(
  0  -1  0  
  -1  0  0  
  0  0  -1
)'
 2-xy'
26 -y,x,z, -1
my, -mx, -mz
(
  0  -1  0  
  1  0  0  
  0  0  1
)'
 4z'
27 y,-x,z, -1
-my, mx, -mz
(
  0  1  0  
  -1  0  0  
  0  0  1
)'
 4z-1'
28 y,x,-z, -1
-my, -mx, mz
(
  0  1  0  
  1  0  0  
  0  0  -1
)'
 2xy'
29 -x,-z,-y, -1
mx, mz, my
(
  -1  0  0  
  0  0  -1  
  0  -1  0
)'
 2-yz'
30 -x,z,y, -1
mx, -mz, -my
(
  -1  0  0  
  0  0  1  
  0  1  0
)'
 2yz'
31 x,-z,y, -1
-mx, mz, -my
(
  1  0  0  
  0  0  -1  
  0  1  0
)'
 4x'
32 x,z,-y, -1
-mx, -mz, my
(
  1  0  0  
  0  0  1  
  0  -1  0
)'
 4x-1'
33 -z,-y,-x, -1
mz, my, mx
(
  0  0  -1  
  0  -1  0  
  -1  0  0
)'
 2-xz'
34 -z,y,x, -1
mz, -my, -mx
(
  0  0  -1  
  0  1  0  
  1  0  0
)'
 4y-1'
35 z,-y,x, -1
-mz, my, -mx
(
  0  0  1  
  0  -1  0  
  1  0  0
)'
 2xz'
36 z,y,-x, -1
-mz, -my, mx
(
  0  0  1  
  0  1  0  
  -1  0  0
)'
 4y'
37 y,x,z, -1
my,mx,mz
(
  0  1  0  
  1  0  0  
  0  0  1
)'
 m-xy'
38 y,-x,-z, -1
my,-mx,-mz
(
  0  1  0  
  -1  0  0  
  0  0  -1
)'
 -4z'
39 -y,x,-z, -1
-my,mx,-mz
(
  0  -1  0  
  1  0  0  
  0  0  -1
)'
 -4z-1'
40 -y,-x,z, -1
-my,-mx,mz
(
  0  -1  0  
  -1  0  0  
  0  0  1
)'
 mxy'
41 x,z,y, -1
mx,mz,my
(
  1  0  0  
  0  0  1  
  0  1  0
)'
 m-yz'
42 x,-z,-y, -1
mx,-mz,-my
(
  1  0  0  
  0  0  -1  
  0  -1  0
)'
 myz'
43 -x,z,-y, -1
-mx,mz,-my
(
  -1  0  0  
  0  0  1  
  0  -1  0
)'
 -4x'
44 -x,-z,y, -1
-mx,-mz,my
(
  -1  0  0  
  0  0  -1  
  0  1  0
)'
 -4x-1'
45 z,y,x, -1
mz,my,mx
(
  0  0  1  
  0  1  0  
  1  0  0
)'
 m-xz'
46 z,-y,-x, -1
mz,-my,-mx
(
  0  0  1  
  0  -1  0  
  -1  0  0
)'
 -4y-1'
47 -z,y,-x, -1
-mz,my,-mx
(
  0  0  -1  
  0  1  0  
  -1  0  0
)'
 mxz'
48 -z,-y,x, -1
-mz,-my,mx
(
  0  0  -1  
  0  -1  0  
  1  0  0
)'
 -4y'

Subgroups Table

Symmetry-adapted form of material tensors for the magnetic point group m-3m' (#32.4.121) via MTENSOR


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