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Magnetic Point Group Tables of 4321' (#30.2.113)


Useful data about magnetic point group 4321'


Number of elements of the group (order): 48
This group is not 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 -y,-x,-z, +1
-my,-mx,-mz
(
  0  -1  0  
  -1  0  0  
  0  0  -1  
)
2-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  
)
2xy
17 -x,-z,-y, +1
-mx,-mz,-my
(
  -1  0  0  
  0  0  -1  
  0  -1  0  
)
2-yz
18 -x,z,y, +1
-mx,mz,my
(
  -1  0  0  
  0  0  1  
  0  1  0  
)
2yz
19 x,-z,y, +1
mx,-mz,my
(
  1  0  0  
  0  0  -1  
  0  1  0  
)
4x
20 x,z,-y, +1
mx,mz,-my
(
  1  0  0  
  0  0  1  
  0  -1  0  
)
4x-1
21 -z,-y,-x, +1
-mz,-my,-mx
(
  0  0  -1  
  0  -1  0  
  -1  0  0  
)
2-xz
22 -z,y,x, +1
-mz,my,mx
(
  0  0  -1  
  0  1  0  
  1  0  0  
)
4y-1
23 z,-y,x, +1
mz,-my,mx
(
  0  0  1  
  0  -1  0  
  1  0  0  
)
2xz
24 z,y,-x, +1
mz,my,-mx
(
  0  0  1  
  0  1  0  
  -1  0  0  
)
4y
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  
)'
2x'
27 -x,y,-z, -1
mx, -my, mz
(
  -1  0  0  
  0  1  0  
  0  0  -1  
)'
2y'
28 -x,-y,z, -1
mx, my, -mz
(
  -1  0  0  
  0  -1  0  
  0  0  1  
)'
2z'
29 y,z,x, -1
-my, -mz, -mx
(
  0  1  0  
  0  0  1  
  1  0  0  
)'
3xyz-1'
30 y,-z,-x, -1
-my, mz, mx
(
  0  1  0  
  0  0  -1  
  -1  0  0  
)'
3xy-z'
31 -y,z,-x, -1
my, -mz, mx
(
  0  -1  0  
  0  0  1  
  -1  0  0  
)'
3-xyz'
32 -y,-z,x, -1
my, mz, -mx
(
  0  -1  0  
  0  0  -1  
  1  0  0  
)'
3x-yz'
33 z,x,y, -1
-mz, -mx, -my
(
  0  0  1  
  1  0  0  
  0  1  0  
)'
3xyz'
34 z,-x,-y, -1
-mz, mx, my
(
  0  0  1  
  -1  0  0  
  0  -1  0  
)'
3x-yz-1'
35 -z,x,-y, -1
mz, -mx, my
(
  0  0  -1  
  1  0  0  
  0  -1  0  
)'
3xy-z-1'
36 -z,-x,y, -1
mz, mx, -my
(
  0  0  -1  
  -1  0  0  
  0  1  0  
)'
3-xyz-1'
37 -y,-x,-z, -1
my, mx, mz
(
  0  -1  0  
  -1  0  0  
  0  0  -1  
)'
2-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  
)'
2xy'
41 -x,-z,-y, -1
mx, mz, my
(
  -1  0  0  
  0  0  -1  
  0  -1  0  
)'
2-yz'
42 -x,z,y, -1
mx, -mz, -my
(
  -1  0  0  
  0  0  1  
  0  1  0  
)'
2yz'
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  
)'
2-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  
)'
2xz'
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 4321' (#30.2.113) via MTENSOR


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