Bilbao Crystallographic Server arrow MPOINT - Magnetic Point Group Tables


Magnetic Point Group Tables of m-31' (#29.2.110)


Useful data about magnetic point group m-31'


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 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 -x,-y,-z, -1
-mx,-my,-mz
(
  -1  0  0  
  0  -1  0  
  0  0  -1  
)'
-1'
38 -x,y,z, -1
-mx,my,mz
(
  -1  0  0  
  0  1  0  
  0  0  1  
)'
mx'
39 x,-y,z, -1
mx,-my,mz
(
  1  0  0  
  0  -1  0  
  0  0  1  
)'
my'
40 x,y,-z, -1
mx,my,-mz
(
  1  0  0  
  0  1  0  
  0  0  -1  
)'
mz'
41 -y,-z,-x, -1
-my,-mz,-mx
(
  0  -1  0  
  0  0  -1  
  -1  0  0  
)'
-3xyz-1'
42 -y,z,x, -1
-my,mz,mx
(
  0  -1  0  
  0  0  1  
  1  0  0  
)'
-3xy-z'
43 y,-z,x, -1
my,-mz,mx
(
  0  1  0  
  0  0  -1  
  1  0  0  
)'
-3-xyz'
44 y,z,-x, -1
my,mz,-mx
(
  0  1  0  
  0  0  1  
  -1  0  0  
)'
-3x-yz'
45 -z,-x,-y, -1
-mz,-mx,-my
(
  0  0  -1  
  -1  0  0  
  0  -1  0  
)'
-3xyz'
46 -z,x,y, -1
-mz,mx,my
(
  0  0  -1  
  1  0  0  
  0  1  0  
)'
-3x-yz-1'
47 z,-x,y, -1
mz,-mx,my
(
  0  0  1  
  -1  0  0  
  0  1  0  
)'
-3xy-z-1'
48 z,x,-y, -1
mz,mx,-my
(
  0  0  1  
  1  0  0  
  0  -1  0  
)'
-3-xyz-1'

Subgroups Table

Symmetry-adapted form of material tensors for the magnetic point group m-31' (#29.2.110) via MTENSOR


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