Bilbao Crystallographic Server arrow MPOINT - Magnetic Point Group Tables


Magnetic Point Group Tables of m-3m.1' (#32.2.119)


Useful data about magnetic point group m-3m.1'


Number of elements of the group (order): 96
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 -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
)
 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,-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
)
 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
49 x,y,z, -1
-mx, -my, -mz
(
  1  0  0  
  0  1  0  
  0  0  1
)'
 1'
50 x,-y,-z, -1
-mx, my, mz
(
  1  0  0  
  0  -1  0  
  0  0  -1
)'
 2x'
51 -x,y,-z, -1
mx, -my, mz
(
  -1  0  0  
  0  1  0  
  0  0  -1
)'
 2y'
52 -x,-y,z, -1
mx, my, -mz
(
  -1  0  0  
  0  -1  0  
  0  0  1
)'
 2z'
53 y,z,x, -1
-my, -mz, -mx
(
  0  1  0  
  0  0  1  
  1  0  0
)'
 3xyz-1'
54 y,-z,-x, -1
-my, mz, mx
(
  0  1  0  
  0  0  -1  
  -1  0  0
)'
 3xy-z'
55 -y,z,-x, -1
my, -mz, mx
(
  0  -1  0  
  0  0  1  
  -1  0  0
)'
 3-xyz'
56 -y,-z,x, -1
my, mz, -mx
(
  0  -1  0  
  0  0  -1  
  1  0  0
)'
 3x-yz'
57 z,x,y, -1
-mz, -mx, -my
(
  0  0  1  
  1  0  0  
  0  1  0
)'
 3xyz'
58 z,-x,-y, -1
-mz, mx, my
(
  0  0  1  
  -1  0  0  
  0  -1  0
)'
 3x-yz-1'
59 -z,x,-y, -1
mz, -mx, my
(
  0  0  -1  
  1  0  0  
  0  -1  0
)'
 3xy-z-1'
60 -z,-x,y, -1
mz, mx, -my
(
  0  0  -1  
  -1  0  0  
  0  1  0
)'
 3-xyz-1'
61 -y,-x,-z, -1
my, mx, mz
(
  0  -1  0  
  -1  0  0  
  0  0  -1
)'
 2-xy'
62 -y,x,z, -1
my, -mx, -mz
(
  0  -1  0  
  1  0  0  
  0  0  1
)'
 4z'
63 y,-x,z, -1
-my, mx, -mz
(
  0  1  0  
  -1  0  0  
  0  0  1
)'
 4z-1'
64 y,x,-z, -1
-my, -mx, mz
(
  0  1  0  
  1  0  0  
  0  0  -1
)'
 2xy'
65 -x,-z,-y, -1
mx, mz, my
(
  -1  0  0  
  0  0  -1  
  0  -1  0
)'
 2-yz'
66 -x,z,y, -1
mx, -mz, -my
(
  -1  0  0  
  0  0  1  
  0  1  0
)'
 2yz'
67 x,-z,y, -1
-mx, mz, -my
(
  1  0  0  
  0  0  -1  
  0  1  0
)'
 4x'
68 x,z,-y, -1
-mx, -mz, my
(
  1  0  0  
  0  0  1  
  0  -1  0
)'
 4x-1'
69 -z,-y,-x, -1
mz, my, mx
(
  0  0  -1  
  0  -1  0  
  -1  0  0
)'
 2-xz'
70 -z,y,x, -1
mz, -my, -mx
(
  0  0  -1  
  0  1  0  
  1  0  0
)'
 4y-1'
71 z,-y,x, -1
-mz, my, -mx
(
  0  0  1  
  0  -1  0  
  1  0  0
)'
 2xz'
72 z,y,-x, -1
-mz, -my, mx
(
  0  0  1  
  0  1  0  
  -1  0  0
)'
 4y'
73 -x,-y,-z, -1
-mx,-my,-mz
(
  -1  0  0  
  0  -1  0  
  0  0  -1
)'
 -1'
74 -x,y,z, -1
-mx,my,mz
(
  -1  0  0  
  0  1  0  
  0  0  1
)'
 mx'
75 x,-y,z, -1
mx,-my,mz
(
  1  0  0  
  0  -1  0  
  0  0  1
)'
 my'
76 x,y,-z, -1
mx,my,-mz
(
  1  0  0  
  0  1  0  
  0  0  -1
)'
 mz'
77 -y,-z,-x, -1
-my,-mz,-mx
(
  0  -1  0  
  0  0  -1  
  -1  0  0
)'
 -3xyz-1'
78 -y,z,x, -1
-my,mz,mx
(
  0  -1  0  
  0  0  1  
  1  0  0
)'
 -3xy-z'
79 y,-z,x, -1
my,-mz,mx
(
  0  1  0  
  0  0  -1  
  1  0  0
)'
 -3-xyz'
80 y,z,-x, -1
my,mz,-mx
(
  0  1  0  
  0  0  1  
  -1  0  0
)'
 -3x-yz'
81 -z,-x,-y, -1
-mz,-mx,-my
(
  0  0  -1  
  -1  0  0  
  0  -1  0
)'
 -3xyz'
82 -z,x,y, -1
-mz,mx,my
(
  0  0  -1  
  1  0  0  
  0  1  0
)'
 -3x-yz-1'
83 z,-x,y, -1
mz,-mx,my
(
  0  0  1  
  -1  0  0  
  0  1  0
)'
 -3xy-z-1'
84 z,x,-y, -1
mz,mx,-my
(
  0  0  1  
  1  0  0  
  0  -1  0
)'
 -3-xyz-1'
85 y,x,z, -1
my,mx,mz
(
  0  1  0  
  1  0  0  
  0  0  1
)'
 m-xy'
86 y,-x,-z, -1
my,-mx,-mz
(
  0  1  0  
  -1  0  0  
  0  0  -1
)'
 -4z'
87 -y,x,-z, -1
-my,mx,-mz
(
  0  -1  0  
  1  0  0  
  0  0  -1
)'
 -4z-1'
88 -y,-x,z, -1
-my,-mx,mz
(
  0  -1  0  
  -1  0  0  
  0  0  1
)'
 mxy'
89 x,z,y, -1
mx,mz,my
(
  1  0  0  
  0  0  1  
  0  1  0
)'
 m-yz'
90 x,-z,-y, -1
mx,-mz,-my
(
  1  0  0  
  0  0  -1  
  0  -1  0
)'
 myz'
91 -x,z,-y, -1
-mx,mz,-my
(
  -1  0  0  
  0  0  1  
  0  -1  0
)'
 -4x'
92 -x,-z,y, -1
-mx,-mz,my
(
  -1  0  0  
  0  0  -1  
  0  1  0
)'
 -4x-1'
93 z,y,x, -1
mz,my,mx
(
  0  0  1  
  0  1  0  
  1  0  0
)'
 m-xz'
94 z,-y,-x, -1
mz,-my,-mx
(
  0  0  1  
  0  -1  0  
  -1  0  0
)'
 -4y-1'
95 -z,y,-x, -1
-mz,my,-mx
(
  0  0  -1  
  0  1  0  
  -1  0  0
)'
 mxz'
96 -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.1' (#32.2.119) via MTENSOR


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