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Magnetic Point Group Tables of 6/mmm (#27.1.100)


Useful data about magnetic point group 6/mmm


Number of elements of the group (order): 24
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,x,z, +1
mx-my,mx,mz
(
  1  -1  0  
  1  0  0  
  0  0  1  
)
6z
3 -y,x-y,z, +1
-my,mx-my,mz
(
  0  -1  0  
  1  -1  0  
  0  0  1  
)
3z
4 -x,-y,z, +1
-mx,-my,mz
(
  -1  0  0  
  0  -1  0  
  0  0  1  
)
2z
5 -x+y,-x,z, +1
-mx+my,-mx,mz
(
  -1  1  0  
  -1  0  0  
  0  0  1  
)
3z-1
6 y,-x+y,z, +1
my,-mx+my,mz
(
  0  1  0  
  -1  1  0  
  0  0  1  
)
6z-1
7 x-y,-y,-z, +1
mx-my,-my,-mz
(
  1  -1  0  
  0  -1  0  
  0  0  -1  
)
2x
8 x,x-y,-z, +1
mx,mx-my,-mz
(
  1  0  0  
  1  -1  0  
  0  0  -1  
)
21
9 y,x,-z, +1
my,mx,-mz
(
  0  1  0  
  1  0  0  
  0  0  -1  
)
2xy
10 -x+y,y,-z, +1
-mx+my,my,-mz
(
  -1  1  0  
  0  1  0  
  0  0  -1  
)
22
11 -x,-x+y,-z, +1
-mx,-mx+my,-mz
(
  -1  0  0  
  -1  1  0  
  0  0  -1  
)
2y
12 -y,-x,-z, +1
-my,-mx,-mz
(
  0  -1  0  
  -1  0  0  
  0  0  -1  
)
23
13 -x,-y,-z, +1
mx, my, mz
(
  -1  0  0  
  0  -1  0  
  0  0  -1  
)
-1
14 -x+y,-x,-z, +1
mx-my, mx, mz
(
  -1  1  0  
  -1  0  0  
  0  0  -1  
)
-6z
15 y,-x+y,-z, +1
-my, mx-my, mz
(
  0  1  0  
  -1  1  0  
  0  0  -1  
)
-3z
16 x,y,-z, +1
-mx, -my, mz
(
  1  0  0  
  0  1  0  
  0  0  -1  
)
mz
17 x-y,x,-z, +1
-mx+my, -mx, mz
(
  1  -1  0  
  1  0  0  
  0  0  -1  
)
-3z-1
18 -y,x-y,-z, +1
my, -mx+my, mz
(
  0  -1  0  
  1  -1  0  
  0  0  -1  
)
-6z-1
19 -x+y,y,z, +1
mx-my, -my, -mz
(
  -1  1  0  
  0  1  0  
  0  0  1  
)
mx
20 -x,-x+y,z, +1
mx, mx-my, -mz
(
  -1  0  0  
  -1  1  0  
  0  0  1  
)
m1
21 -y,-x,z, +1
my, mx, -mz
(
  0  -1  0  
  -1  0  0  
  0  0  1  
)
mxy
22 x-y,-y,z, +1
-mx+my, my, -mz
(
  1  -1  0  
  0  -1  0  
  0  0  1  
)
m2
23 x,x-y,z, +1
-mx, -mx+my, -mz
(
  1  0  0  
  1  -1  0  
  0  0  1  
)
my
24 y,x,z, +1
-my, -mx, -mz
(
  0  1  0  
  1  0  0  
  0  0  1  
)
m3

Subgroups Table

Symmetry-adapted form of material tensors for the magnetic point group 6/mmm (#27.1.100) via MTENSOR


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