Table of Magnetic Space Group Symbols

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F_Sm-3c [#226.127] (Type: 4 -- Type IV (klassengleiche))

[OG: P_Fm-3m' #221.7.1600]

Operators of Group 226.127 (F_Sm-3c)

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x,y,z
m_x,m_y,m_z

  1   0   0     0
  0   1   0     0
  0   0   1     0

1 +1

{1|0,0,0}

-x,-y,z
-m_x,-m_y,m_z

 -1   0   0     0
  0  -1   0     0
  0   0   1     0

2 0,0,z +1

{2z|0,0,0}

-x,y,-z
-m_x,m_y,-m_z

 -1   0   0     0
  0   1   0     0
  0   0  -1     0

2 0,y,0 +1

{2y|0,0,0}

x,-y,-z
m_x,-m_y,-m_z

  1   0   0     0
  0  -1   0     0
  0   0  -1     0

2 x,0,0 +1

{2x|0,0,0}

z,x,y
m_z,m_x,m_y

  0   0   1     0
  1   0   0     0
  0   1   0     0

3⁺ x,x,x +1

{3xyz|0,0,0}

z,-x,-y
m_z,-m_x,-m_y

  0   0   1     0
 -1   0   0     0
  0  -1   0     0

3⁺ -x,x,-x +1

{3x-yz-1|0,0,0}

-z,-x,y
-m_z,-m_x,m_y

  0   0  -1     0
 -1   0   0     0
  0   1   0     0

3⁺ x,-x,-x +1

{3-xyz-1|0,0,0}

-z,x,-y
-m_z,m_x,-m_y

  0   0  -1     0
  1   0   0     0
  0  -1   0     0

3⁺ -x,-x,x +1

{3xy-z-1|0,0,0}

y,z,x
m_y,m_z,m_x

  0   1   0     0
  0   0   1     0
  1   0   0     0

3^- x,x,x +1

{3xyz-1|0,0,0}

10.

-y,z,-x
-m_y,m_z,-m_x

  0  -1   0     0
  0   0   1     0
 -1   0   0     0

3^- x,-x,-x +1

{3-xyz|0,0,0}

11.

y,-z,-x
m_y,-m_z,-m_x

  0   1   0     0
  0   0  -1     0
 -1   0   0     0

3^- -x,-x,x +1

{3xy-z|0,0,0}

12.

-y,-z,x
-m_y,-m_z,m_x

  0  -1   0     0
  0   0  -1     0
  1   0   0     0

3^- -x,x,-x +1

{3x-yz|0,0,0}

13.

y+1/2,x+1/2,-z+1/2
m_y,m_x,-m_z

  0   1   0   1/2
  1   0   0   1/2
  0   0  -1   1/2

2 (1/2,1/2,0) x,x,1/4 +1

{2xy|1/2,1/2,1/2}

14.

-y+1/2,-x+1/2,-z+1/2
-m_y,-m_x,-m_z

  0  -1   0   1/2
 -1   0   0   1/2
  0   0  -1   1/2

2 x,-x+1/2,1/4 +1

{2-xy|1/2,1/2,1/2}

15.

y+1/2,-x+1/2,z+1/2
m_y,-m_x,m_z

  0   1   0   1/2
 -1   0   0   1/2
  0   0   1   1/2

4^- (0,0,1/2) 1/2,0,z +1

{4z-1|1/2,1/2,1/2}

16.

-y+1/2,x+1/2,z+1/2
-m_y,m_x,m_z

  0  -1   0   1/2
  1   0   0   1/2
  0   0   1   1/2

4⁺ (0,0,1/2) 0,1/2,z +1

{4z|1/2,1/2,1/2}

17.

x+1/2,z+1/2,-y+1/2
m_x,m_z,-m_y

  1   0   0   1/2
  0   0   1   1/2
  0  -1   0   1/2

4^- (1/2,0,0) x,1/2,0 +1

{4x-1|1/2,1/2,1/2}

18.

-x+1/2,z+1/2,y+1/2
-m_x,m_z,m_y

 -1   0   0   1/2
  0   0   1   1/2
  0   1   0   1/2

2 (0,1/2,1/2) 1/4,y,y +1

{2yz|1/2,1/2,1/2}

19.

-x+1/2,-z+1/2,-y+1/2
-m_x,-m_z,-m_y

 -1   0   0   1/2
  0   0  -1   1/2
  0  -1   0   1/2

2 1/4,y+1/2,-y +1

{2-yz|1/2,1/2,1/2}

20.

x+1/2,-z+1/2,y+1/2
m_x,-m_z,m_y

  1   0   0   1/2
  0   0  -1   1/2
  0   1   0   1/2

4⁺ (1/2,0,0) x,0,1/2 +1

{4x|1/2,1/2,1/2}

21.

z+1/2,y+1/2,-x+1/2
m_z,m_y,-m_x

  0   0   1   1/2
  0   1   0   1/2
 -1   0   0   1/2

4⁺ (0,1/2,0) 1/2,y,0 +1

{4y|1/2,1/2,1/2}

22.

z+1/2,-y+1/2,x+1/2
m_z,-m_y,m_x

  0   0   1   1/2
  0  -1   0   1/2
  1   0   0   1/2

2 (1/2,0,1/2) x,1/4,x +1

{2xz|1/2,1/2,1/2}

23.

-z+1/2,y+1/2,x+1/2
-m_z,m_y,m_x

  0   0  -1   1/2
  0   1   0   1/2
  1   0   0   1/2

4^- (0,1/2,0) 0,y,1/2 +1

{4y-1|1/2,1/2,1/2}

24.

-z+1/2,-y+1/2,-x+1/2
-m_z,-m_y,-m_x

  0   0  -1   1/2
  0  -1   0   1/2
 -1   0   0   1/2

2 -x+1/2,1/4,x +1

{2-xz|1/2,1/2,1/2}

25.

-x,-y,-z
m_x,m_y,m_z

 -1   0   0     0
  0  -1   0     0
  0   0  -1     0

-1 0,0,0 +1

{-1|0,0,0}

26.

x,y,-z
-m_x,-m_y,m_z

  1   0   0     0
  0   1   0     0
  0   0  -1     0

m x,y,0 +1

{mz|0,0,0}

27.

x,-y,z
-m_x,m_y,-m_z

  1   0   0     0
  0  -1   0     0
  0   0   1     0

m x,0,z +1

{my|0,0,0}

28.

-x,y,z
m_x,-m_y,-m_z

 -1   0   0     0
  0   1   0     0
  0   0   1     0

m 0,y,z +1

{mx|0,0,0}

29.

-z,-x,-y
m_z,m_x,m_y

  0   0  -1     0
 -1   0   0     0
  0  -1   0     0

-3⁺ x,x,x 0,0,0 +1

{-3xyz|0,0,0}

30.

-z,x,y
m_z,-m_x,-m_y

  0   0  -1     0
  1   0   0     0
  0   1   0     0

-3⁺ -x,x,-x 0,0,0 +1

{-3x-yz-1|0,0,0}

31.

z,x,-y
-m_z,-m_x,m_y

  0   0   1     0
  1   0   0     0
  0  -1   0     0

-3⁺ x,-x,-x 0,0,0 +1

{-3-xyz-1|0,0,0}

32.

z,-x,y
-m_z,m_x,-m_y

  0   0   1     0
 -1   0   0     0
  0   1   0     0

-3⁺ -x,-x,x 0,0,0 +1

{-3xy-z-1|0,0,0}

33.

-y,-z,-x
m_y,m_z,m_x

  0  -1   0     0
  0   0  -1     0
 -1   0   0     0

-3^- x,x,x 0,0,0 +1

{-3xyz-1|0,0,0}

34.

y,-z,x
-m_y,m_z,-m_x

  0   1   0     0
  0   0  -1     0
  1   0   0     0

-3^- x,-x,-x 0,0,0 +1

{-3-xyz|0,0,0}

35.

-y,z,x
m_y,-m_z,-m_x

  0  -1   0     0
  0   0   1     0
  1   0   0     0

-3^- -x,-x,x 0,0,0 +1

{-3xy-z|0,0,0}

36.

y,z,-x
-m_y,-m_z,m_x

  0   1   0     0
  0   0   1     0
 -1   0   0     0

-3^- -x,x,-x 0,0,0 +1

{-3x-yz|0,0,0}

37.

-y+1/2,-x+1/2,z+1/2
m_y,m_x,-m_z

  0  -1   0   1/2
 -1   0   0   1/2
  0   0   1   1/2

c x+1/2,-x,z +1

{mxy|1/2,1/2,1/2}

38.

y+1/2,x+1/2,z+1/2
-m_y,-m_x,-m_z

  0   1   0   1/2
  1   0   0   1/2
  0   0   1   1/2

n (1/2,1/2,1/2) x,x,z +1

{m-xy|1/2,1/2,1/2}

39.

-y+1/2,x+1/2,-z+1/2
m_y,-m_x,m_z

  0  -1   0   1/2
  1   0   0   1/2
  0   0  -1   1/2

-4^- 0,1/2,z 0,1/2,1/4 +1

{-4z-1|1/2,1/2,1/2}

40.

y+1/2,-x+1/2,-z+1/2
-m_y,m_x,m_z

  0   1   0   1/2
 -1   0   0   1/2
  0   0  -1   1/2

-4⁺ 1/2,0,z 1/2,0,1/4 +1

{-4z|1/2,1/2,1/2}

41.

-x+1/2,-z+1/2,y+1/2
m_x,m_z,-m_y

 -1   0   0   1/2
  0   0  -1   1/2
  0   1   0   1/2

-4^- x,0,1/2 1/4,0,1/2 +1

{-4x-1|1/2,1/2,1/2}

42.

x+1/2,-z+1/2,-y+1/2
-m_x,m_z,m_y

  1   0   0   1/2
  0   0  -1   1/2
  0  -1   0   1/2

a x,y+1/2,-y +1

{myz|1/2,1/2,1/2}

43.

x+1/2,z+1/2,y+1/2
-m_x,-m_z,-m_y

  1   0   0   1/2
  0   0   1   1/2
  0   1   0   1/2

n (1/2,1/2,1/2) x,y,y +1

{m-yz|1/2,1/2,1/2}

44.

-x+1/2,z+1/2,-y+1/2
m_x,-m_z,m_y

 -1   0   0   1/2
  0   0   1   1/2
  0  -1   0   1/2

-4⁺ x,1/2,0 1/4,1/2,0 +1

{-4x|1/2,1/2,1/2}

45.

-z+1/2,-y+1/2,x+1/2
m_z,m_y,-m_x

  0   0  -1   1/2
  0  -1   0   1/2
  1   0   0   1/2

-4⁺ 0,y,1/2 0,1/4,1/2 +1

{-4y|1/2,1/2,1/2}

46.

-z+1/2,y+1/2,-x+1/2
m_z,-m_y,m_x

  0   0  -1   1/2
  0   1   0   1/2
 -1   0   0   1/2

b -x+1/2,y,x +1

{mxz|1/2,1/2,1/2}

47.

z+1/2,-y+1/2,-x+1/2
-m_z,m_y,m_x

  0   0   1   1/2
  0  -1   0   1/2
 -1   0   0   1/2

-4^- 1/2,y,0 1/2,1/4,0 +1

{-4y-1|1/2,1/2,1/2}

48.

z+1/2,y+1/2,x+1/2
-m_z,-m_y,-m_x

  0   0   1   1/2
  0   1   0   1/2
  1   0   0   1/2

n (1/2,1/2,1/2) x,y,x +1

{m-xz|1/2,1/2,1/2}

49.

x,y+1/2,z+1/2
m_x,m_y,m_z

  1   0   0     0
  0   1   0   1/2
  0   0   1   1/2

t (0,1/2,1/2) +1

{1|0,1/2,1/2}

50^d.

-x,-y+1/2,z+1/2
-m_x,-m_y,m_z

 -1   0   0     0
  0  -1   0   1/2
  0   0   1   1/2

2 (0,0,1/2) 0,1/4,z +1

{2z|0,1/2,1/2}

51^d.

-x,y+1/2,-z+1/2
-m_x,m_y,-m_z

 -1   0   0     0
  0   1   0   1/2
  0   0  -1   1/2

2 (0,1/2,0) 0,y,1/4 +1

{2y|0,1/2,1/2}

52^d.

x,-y+1/2,-z+1/2
m_x,-m_y,-m_z

  1   0   0     0
  0  -1   0   1/2
  0   0  -1   1/2

2 x,1/4,1/4 +1

{2x|0,1/2,1/2}

53^d.

z,x+1/2,y+1/2
m_z,m_x,m_y

  0   0   1     0
  1   0   0   1/2
  0   1   0   1/2

3⁺ (1/3,1/3,1/3) x-0.33333,x-1/6,x +1

{3xyz|0,1/2,1/2}

54^d.

z,-x+1/2,-y+1/2
m_z,-m_x,-m_y

  0   0   1     0
 -1   0   0   1/2
  0  -1   0   1/2

3⁺ -x,x+1/2,-x +1

{3x-yz-1|0,1/2,1/2}

55^d.

-z,-x+1/2,y+1/2
-m_z,-m_x,m_y

  0   0  -1     0
 -1   0   0   1/2
  0   1   0   1/2

3⁺ (-1/3,1/3,1/3) x+1/3,-x,-x +1

{3-xyz-1|0,1/2,1/2}

56^d.

-z,x+1/2,-y+1/2
-m_z,m_x,-m_y

  0   0  -1     0
  1   0   0   1/2
  0  -1   0   1/2

3⁺ -x,-x+1/2,x +1

{3xy-z-1|0,1/2,1/2}

57^d.

y,z+1/2,x+1/2
m_y,m_z,m_x

  0   1   0     0
  0   0   1   1/2
  1   0   0   1/2

3^- (1/3,1/3,1/3) x-0.16666,x+1/6,x +1

{3xyz-1|0,1/2,1/2}

58^d.

-y,z+1/2,-x+1/2
-m_y,m_z,-m_x

  0  -1   0     0
  0   0   1   1/2
 -1   0   0   1/2

3^- (-1/3,1/3,1/3) x+1/6,-x+1/6,-x +1

{3-xyz|0,1/2,1/2}

59^d.

y,-z+1/2,-x+1/2
m_y,-m_z,-m_x

  0   1   0     0
  0   0  -1   1/2
 -1   0   0   1/2

3^- -x+1/2,-x+1/2,x +1

{3xy-z|0,1/2,1/2}

60^d.

-y,-z+1/2,x+1/2
-m_y,-m_z,m_x

  0  -1   0     0
  0   0  -1   1/2
  1   0   0   1/2

3^- -x-1/2,x+1/2,-x +1

{3x-yz|0,1/2,1/2}

61^d.

y+1/2,x,-z
m_y,m_x,-m_z

  0   1   0   1/2
  1   0   0     0
  0   0  -1     0

2 (1/4,1/4,0) x,x-1/4,0 +1

{2xy|1/2,0,0}

62^d.

-y+1/2,-x,-z
-m_y,-m_x,-m_z

  0  -1   0   1/2
 -1   0   0     0
  0   0  -1     0

2 (1/4,-1/4,0) x,-x+1/4,0 +1

{2-xy|1/2,0,0}

63^d.

y+1/2,-x,z
m_y,-m_x,m_z

  0   1   0   1/2
 -1   0   0     0
  0   0   1     0

4^- 1/4,-1/4,z +1

{4z-1|1/2,0,0}

64^d.

-y+1/2,x,z
-m_y,m_x,m_z

  0  -1   0   1/2
  1   0   0     0
  0   0   1     0

4⁺ 1/4,1/4,z +1

{4z|1/2,0,0}

65^d.

x+1/2,z,-y
m_x,m_z,-m_y

  1   0   0   1/2
  0   0   1     0
  0  -1   0     0

4^- (1/2,0,0) x,0,0 +1

{4x-1|1/2,0,0}

66^d.

-x+1/2,z,y
-m_x,m_z,m_y

 -1   0   0   1/2
  0   0   1     0
  0   1   0     0

2 1/4,y,y +1

{2yz|1/2,0,0}

67^d.

-x+1/2,-z,-y
-m_x,-m_z,-m_y

 -1   0   0   1/2
  0   0  -1     0
  0  -1   0     0

2 1/4,y,-y +1

{2-yz|1/2,0,0}

68^d.

x+1/2,-z,y
m_x,-m_z,m_y

  1   0   0   1/2
  0   0  -1     0
  0   1   0     0

4⁺ (1/2,0,0) x,0,0 +1

{4x|1/2,0,0}

69^d.

z+1/2,y,-x
m_z,m_y,-m_x

  0   0   1   1/2
  0   1   0     0
 -1   0   0     0

4⁺ 1/4,y,-1/4 +1

{4y|1/2,0,0}

70^d.

z+1/2,-y,x
m_z,-m_y,m_x

  0   0   1   1/2
  0  -1   0     0
  1   0   0     0

2 (1/4,0,1/4) x+1/4,0,x +1

{2xz|1/2,0,0}

71^d.

-z+1/2,y,x
-m_z,m_y,m_x

  0   0  -1   1/2
  0   1   0     0
  1   0   0     0

4^- 1/4,y,1/4 +1

{4y-1|1/2,0,0}

72^d.

-z+1/2,-y,-x
-m_z,-m_y,-m_x

  0   0  -1   1/2
  0  -1   0     0
 -1   0   0     0

2 (1/4,0,-1/4) -x+1/4,0,x +1

{2-xz|1/2,0,0}

FSm-3c [#226.127] (Type: 4 -- Type IV (klassengleiche))

[OG: PFm-3m' #221.7.1600]

Operators of Group 226.127 (FSm-3c)

F_Sm-3c [#226.127] (Type: 4 -- Type IV (klassengleiche))

[OG: P_Fm-3m' #221.7.1600]

Operators of Group 226.127 (F_Sm-3c)