Table of Magnetic Space Group Symbols

Bilbao Crystallographic Server

MGENPOS

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F-4'3c' [#219.87] (Type: 3 -- Type III (translationgleiche))

[OG: F-4'3c' #219.3.1590]

Operators of Group 219.87 (F-4'3c')

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.

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}

14^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}

15^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}

16^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}

17^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}

18^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}

19^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}

20^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}

21^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}

22^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}

23^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}

24^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}

25.

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

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

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

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

26^d.

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

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

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

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

27^d.

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

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

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

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

28^d.

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

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

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

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

29^d.

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

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

3⁺ (1/3,1/3,1/3) x+1/6,x-1/6,x +1

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

30^d.

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

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

3⁺ (1/3,-1/3,1/3) -x+1/6,x+1/6,-x +1

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

31^d.

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

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

3⁺ x+1/2,-x,-x +1

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

32^d.

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

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

3⁺ -x+1/2,-x+1/2,x +1

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

33^d.

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

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

3^- (1/3,1/3,1/3) x-0.16667,x-1/3,x +1

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

34^d.

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

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

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

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

35^d.

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

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

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

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

36^d.

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

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

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

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

37.

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

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

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

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

38^d.

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

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

2 1/4,1/4,z +1

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

39^d.

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

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

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

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

40^d.

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

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

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

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

41^d.

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

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

3⁺ (1/3,1/3,1/3) x+1/6,x+1/3,x +1

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

42^d.

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

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

3⁺ -x+1/2,x,-x +1

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

43^d.

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

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

3⁺ x+1/2,-x,-x +1

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

44^d.

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

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

3⁺ (1/3,1/3,-1/3) -x+1/6,-x+1/3,x +1

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

45^d.

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

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

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

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

46^d.

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

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

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

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

47^d.

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

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

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

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

48^d.

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

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

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

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

49.

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}'

50.

-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}'

51.

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}'

52.

-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}'

53.

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}'

54.

-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}'

55.

-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}'

56.

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}'

57.

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}'

58.

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}'

59.

-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}'

60.

-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}'

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

g (1/4,1/4,0) x+1/4,x,z -1

{m-xy|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

g (1/4,-1/4,0) x+1/4,-x,z -1

{mxy|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 1/4,-1/4,0 -1

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

{-4z-1|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

a x,y,y -1

{m-yz|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

-4⁺ x,0,0 1/4,0,0 -1

{-4x|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

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

{-4x-1|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

a x,y,-y -1

{myz|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

g (1/4,0,1/4) x+1/4,y,x -1

{m-xz|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

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

{-4y-1|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

g (1/4,0,-1/4) -x+1/4,y,x -1

{mxz|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

-4⁺ 1/4,y,1/4 1/4,0,1/4 -1

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

73^d.

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

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

g (1/4,1/4,0) x-0.25,x,z -1

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

74^d.

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

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

g (-1/4,1/4,0) x+1/4,-x,z -1

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

75^d.

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

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

-4⁺ 1/4,1/4,z 1/4,1/4,0 -1

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

76^d.

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

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

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

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

77^d.

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

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

g (0,1/4,1/4) x,y+1/4,y -1

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

78^d.

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

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

-4⁺ x,1/4,-1/4 0,1/4,-1/4 -1

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

79^d.

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

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

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

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

80^d.

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

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

g (0,1/4,-1/4) x,y+1/4,-y -1

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

81^d.

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

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

b x,y,x -1

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

82^d.

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

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

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

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

83^d.

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

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

b -x,y,x -1

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

84^d.

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

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

-4⁺ 0,y,0 0,1/4,0 -1

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

85^d.

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

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

c x,x,z -1

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

86^d.

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

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

c x,-x,z -1

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

87^d.

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

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

-4⁺ 0,0,z 0,0,1/4 -1

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

88^d.

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

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

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

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

89^d.

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

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

g (0,1/4,1/4) x,y-1/4,y -1

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

90^d.

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

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

-4⁺ x,1/4,1/4 0,1/4,1/4 -1

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

91^d.

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

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

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

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

92^d.

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

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

g (0,-1/4,1/4) x,y+1/4,-y -1

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

93^d.

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

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

g (1/4,0,1/4) x-0.25,y,x -1

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

94^d.

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

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

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

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

95^d.

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

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

g (-1/4,0,1/4) -x+1/4,y,x -1

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

96^d.

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

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

-4⁺ -1/4,y,1/4 -1/4,0,1/4 -1

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

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