Table of Magnetic Space Group Symbols

Bilbao Crystallographic Server

MGENPOS

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I_Pm'-3'm [#229.7.1644] (Type: 4 -- Type IV (klassengleiche))

[BNS: P_In-3m] #224.115

Operators of Group 229.7.1644 (I_Pm'-3'm)

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 x,0,0 +1

{2x|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 0,0,z +1

{2z|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}

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}

-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}

-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}

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}

10.

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}

11.

-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}

12.

-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}

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

{2-xy|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

4⁺ (0,0,1/2) 0,1/2,z +1

{4z|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

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

{2xy|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

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

{2-yz|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

4⁺ (1/2,0,0) x,0,1/2 +1

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

{4x-1|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

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

{2-xz|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

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

{4y-1|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

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

{2xz|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

4⁺ (0,1/2,0) 1/2,y,0 +1

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

25.

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

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

-1 1/4,1/4,1/4 +1

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

26.

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

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

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

{mx|1/2,1/2,1/2}

27.

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

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

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

{my|1/2,1/2,1/2}

28.

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

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

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

{mz|1/2,1/2,1/2}

29.

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

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

-3^- x,x,x; 1/4,1/4,1/4 +1

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

30.

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

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

-3^- -x,-x+1,x; -1/4,3/4,1/4 +1

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

31.

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

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

-3^- x+1,-x,-x; 1/4,-1/4,3/4 +1

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

32.

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

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

-3^- -x+1,x,-x; 3/4,1/4,-1/4 +1

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

33.

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

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

-3⁺ x,x,x; 1/4,1/4,1/4 +1

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

34.

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

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

-3⁺ -x-1,x+1,-x; -1/4,1/4,3/4 +1

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

35.

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

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

-3⁺ -x+1,-x,x; 3/4,-1/4,1/4 +1

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

36.

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

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

-3⁺ x,-x+1,-x; 1/4,3/4,-1/4 +1

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

37.

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

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

m x,x,z +1

{m-xy|0,0,0}

38.

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

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

-4⁺ 0,0,z; 0,0,0 +1

{-4z|0,0,0}

39.

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

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

-4^- 0,0,z; 0,0,0 +1

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

40.

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

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

m x,-x,z +1

{mxy|0,0,0}

41.

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

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

m x,y,y +1

{m-yz|0,0,0}

42.

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

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

m x,y,-y +1

{myz|0,0,0}

43.

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

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

-4⁺ x,0,0; 0,0,0 +1

{-4x|0,0,0}

44.

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

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

-4^- x,0,0; 0,0,0 +1

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

45.

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

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

m x,y,x +1

{m-xz|0,0,0}

46.

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

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

-4^- 0,y,0; 0,0,0 +1

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

47.

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

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

m -x,y,x +1

{mxz|0,0,0}

48.

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

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

-4⁺ 0,y,0; 0,0,0 +1

{-4y|0,0,0}

49.

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

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

t (1/2,1/2,1/2) -1

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

50.

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

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

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

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

51.

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

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

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

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

52.

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

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

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

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

53.

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

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

3^- (1/2,1/2,1/2) x,x,x -1

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

54.

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

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

3^- (1/6,1/6,-1/6) -x+2/3,-x+1/3,x -1

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

55.

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

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

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

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

56.

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

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

3^- (1/6,-1/6,1/6) -x-1/3,x+2/3,-x -1

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

57.

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

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

3⁺ (1/2,1/2,1/2) x,x,x -1

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

58.

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

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

3⁺ (1/6,-1/6,1/6) -x+1/3,x+1/3,-x -1

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

59.

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

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

3⁺ (1/6,1/6,-1/6) -x+1/3,-x+2/3,x -1

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

60.

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

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

3⁺ (-1/6,1/6,1/6) x+2/3,-x,-x -1

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

61.

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

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

2 x,-x,0 -1

{2-xy|0,0,0}'

62.

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

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

4⁺ 0,0,z -1

{4z|0,0,0}'

63.

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

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

4^- 0,0,z -1

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

64.

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

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

2 x,x,0 -1

{2xy|0,0,0}'

65.

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

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

2 0,y,-y -1

{2-yz|0,0,0}'

66.

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

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

2 0,y,y -1

{2yz|0,0,0}'

67.

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

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

4⁺ x,0,0 -1

{4x|0,0,0}'

68.

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

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

4^- x,0,0 -1

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

69.

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

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

2 -x,0,x -1

{2-xz|0,0,0}'

70.

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

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

4^- 0,y,0 -1

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

71.

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

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

2 x,0,x -1

{2xz|0,0,0}'

72.

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

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

4⁺ 0,y,0 -1

{4y|0,0,0}'

73.

-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}'

74.

-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}'

75.

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}'

76.

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}'

77.

-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}'

78.

-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}'

79.

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}'

80.

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}'

81.

-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}'

82.

-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}'

83.

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}'

84.

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}'

85.

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}'

86.

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}'

87.

-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}'

88.

-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}'

89.

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}'

90.

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}'

91.

-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}'

92.

-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}'

93.

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}'

94.

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}'

95.

-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}'

96.

-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}'

Go to the Wyckoff Positions of 229.7.1644 (I_Pm'-3'm)
Go to the extinction rules of 224.115 (P_In-3m) ← Corresponding space group in BNS settings

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IPm'-3'm [#229.7.1644] (Type: 4 -- Type IV (klassengleiche))

[BNS: PIn-3m] #224.115

Operators of Group 229.7.1644 (IPm'-3'm)

I_Pm'-3'm [#229.7.1644] (Type: 4 -- Type IV (klassengleiche))

[BNS: P_In-3m] #224.115

Operators of Group 229.7.1644 (I_Pm'-3'm)