Table of Magnetic Space Group Symbols

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F432 [#209.48] (Type: 1 -- Type I (Fedorov))

[OG: F432 #209.1.1550]

Operators of Group 209.48 (F432)

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,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}

14.

-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}

15.

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}

16.

-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}

17.

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}

18.

-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}

19.

-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}

20.

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}

21.

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}

22.

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}

23.

-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}

24.

-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}

25.

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}

26^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}

27^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}

28^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}

29^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}

30^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}

31^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}

32^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}

33^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}

34^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}

35^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}

36^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}

37^d.

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

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

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

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

38^d.

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

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

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

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

39^d.

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

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

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

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

40^d.

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

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

4⁺ (0,0,1/2) -1/4,1/4,z +1

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

41^d.

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

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

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

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

42^d.

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

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

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

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

43^d.

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

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

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

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

44^d.

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

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

4⁺ x,0,1/2 +1

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

45^d.

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

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

4⁺ (0,1/2,0) 1/4,y,1/4 +1

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

46^d.

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

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

2 (1/4,0,1/4) x-0.25,1/4,x +1

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

47^d.

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

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

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

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

48^d.

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

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

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

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

49.

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}

50^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}

51^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}

52^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}

53^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}

54^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}

55^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}

56^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}

57^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}

58^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}

59^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}

60^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}

61^d.

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

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

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

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

62^d.

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

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

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

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

63^d.

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

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

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

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

64^d.

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

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

4⁺ (0,0,1/2) 1/4,1/4,z +1

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

65^d.

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

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

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

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

66^d.

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

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

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

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

67^d.

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

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

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

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

68^d.

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

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

4⁺ (1/2,0,0) x,-1/4,1/4 +1

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

69^d.

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

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

4⁺ 1/2,y,0 +1

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

70^d.

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

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

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

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

71^d.

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

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

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

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

72^d.

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

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

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

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

73.

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}

74^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}

75^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}

76^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}

77^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}

78^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}

79^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}

80^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}

81^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}

82^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}

83^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}

84^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}

85^d.

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

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

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

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

86^d.

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

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

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

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

87^d.

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

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

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

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

88^d.

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

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

4⁺ 0,1/2,z +1

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

89^d.

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

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

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

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

90^d.

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

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

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

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

91^d.

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

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

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

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

92^d.

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

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

4⁺ (1/2,0,0) x,1/4,1/4 +1

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

93^d.

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

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

4⁺ (0,1/2,0) 1/4,y,-1/4 +1

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

94^d.

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

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

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

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

95^d.

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

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

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

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

96^d.

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

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

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

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

Show/Hide Derived operators due to the centring translations

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