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Pn-3m1' [#224.111] (Type: 2 -- Type II (grey group))

[OG: Pn-3m1' #224.2.1612]

Operators of Group 224.111 (Pn-3m1')

1.x,y,z
0,0,0
( 
  1   0   0     0
  0   1   0     0
  0   0   1     0
 )
1 +1 {1|0,0,0}
2.-x+1/2,-y+1/2,z
0,0,0
( 
 -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}
3.-x+1/2,y,-z+1/2
0,0,0
( 
 -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}
4.x,-y+1/2,-z+1/2
0,0,0
( 
  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}
5.z,x,y
0,0,0
( 
  0   0   1     0
  1   0   0     0
  0   1   0     0
 )
3+ x,x,x +1 {3xyz|0,0,0}
6.z,-x+1/2,-y+1/2
0,0,0
( 
  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}
7.-z+1/2,-x+1/2,y
0,0,0
( 
  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}
8.-z+1/2,x,-y+1/2
0,0,0
( 
  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}
9.y,z,x
0,0,0
( 
  0   1   0     0
  0   0   1     0
  1   0   0     0
 )
3- x,x,x +1 {3xyz-1|0,0,0}
10.-y+1/2,z,-x+1/2
0,0,0
( 
  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}
11.y,-z+1/2,-x+1/2
0,0,0
( 
  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}
12.-y+1/2,-z+1/2,x
0,0,0
( 
  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}
13.y+1/2,x+1/2,-z
0,0,0
( 
  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}
14.-y,-x,-z
0,0,0
( 
  0  -1   0     0
 -1   0   0     0
  0   0  -1     0
 )
2 x,-x,0 +1 {2-xy|0,0,0}
15.y+1/2,-x,z+1/2
0,0,0
( 
  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}
16.-y,x+1/2,z+1/2
0,0,0
( 
  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}
17.x+1/2,z+1/2,-y
0,0,0
( 
  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}
18.-x,z+1/2,y+1/2
0,0,0
( 
 -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}
19.-x,-z,-y
0,0,0
( 
 -1   0   0     0
  0   0  -1     0
  0  -1   0     0
 )
2 0,y,-y +1 {2-yz|0,0,0}
20.x+1/2,-z,y+1/2
0,0,0
( 
  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}
21.z+1/2,y+1/2,-x
0,0,0
( 
  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}
22.z+1/2,-y,x+1/2
0,0,0
( 
  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}
23.-z,y+1/2,x+1/2
0,0,0
( 
  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}
24.-z,-y,-x
0,0,0
( 
  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,-z
0,0,0
( 
 -1   0   0     0
  0  -1   0     0
  0   0  -1     0
 )
-1 0,0,0 +1 {-1|0,0,0}
26.x+1/2,y+1/2,-z
0,0,0
( 
  1   0   0   1/2
  0   1   0   1/2
  0   0  -1     0
 )
n (1/2,1/2,0) x,y,0 +1 {mz|1/2,1/2,0}
27.x+1/2,-y,z+1/2
0,0,0
( 
  1   0   0   1/2
  0  -1   0     0
  0   0   1   1/2
 )
n (1/2,0,1/2) x,0,z +1 {my|1/2,0,1/2}
28.-x,y+1/2,z+1/2
0,0,0
( 
 -1   0   0     0
  0   1   0   1/2
  0   0   1   1/2
 )
n (0,1/2,1/2) 0,y,z +1 {mx|0,1/2,1/2}
29.-z,-x,-y
0,0,0
( 
  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+1/2,y+1/2
0,0,0
( 
  0   0  -1     0
  1   0   0   1/2
  0   1   0   1/2
 )
-3+ -x-1,x+1/2,-x -1/2,0,1/2 +1 {-3x-yz-1|0,1/2,1/2}
31.z+1/2,x+1/2,-y
0,0,0
( 
  0   0   1   1/2
  1   0   0   1/2
  0  -1   0     0
 )
-3+ x-0.5,-x+1,-x 0,1/2,-1/2 +1 {-3-xyz-1|1/2,1/2,0}
32.z+1/2,-x,y+1/2
0,0,0
( 
  0   0   1   1/2
 -1   0   0     0
  0   1   0   1/2
 )
-3+ -x+1/2,-x,x 1/2,-1/2,0 +1 {-3xy-z-1|1/2,0,1/2}
33.-y,-z,-x
0,0,0
( 
  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+1/2,-z,x+1/2
0,0,0
( 
  0   1   0   1/2
  0   0  -1     0
  1   0   0   1/2
 )
-3- x+1/2,-x,-x 0,-1/2,1/2 +1 {-3-xyz|1/2,0,1/2}
35.-y,z+1/2,x+1/2
0,0,0
( 
  0  -1   0     0
  0   0   1   1/2
  1   0   0   1/2
 )
-3- -x-1/2,-x+1/2,x -1/2,1/2,0 +1 {-3xy-z|0,1/2,1/2}
36.y+1/2,z+1/2,-x
0,0,0
( 
  0   1   0   1/2
  0   0   1   1/2
 -1   0   0     0
 )
-3- -x+1,x-1/2,-x 1/2,0,-1/2 +1 {-3x-yz|1/2,1/2,0}
37.-y+1/2,-x+1/2,z
0,0,0
( 
  0  -1   0   1/2
 -1   0   0   1/2
  0   0   1     0
 )
m x+1/2,-x,z +1 {mxy|1/2,1/2,0}
38.y,x,z
0,0,0
( 
  0   1   0     0
  1   0   0     0
  0   0   1     0
 )
m x,x,z +1 {m-xy|0,0,0}
39.-y+1/2,x,-z+1/2
0,0,0
( 
  0  -1   0   1/2
  1   0   0     0
  0   0  -1   1/2
 )
-4- 1/4,1/4,z 1/4,1/4,1/4 +1 {-4z-1|1/2,0,1/2}
40.y,-x+1/2,-z+1/2
0,0,0
( 
  0   1   0     0
 -1   0   0   1/2
  0   0  -1   1/2
 )
-4+ 1/4,1/4,z 1/4,1/4,1/4 +1 {-4z|0,1/2,1/2}
41.-x+1/2,-z+1/2,y
0,0,0
( 
 -1   0   0   1/2
  0   0  -1   1/2
  0   1   0     0
 )
-4- x,1/4,1/4 1/4,1/4,1/4 +1 {-4x-1|1/2,1/2,0}
42.x,-z+1/2,-y+1/2
0,0,0
( 
  1   0   0     0
  0   0  -1   1/2
  0  -1   0   1/2
 )
m x,y+1/2,-y +1 {myz|0,1/2,1/2}
43.x,z,y
0,0,0
( 
  1   0   0     0
  0   0   1     0
  0   1   0     0
 )
m x,y,y +1 {m-yz|0,0,0}
44.-x+1/2,z,-y+1/2
0,0,0
( 
 -1   0   0   1/2
  0   0   1     0
  0  -1   0   1/2
 )
-4+ x,1/4,1/4 1/4,1/4,1/4 +1 {-4x|1/2,0,1/2}
45.-z+1/2,-y+1/2,x
0,0,0
( 
  0   0  -1   1/2
  0  -1   0   1/2
  1   0   0     0
 )
-4+ 1/4,y,1/4 1/4,1/4,1/4 +1 {-4y|1/2,1/2,0}
46.-z+1/2,y,-x+1/2
0,0,0
( 
  0   0  -1   1/2
  0   1   0     0
 -1   0   0   1/2
 )
m -x+1/2,y,x +1 {mxz|1/2,0,1/2}
47.z,-y+1/2,-x+1/2
0,0,0
( 
  0   0   1     0
  0  -1   0   1/2
 -1   0   0   1/2
 )
-4- 1/4,y,1/4 1/4,1/4,1/4 +1 {-4y-1|0,1/2,1/2}
48.z,y,x
0,0,0
( 
  0   0   1     0
  0   1   0     0
  1   0   0     0
 )
m x,y,x +1 {m-xz|0,0,0}
49.x,y,z
0,0,0
( 
  1   0   0     0
  0   1   0     0
  0   0   1     0
 ) '
1 -1 {1|0,0,0}'
50.-x+1/2,-y+1/2,z
0,0,0
( 
 -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}'
51.-x+1/2,y,-z+1/2
0,0,0
( 
 -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.x,-y+1/2,-z+1/2
0,0,0
( 
  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.z,x,y
0,0,0
( 
  0   0   1     0
  1   0   0     0
  0   1   0     0
 ) '
3+ x,x,x -1 {3xyz|0,0,0}'
54.z,-x+1/2,-y+1/2
0,0,0
( 
  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.-z+1/2,-x+1/2,y
0,0,0
( 
  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}'
56.-z+1/2,x,-y+1/2
0,0,0
( 
  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.y,z,x
0,0,0
( 
  0   1   0     0
  0   0   1     0
  1   0   0     0
 ) '
3- x,x,x -1 {3xyz-1|0,0,0}'
58.-y+1/2,z,-x+1/2
0,0,0
( 
  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.y,-z+1/2,-x+1/2
0,0,0
( 
  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.-y+1/2,-z+1/2,x
0,0,0
( 
  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}'
61.y+1/2,x+1/2,-z
0,0,0
( 
  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}'
62.-y,-x,-z
0,0,0
( 
  0  -1   0     0
 -1   0   0     0
  0   0  -1     0
 ) '
2 x,-x,0 -1 {2-xy|0,0,0}'
63.y+1/2,-x,z+1/2
0,0,0
( 
  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.-y,x+1/2,z+1/2
0,0,0
( 
  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}'
65.x+1/2,z+1/2,-y
0,0,0
( 
  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}'
66.-x,z+1/2,y+1/2
0,0,0
( 
 -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}'
67.-x,-z,-y
0,0,0
( 
 -1   0   0     0
  0   0  -1     0
  0  -1   0     0
 ) '
2 0,y,-y -1 {2-yz|0,0,0}'
68.x+1/2,-z,y+1/2
0,0,0
( 
  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.z+1/2,y+1/2,-x
0,0,0
( 
  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}'
70.z+1/2,-y,x+1/2
0,0,0
( 
  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.-z,y+1/2,x+1/2
0,0,0
( 
  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}'
72.-z,-y,-x
0,0,0
( 
  0   0  -1     0
  0  -1   0     0
 -1   0   0     0
 ) '
2 -x,0,x -1 {2-xz|0,0,0}'
73.-x,-y,-z
0,0,0
( 
 -1   0   0     0
  0  -1   0     0
  0   0  -1     0
 ) '
-1 0,0,0 -1 {-1|0,0,0}'
74.x+1/2,y+1/2,-z
0,0,0
( 
  1   0   0   1/2
  0   1   0   1/2
  0   0  -1     0
 ) '
n (1/2,1/2,0) x,y,0 -1 {mz|1/2,1/2,0}'
75.x+1/2,-y,z+1/2
0,0,0
( 
  1   0   0   1/2
  0  -1   0     0
  0   0   1   1/2
 ) '
n (1/2,0,1/2) x,0,z -1 {my|1/2,0,1/2}'
76.-x,y+1/2,z+1/2
0,0,0
( 
 -1   0   0     0
  0   1   0   1/2
  0   0   1   1/2
 ) '
n (0,1/2,1/2) 0,y,z -1 {mx|0,1/2,1/2}'
77.-z,-x,-y
0,0,0
( 
  0   0  -1     0
 -1   0   0     0
  0  -1   0     0
 ) '
-3+ x,x,x 0,0,0 -1 {-3xyz|0,0,0}'
78.-z,x+1/2,y+1/2
0,0,0
( 
  0   0  -1     0
  1   0   0   1/2
  0   1   0   1/2
 ) '
-3+ -x-1,x+1/2,-x -1/2,0,1/2 -1 {-3x-yz-1|0,1/2,1/2}'
79.z+1/2,x+1/2,-y
0,0,0
( 
  0   0   1   1/2
  1   0   0   1/2
  0  -1   0     0
 ) '
-3+ x-0.5,-x+1,-x 0,1/2,-1/2 -1 {-3-xyz-1|1/2,1/2,0}'
80.z+1/2,-x,y+1/2
0,0,0
( 
  0   0   1   1/2
 -1   0   0     0
  0   1   0   1/2
 ) '
-3+ -x+1/2,-x,x 1/2,-1/2,0 -1 {-3xy-z-1|1/2,0,1/2}'
81.-y,-z,-x
0,0,0
( 
  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}'
82.y+1/2,-z,x+1/2
0,0,0
( 
  0   1   0   1/2
  0   0  -1     0
  1   0   0   1/2
 ) '
-3- x+1/2,-x,-x 0,-1/2,1/2 -1 {-3-xyz|1/2,0,1/2}'
83.-y,z+1/2,x+1/2
0,0,0
( 
  0  -1   0     0
  0   0   1   1/2
  1   0   0   1/2
 ) '
-3- -x-1/2,-x+1/2,x -1/2,1/2,0 -1 {-3xy-z|0,1/2,1/2}'
84.y+1/2,z+1/2,-x
0,0,0
( 
  0   1   0   1/2
  0   0   1   1/2
 -1   0   0     0
 ) '
-3- -x+1,x-1/2,-x 1/2,0,-1/2 -1 {-3x-yz|1/2,1/2,0}'
85.-y+1/2,-x+1/2,z
0,0,0
( 
  0  -1   0   1/2
 -1   0   0   1/2
  0   0   1     0
 ) '
m x+1/2,-x,z -1 {mxy|1/2,1/2,0}'
86.y,x,z
0,0,0
( 
  0   1   0     0
  1   0   0     0
  0   0   1     0
 ) '
m x,x,z -1 {m-xy|0,0,0}'
87.-y+1/2,x,-z+1/2
0,0,0
( 
  0  -1   0   1/2
  1   0   0     0
  0   0  -1   1/2
 ) '
-4- 1/4,1/4,z 1/4,1/4,1/4 -1 {-4z-1|1/2,0,1/2}'
88.y,-x+1/2,-z+1/2
0,0,0
( 
  0   1   0     0
 -1   0   0   1/2
  0   0  -1   1/2
 ) '
-4+ 1/4,1/4,z 1/4,1/4,1/4 -1 {-4z|0,1/2,1/2}'
89.-x+1/2,-z+1/2,y
0,0,0
( 
 -1   0   0   1/2
  0   0  -1   1/2
  0   1   0     0
 ) '
-4- x,1/4,1/4 1/4,1/4,1/4 -1 {-4x-1|1/2,1/2,0}'
90.x,-z+1/2,-y+1/2
0,0,0
( 
  1   0   0     0
  0   0  -1   1/2
  0  -1   0   1/2
 ) '
m x,y+1/2,-y -1 {myz|0,1/2,1/2}'
91.x,z,y
0,0,0
( 
  1   0   0     0
  0   0   1     0
  0   1   0     0
 ) '
m x,y,y -1 {m-yz|0,0,0}'
92.-x+1/2,z,-y+1/2
0,0,0
( 
 -1   0   0   1/2
  0   0   1     0
  0  -1   0   1/2
 ) '
-4+ x,1/4,1/4 1/4,1/4,1/4 -1 {-4x|1/2,0,1/2}'
93.-z+1/2,-y+1/2,x
0,0,0
( 
  0   0  -1   1/2
  0  -1   0   1/2
  1   0   0     0
 ) '
-4+ 1/4,y,1/4 1/4,1/4,1/4 -1 {-4y|1/2,1/2,0}'
94.-z+1/2,y,-x+1/2
0,0,0
( 
  0   0  -1   1/2
  0   1   0     0
 -1   0   0   1/2
 ) '
m -x+1/2,y,x -1 {mxz|1/2,0,1/2}'
95.z,-y+1/2,-x+1/2
0,0,0
( 
  0   0   1     0
  0  -1   0   1/2
 -1   0   0   1/2
 ) '
-4- 1/4,y,1/4 1/4,1/4,1/4 -1 {-4y-1|0,1/2,1/2}'
96.z,y,x
0,0,0
( 
  0   0   1     0
  0   1   0     0
  1   0   0     0
 ) '
m x,y,x -1 {m-xz|0,0,0}'


Go to the Wyckoff Positions of 224.111 (Pn-3m1')
Go to the extinction rules of 224.111 (Pn-3m1')


Back to the list of magnetic space groups derived from Pn-3m
Back to the list of Magnetic Space Groups

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