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I4321' [#211.57] (Type: 2 -- Type II (grey group))

[OG: I4321' #211.2.1557]

Operators of Group 211.57 (I4321')


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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,-y,z
0,0,0
( 
 -1   0   0     0
  0  -1   0     0
  0   0   1     0
 )
2 0,0,z +1 {2z|0,0,0}
3.-x,y,-z
0,0,0
( 
 -1   0   0     0
  0   1   0     0
  0   0  -1     0
 )
2 0,y,0 +1 {2y|0,0,0}
4.x,-y,-z
0,0,0
( 
  1   0   0     0
  0  -1   0     0
  0   0  -1     0
 )
2 x,0,0 +1 {2x|0,0,0}
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,-y
0,0,0
( 
  0   0   1     0
 -1   0   0     0
  0  -1   0     0
 )
3+ -x,x,-x +1 {3x-yz-1|0,0,0}
7.-z,-x,y
0,0,0
( 
  0   0  -1     0
 -1   0   0     0
  0   1   0     0
 )
3+ x,-x,-x +1 {3-xyz-1|0,0,0}
8.-z,x,-y
0,0,0
( 
  0   0  -1     0
  1   0   0     0
  0  -1   0     0
 )
3+ -x,-x,x +1 {3xy-z-1|0,0,0}
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,z,-x
0,0,0
( 
  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
0,0,0
( 
  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
0,0,0
( 
  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
0,0,0
( 
  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
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,-x,z
0,0,0
( 
  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
0,0,0
( 
  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
0,0,0
( 
  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
0,0,0
( 
 -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
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,-z,y
0,0,0
( 
  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
0,0,0
( 
  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
0,0,0
( 
  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
0,0,0
( 
  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
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+1/2,y+1/2,z+1/2
mx,my,mz
( 
  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}
26d.-x+1/2,-y+1/2,z+1/2
-mx,-my,mz
( 
 -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}
27d.-x+1/2,y+1/2,-z+1/2
-mx,my,-mz
( 
 -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}
28d.x+1/2,-y+1/2,-z+1/2
mx,-my,-mz
( 
  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}
29d.z+1/2,x+1/2,y+1/2
mz,mx,my
( 
  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}
30d.z+1/2,-x+1/2,-y+1/2
mz,-mx,-my
( 
  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}
31d.-z+1/2,-x+1/2,y+1/2
-mz,-mx,my
( 
  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}
32d.-z+1/2,x+1/2,-y+1/2
-mz,mx,-my
( 
  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}
33d.y+1/2,z+1/2,x+1/2
my,mz,mx
( 
  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}
34d.-y+1/2,z+1/2,-x+1/2
-my,mz,-mx
( 
  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}
35d.y+1/2,-z+1/2,-x+1/2
my,-mz,-mx
( 
  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}
36d.-y+1/2,-z+1/2,x+1/2
-my,-mz,mx
( 
  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}
37d.y+1/2,x+1/2,-z+1/2
my,mx,-mz
( 
  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}
38d.-y+1/2,-x+1/2,-z+1/2
-my,-mx,-mz
( 
  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}
39d.y+1/2,-x+1/2,z+1/2
my,-mx,mz
( 
  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}
40d.-y+1/2,x+1/2,z+1/2
-my,mx,mz
( 
  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}
41d.x+1/2,z+1/2,-y+1/2
mx,mz,-my
( 
  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}
42d.-x+1/2,z+1/2,y+1/2
-mx,mz,my
( 
 -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}
43d.-x+1/2,-z+1/2,-y+1/2
-mx,-mz,-my
( 
 -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}
44d.x+1/2,-z+1/2,y+1/2
mx,-mz,my
( 
  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}
45d.z+1/2,y+1/2,-x+1/2
mz,my,-mx
( 
  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}
46d.z+1/2,-y+1/2,x+1/2
mz,-my,mx
( 
  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}
47d.-z+1/2,y+1/2,x+1/2
-mz,my,mx
( 
  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}
48d.-z+1/2,-y+1/2,-x+1/2
-mz,-my,-mx
( 
  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}
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,-y,z
0,0,0
( 
 -1   0   0     0
  0  -1   0     0
  0   0   1     0
 ) '
2 0,0,z -1 {2z|0,0,0}'
51.-x,y,-z
0,0,0
( 
 -1   0   0     0
  0   1   0     0
  0   0  -1     0
 ) '
2 0,y,0 -1 {2y|0,0,0}'
52.x,-y,-z
0,0,0
( 
  1   0   0     0
  0  -1   0     0
  0   0  -1     0
 ) '
2 x,0,0 -1 {2x|0,0,0}'
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,-y
0,0,0
( 
  0   0   1     0
 -1   0   0     0
  0  -1   0     0
 ) '
3+ -x,x,-x -1 {3x-yz-1|0,0,0}'
55.-z,-x,y
0,0,0
( 
  0   0  -1     0
 -1   0   0     0
  0   1   0     0
 ) '
3+ x,-x,-x -1 {3-xyz-1|0,0,0}'
56.-z,x,-y
0,0,0
( 
  0   0  -1     0
  1   0   0     0
  0  -1   0     0
 ) '
3+ -x,-x,x -1 {3xy-z-1|0,0,0}'
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,z,-x
0,0,0
( 
  0  -1   0     0
  0   0   1     0
 -1   0   0     0
 ) '
3- x,-x,-x -1 {3-xyz|0,0,0}'
59.y,-z,-x
0,0,0
( 
  0   1   0     0
  0   0  -1     0
 -1   0   0     0
 ) '
3- -x,-x,x -1 {3xy-z|0,0,0}'
60.-y,-z,x
0,0,0
( 
  0  -1   0     0
  0   0  -1     0
  1   0   0     0
 ) '
3- -x,x,-x -1 {3x-yz|0,0,0}'
61.y,x,-z
0,0,0
( 
  0   1   0     0
  1   0   0     0
  0   0  -1     0
 ) '
2 x,x,0 -1 {2xy|0,0,0}'
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,-x,z
0,0,0
( 
  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
0,0,0
( 
  0  -1   0     0
  1   0   0     0
  0   0   1     0
 ) '
4+ 0,0,z -1 {4z|0,0,0}'
65.x,z,-y
0,0,0
( 
  1   0   0     0
  0   0   1     0
  0  -1   0     0
 ) '
4- x,0,0 -1 {4x-1|0,0,0}'
66.-x,z,y
0,0,0
( 
 -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
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,-z,y
0,0,0
( 
  1   0   0     0
  0   0  -1     0
  0   1   0     0
 ) '
4+ x,0,0 -1 {4x|0,0,0}'
69.z,y,-x
0,0,0
( 
  0   0   1     0
  0   1   0     0
 -1   0   0     0
 ) '
4+ 0,y,0 -1 {4y|0,0,0}'
70.z,-y,x
0,0,0
( 
  0   0   1     0
  0  -1   0     0
  1   0   0     0
 ) '
2 x,0,x -1 {2xz|0,0,0}'
71.-z,y,x
0,0,0
( 
  0   0  -1     0
  0   1   0     0
  1   0   0     0
 ) '
4- 0,y,0 -1 {4y-1|0,0,0}'
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}'