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PI4/mm'm' [#123.19.1017] (Type: 4 -- Type IV (klassengleiche))

[BNS: Ic4/mcm] #140.550

Operators of Group 123.19.1017 (PI4/mm'm')


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1.x,y,z
mx,my,mz
( 
  1   0   0     0
  0   1   0     0
  0   0   1     0
 )
1 +1 {1|0,0,0}
2.x,-y,-z+1
mx,-my,-mz
( 
  1   0   0     0
  0  -1   0     0
  0   0  -1     1
 )
2 x,0,1/2 +1 {2x|0,0,1}
3.-x,y,-z+1
-mx,my,-mz
( 
 -1   0   0     0
  0   1   0     0
  0   0  -1     1
 )
2 0,y,1/2 +1 {2y|0,0,1}
4.-x,-y,z
-mx,-my,mz
( 
 -1   0   0     0
  0  -1   0     0
  0   0   1     0
 )
2 0,0,z +1 {2z|0,0,0}
5.-y,-x,-z+1
-my,-mx,-mz
( 
  0  -1   0     0
 -1   0   0     0
  0   0  -1     1
 )
2 x,-x,1/2 +1 {2-xy|0,0,1}
6.-y,x,z
-my,mx,mz
( 
  0  -1   0     0
  1   0   0     0
  0   0   1     0
 )
4+ 0,0,z +1 {4z|0,0,0}
7.y,-x,z
my,-mx,mz
( 
  0   1   0     0
 -1   0   0     0
  0   0   1     0
 )
4- 0,0,z +1 {4z-1|0,0,0}
8.y,x,-z+1
my,mx,-mz
( 
  0   1   0     0
  1   0   0     0
  0   0  -1     1
 )
2 x,x,1/2 +1 {2xy|0,0,1}
9.-x,-y,-z
mx,my,mz
( 
 -1   0   0     0
  0  -1   0     0
  0   0  -1     0
 )
-1 0,0,0 +1 {-1|0,0,0}
10.-x,y,z+1
mx,-my,-mz
( 
 -1   0   0     0
  0   1   0     0
  0   0   1     1
 )
g (0,0,1) 0,y,z +1 {mx|0,0,1}
11.x,-y,z+1
-mx,my,-mz
( 
  1   0   0     0
  0  -1   0     0
  0   0   1     1
 )
g (0,0,1) x,0,z +1 {my|0,0,1}
12.x,y,-z
-mx,-my,mz
( 
  1   0   0     0
  0   1   0     0
  0   0  -1     0
 )
m x,y,0 +1 {mz|0,0,0}
13.y,x,z+1
-my,-mx,-mz
( 
  0   1   0     0
  1   0   0     0
  0   0   1     1
 )
g (0,0,1) x,x,z +1 {m-xy|0,0,1}
14.y,-x,-z
-my,mx,mz
( 
  0   1   0     0
 -1   0   0     0
  0   0  -1     0
 )
-4+ 0,0,z; 0,0,0 +1 {-4z|0,0,0}
15.-y,x,-z
my,-mx,mz
( 
  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}
16.-y,-x,z+1
my,mx,-mz
( 
  0  -1   0     0
 -1   0   0     0
  0   0   1     1
 )
g (0,0,1) x,-x,z +1 {mxy|0,0,1}