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Input space group symbol: H 32 2 (0 0 4)
Convention: Hall symbol

Number of lattice translations: 3
Space group is acentric.
Space group is chiral.
Space group is enantiomorphic.
Number of representative symmetry operations: 6
Total number of symmetry operations: 18

Parallelepiped containing an asymmetric unit:
  cctbx Error: Brick is not available for the given space group representation.

List of symmetry operations:
Matrix Rotation-part type Axis direction Screw/glide component Origin shift
x,y,z 1---
-y,x-y,z+2/3 3^1[0,0,1]0,0,2/30,0,0
-x+y,-x,z+1/3 3^-1[0,0,1]0,0,1/30,0,0
-y,-x,-z+2/3 2[-1,1,0]0,0,00,0,1/3
x,x-y,-z+1/3 2[2,1,0]0,0,00,0,1/6
-x+y,y,-z 2[1,2,0]0,0,00,0,0
x+2/3,y+1/3,z 1---
-y+2/3,x-y+1/3,z+2/3 3^1[0,0,1]0,0,2/31/3,1/3,0
-x+y+2/3,-x+1/3,z+1/3 3^-1[0,0,1]0,0,1/31/3,0,0
-y+2/3,-x+1/3,-z+2/3 2[-1,1,0]1/6,-1/6,01/2,0,1/3
x+2/3,x-y+1/3,-z+1/3 2[2,1,0]2/3,1/3,00,0,1/6
-x+y+2/3,y+1/3,-z 2[1,2,0]1/6,1/3,01/4,0,0
x+1/3,y+2/3,z 1---
-y+1/3,x-y+2/3,z+2/3 3^1[0,0,1]0,0,2/30,1/3,0
-x+y+1/3,-x+2/3,z+1/3 3^-1[0,0,1]0,0,1/31/3,1/3,0
-y+1/3,-x+2/3,-z+2/3 2[-1,1,0]-1/6,1/6,01/2,0,1/3
x+1/3,x-y+2/3,-z+1/3 2[2,1,0]1/3,1/6,0-1/2,0,1/6
-x+y+1/3,y+2/3,-z 2[1,2,0]1/3,2/3,00,0,0 

Space group number: 154
Conventional Hermann-Mauguin symbol: P 32 2 1
Universal    Hermann-Mauguin symbol: P 32 2 1 (a-b,a+2*b,c)
Hall symbol:  P 32 2" (2/3*x-1/3*y,1/3*x+1/3*y,z)
Change-of-basis matrix: x+y,-x+2*y,z
               Inverse: 2/3*x-1/3*y,1/3*x+1/3*y,z

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type 		Representative special position operator
c181x,y,z
b92x,1/2*x,1/6
a92x,1/2*x,-1/3 

Harker planes:
Algebraic Normal vector A point in the plane
x-y,-x-2*y,2/3[0,0,1]0,0,2/3
x+y,x+y,2*z+2/3[-1,1,0]0,0,2/3
0,x-2*y,2*z+1/3[2,1,0]0,0,1/3
2*x+y,0,2*z[1,2,0]0,0,0 

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant vectors and moduli: 1
    Vector    Modulus
    (0, 0, 1) 2
  Further generators:
Matrix Rotation-part type Axis direction Screw/glide component Origin shift
-x,-y,z 2[0,0,1]0,0,00,0,0 

Grid factors implied by symmetries:
  Space group: (3, 3, 3)
  Structure-seminvariant vectors and moduli: (1, 1, 2)
  Euclidean normalizer: (3, 3, 6)

  All points of a grid over the unit cell are mapped
  exactly onto other grid points only if the factors
  shown above are factors of the grid.
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