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Input space group symbol: C 4aw 2
Convention: Hall symbol

Number of lattice translations: 2
Space group is acentric.
Space group is chiral.
Space group is enantiomorphic.
Number of representative symmetry operations: 8
Total number of symmetry operations: 16

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+1/2,x,z+1/4 4^1[0,0,1]0,0,1/41/4,1/4,0
-x+1/2,-y+1/2,z+1/2 2[0,0,1]0,0,1/21/4,1/4,0
y,-x+1/2,z+3/4 4^-1[0,0,1]0,0,3/41/4,1/4,0
x,-y,-z 2[1,0,0]0,0,00,0,0
y+1/2,x,-z+1/4 2[1,1,0]1/4,1/4,01/4,0,1/8
-x+1/2,y+1/2,-z+1/2 2[0,1,0]0,1/2,01/4,0,1/4
-y,-x+1/2,-z+3/4 2[-1,1,0]-1/4,1/4,01/4,0,3/8
x+1/2,y+1/2,z 1---
-y+1,x+1/2,z+1/4 4^1[0,0,1]0,0,1/41/4,3/4,0
-x+1,-y+1,z+1/2 2[0,0,1]0,0,1/21/2,1/2,0
y+1/2,-x+1,z+3/4 4^-1[0,0,1]0,0,3/43/4,1/4,0
x+1/2,-y+1/2,-z 2[1,0,0]1/2,0,00,1/4,0
y+1,x+1/2,-z+1/4 2[1,1,0]3/4,3/4,01/4,0,1/8
-x+1,y+1,-z+1/2 2[0,1,0]0,1,01/2,0,1/4
-y+1/2,-x+1,-z+3/4 2[-1,1,0]-1/4,1/4,03/4,0,3/8

Space group number: 92
Conventional Hermann-Mauguin symbol: P 41 21 2
Universal    Hermann-Mauguin symbol: P 41 21 2 (a+b,-a+b,c)
Hall symbol:  P 4abw 2nw (1/2*x+1/2*y,-1/2*x+1/2*y,z)
Change-of-basis matrix: x-y,x+y,z
               Inverse: 1/2*x+1/2*y,-1/2*x+1/2*y,z

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type
Representative special position operator
b161x,y,z
a82x,0,0

Harker planes:
Algebraic Normal vector A point in the plane
x-y+1/2,-x-y,1/4[0,0,1]1/2,0,1/4
2*x+1/2,2*y+1/2,1/2[0,0,1]1/2,1/2,1/2
0,2*y,2*z[1,0,0]0,0,0
x+y+1/2,-x-y,2*z+1/4[1,1,0]1/2,0,1/4
2*x+1/2,1/2,2*z+1/2[0,1,0]1/2,1/2,1/2
x+y,x+y+1/2,2*z+3/4[-1,1,0]0,1/2,3/4

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant vectors and moduli: 2
    Vector    Modulus
    (1, 0, 0) 2
    (0, 0, 1) 2

Grid factors implied by symmetries:
  Space group: (2, 2, 4)
  Structure-seminvariant vectors and moduli: (2, 1, 2)
  Euclidean normalizer: (2, 2, 4)

  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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