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Input space group symbol: -C 4acuv 2ac
Convention: Hall symbol

Number of lattice translations: 2
Space group is centric.
Number of representative symmetry operations: 8
Total number of symmetry operations: 32

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+3/4,x+1/4,z+1/2 4^1[0,0,1]0,0,1/21/4,1/2,0
-x+1/2,-y,z 2[0,0,1]0,0,01/4,0,0
y+3/4,-x+3/4,z+1/2 4^-1[0,0,1]0,0,1/23/4,0,0
x+1/2,-y,-z+1/2 2[1,0,0]1/2,0,00,0,1/4
y+3/4,x+3/4,-z 2[1,1,0]3/4,3/4,00,0,0
-x,y,-z+1/2 2[0,1,0]0,0,00,0,1/4
-y+3/4,-x+1/4,-z 2[-1,1,0]1/4,-1/4,01/2,0,0
-x,-y,-z -1--0,0,0
y-3/4,-x-1/4,-z-1/2 -4^1[0,0,1]0,0,0-1/2,1/4,-1/4
x-1/2,y,-z -2[0,0,1]-1/2,0,00,0,0
-y-3/4,x-3/4,-z-1/2 -4^-1[0,0,1]0,0,00,-3/4,-1/4
-x-1/2,y,z-1/2 -2[1,0,0]0,0,-1/2-1/4,0,0
-y-3/4,-x-3/4,z -2[1,1,0]0,0,0-3/4,0,0
x,-y,z-1/2 -2[0,1,0]0,0,-1/20,0,0
y-3/4,x-1/4,z -2[-1,1,0]-1/2,-1/2,0-1/4,0,0
x+1/2,y+1/2,z 1---
-y+5/4,x+3/4,z+1/2 4^1[0,0,1]0,0,1/21/4,1,0
-x+1,-y+1/2,z 2[0,0,1]0,0,01/2,1/4,0
y+5/4,-x+5/4,z+1/2 4^-1[0,0,1]0,0,1/25/4,0,0
x+1,-y+1/2,-z+1/2 2[1,0,0]1,0,00,1/4,1/4
y+5/4,x+5/4,-z 2[1,1,0]5/4,5/4,00,0,0
-x+1/2,y+1/2,-z+1/2 2[0,1,0]0,1/2,01/4,0,1/4
-y+5/4,-x+3/4,-z 2[-1,1,0]1/4,-1/4,01,0,0
-x+1/2,-y+1/2,-z -1--1/4,1/4,0
y-1/4,-x+1/4,-z-1/2 -4^1[0,0,1]0,0,00,1/4,-1/4
x,y+1/2,-z -2[0,0,1]0,1/2,00,0,0
-y-1/4,x-1/4,-z-1/2 -4^-1[0,0,1]0,0,00,-1/4,-1/4
-x,y+1/2,z-1/2 -2[1,0,0]0,1/2,-1/20,0,0
-y-1/4,-x-1/4,z -2[1,1,0]0,0,0-1/4,0,0
x+1/2,-y+1/2,z-1/2 -2[0,1,0]1/2,0,-1/20,1/4,0
y-1/4,x+1/4,z -2[-1,1,0]0,0,0-1/4,0,0 

Space group number: 137
Conventional Hermann-Mauguin symbol: P 42/n m c :2
Universal    Hermann-Mauguin symbol: P 42/n m c :2 (a+b,-a+b,c)
Hall symbol: -P 4ac 2a (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
h321x,y,z
g16mx,x-1/4,z
f1620,y,1/4
e16-10,0,0
d8mm21/4,0,z
c8mm20,1/4,z
b4-42m0,1/4,1/4
a4-42m0,1/4,-1/4 

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

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: (4, 4, 2)
  Structure-seminvariant vectors and moduli: (2, 1, 2)
  Euclidean normalizer: (4, 4, 2)

  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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