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Result of symbol lookup:
  Space group number: 75
  Schoenflies symbol: C4^1
  Hermann-Mauguin symbol: P 4
  Hall symbol: P 4

Input space group symbol: P 4
Convention: Default

Number of lattice translations: 1
Space group is acentric.
Space group is chiral.
Number of representative symmetry operations: 4
Total number of symmetry operations: 4

Parallelepiped containing an asymmetric unit:
  0<=x<=1/2; 0<=y<=1/2; 0<=z<1

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

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type
Representative special position operator

Harker planes:
Algebraic Normal vector A point in the plane

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

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

  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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