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Result of symbol lookup:
  Space group number: 170
  Schoenflies symbol: C6^3
  Hermann-Mauguin symbol: P 65
  Hall symbol: P 65

Input space group symbol: P 65
Convention: Default

Number of lattice translations: 1
Space group is acentric.
Space group is chiral.
Space group is enantiomorphic.
Number of representative symmetry operations: 6
Total number of symmetry operations: 6

Parallelepiped containing an asymmetric unit:
  0<=x<1; 0<=y<1; 0<=z<1/6

List of symmetry operations:
Matrix Rotation-part type Axis direction Screw/glide component Origin shift
x,y,z 1---
x-y,x,z+5/6 6^1[0,0,1]0,0,5/60,0,0
-y,x-y,z+2/3 3^1[0,0,1]0,0,2/30,0,0
-x,-y,z+1/2 2[0,0,1]0,0,1/20,0,0
-x+y,-x,z+1/3 3^-1[0,0,1]0,0,1/30,0,0
y,-x+y,z+1/6 6^-1[0,0,1]0,0,1/60,0,0

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: 1
    Vector    Modulus
    (0, 0, 1) 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, 6)
  Structure-seminvariant vectors and moduli: (1, 1, 1)
  Euclidean normalizer: (1, 1, 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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