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Result of symbol lookup:
  Space group number: 109
  Schoenflies symbol: C4v^11
  Hermann-Mauguin symbol: I 41 m d
  Hall symbol: I 4bw -2

Input space group symbol: I 41 m d
Convention: Default

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

Parallelepiped containing an asymmetric unit:
  0<=x<=1/4; 0<=y<=1/4; 0<=z<1

List of symmetry operations:
Matrix Rotation-part type Axis direction Screw/glide component Origin shift
x,y,z 1---
-y,x+1/2,z+1/4 4^1[0,0,1]0,0,1/4-1/4,1/4,0
-x+1/2,-y+1/2,z+1/2 2[0,0,1]0,0,1/21/4,1/4,0
y+1/2,-x,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,-x+1/2,z+1/4 -2[1,1,0]-1/4,1/4,1/41/4,0,0
x+1/2,-y+1/2,z+1/2 -2[0,1,0]1/2,0,1/20,1/4,0
y+1/2,x,z+3/4 -2[-1,1,0]1/4,1/4,3/41/4,0,0
x+1/2,y+1/2,z+1/2 1---
-y+1/2,x+1,z+3/4 4^1[0,0,1]0,0,3/4-1/4,3/4,0
-x+1,-y+1,z+1 2[0,0,1]0,0,11/2,1/2,0
y+1,-x+1/2,z+5/4 4^-1[0,0,1]0,0,5/43/4,-1/4,0
-x+1/2,y+1/2,z+1/2 -2[1,0,0]0,1/2,1/21/4,0,0
-y+1/2,-x+1,z+3/4 -2[1,1,0]-1/4,1/4,3/43/4,0,0
x+1,-y+1,z+1 -2[0,1,0]1,0,10,1/2,0
y+1,x+1/2,z+5/4 -2[-1,1,0]3/4,3/4,5/41/4,0,0 

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type 		Representative special position operator
c161x,y,z
b8m0,y,z
a4mm20,0,z 

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

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant vectors and moduli: 1
    Vector    Modulus
    (0, 0, 1) 0
  Inversion through a centre at: 1/4,0,0

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