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Result of symbol lookup:
Space group number: 136
Schoenflies symbol: D4h^14
HermannMauguin symbol: P 42/m n m
Hall symbol: P 4n 2n
Input space group symbol: P 42/m n m
Convention: Default
Number of lattice translations: 1
Space group is centric.
Number of representative symmetry operations: 8
Total number of symmetry operations: 16
Parallelepiped containing an asymmetric unit:
0<=x<3/4; 1/4<=y<=1/2; 0<=z<=1/2
List of symmetry operations:
Matrix
 Rotationpart type
 Axis direction
 Screw/glide component
 Origin shift

x,y,z
 1      

y+1/2,x+1/2,z+1/2
 4^1  [0,0,1]  0,0,1/2  0,1/2,0

x,y,z
 2  [0,0,1]  0,0,0  0,0,0

y+1/2,x+1/2,z+1/2
 4^1  [0,0,1]  0,0,1/2  1/2,0,0

x+1/2,y+1/2,z+1/2
 2  [1,0,0]  1/2,0,0  0,1/4,1/4

y,x,z
 2  [1,1,0]  0,0,0  0,0,0

x+1/2,y+1/2,z+1/2
 2  [0,1,0]  0,1/2,0  1/4,0,1/4

y,x,z
 2  [1,1,0]  0,0,0  0,0,0

x,y,z
 1      0,0,0

y1/2,x1/2,z1/2
 4^1  [0,0,1]  0,0,0  1/2,0,1/4

x,y,z
 2  [0,0,1]  0,0,0  0,0,0

y1/2,x1/2,z1/2
 4^1  [0,0,1]  0,0,0  0,1/2,1/4

x1/2,y1/2,z1/2
 2  [1,0,0]  0,1/2,1/2  1/4,0,0

y,x,z
 2  [1,1,0]  0,0,0  0,0,0

x1/2,y1/2,z1/2
 2  [0,1,0]  1/2,0,1/2  0,1/4,0

y,x,z
 2  [1,1,0]  0,0,0  0,0,0

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

k  16  1  x,y,z

j  8  m  x,x,z

i  8  m  x,y,0

h  8  2  0,1/2,z

g  4  mm2  x,x,0

f  4  mm2  x,x,0

e  4  mm2  0,0,z

d  4  4  0,1/2,1/4

c  4  2/m  0,1/2,0

b  2  mmm  0,0,1/2

a  2  mmm  0,0,0

Harker planes:
Algebraic
 Normal vector
 A point in the plane

xy+1/2,xy+1/2,1/2  [0,0,1]  1/2,1/2,1/2

2*x,2*y,0  [0,0,1]  0,0,0

1/2,2*y+1/2,2*z+1/2  [1,0,0]  1/2,1/2,1/2

x+y,xy,2*z  [1,1,0]  0,0,0

2*x+1/2,1/2,2*z+1/2  [0,1,0]  1/2,1/2,1/2

x+y,x+y,2*z  [1,1,0]  0,0,0

Additional generators of Euclidean normalizer:
Number of structureseminvariant vectors and moduli: 2
Vector Modulus
(0, 0, 1) 2
(1, 1, 0) 2
Grid factors implied by symmetries:
Space group: (2, 2, 2)
Structureseminvariant vectors and moduli: (2, 2, 2)
Euclidean normalizer: (2, 2, 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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