An entry from the Catalogue of Lattices, which is a joint project of
Gabriele Nebe, RWTH Aachen University (nebe@math.rwth-aachen.de) and
Neil J. A. Sloane (njasloane@gmail.com)

Last modified Fri Jul 18 13:14:27 CEST 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
GRAM (floating point or integer Gram matrix)
DIVISORS (elementary divisors)
MINIMAL_NORM
KISSING_NUMBER
GROUP_ORDER
GROUP_GENERATORS
ORBITS
PROPERTIES
REFERENCES
NOTES
URL (links to other sites for this lattice)
LAST_LINE

• NAME
  SL2(17)SS3.2a
  

• DIMENSION
  32
  

• GRAM (floating point or integer Gram matrix)
  32 0
  4
  2 4
  2 2 4
  2 1 1 4
  1 2 1 2 4
  1 1 1 0 0 4
  2 2 1 1 2 1 4
  2 1 1 1 0 0 0 4
  2 1 2 2 2 0 2 1 4
  1 1 0 2 2 1 1 1 2 4
  2 1 2 2 1 1 1 1 1 0 4
  1 2 2 2 2 1 0 0 1 1 2 4
  1 1 1 1 1 0 1 2 1 1 0 0 4
  2 1 1 1 1 0 1 1 2 1 1 1 0 4
  2 1 1 1 0 1 1 1 1 0 2 1 0 1 4
  1 1 0 0 1 2 1 0 0 1 1 1 0 1 1 4
  2 1 0 2 1 0 2 1 1 1 2 0 0 1 1 1 4
  1 0 1 1 1 1 0 1 0 0 2 1 1 0 1 1 0 4
  2 1 1 2 1 1 0 2 1 2 1 1 1 1 0 1 1 1 4
  1 2 2 1 2 0 1 1 2 1 1 1 1 1 1 0 0 1 1 4
  2 2 1 1 1 1 1 2 0 1 1 1 2 0 0 1 1 1 2 0 4
  1 1 1 1 1 1 0 1 1 2 1 2 1 2 1 2 0 1 1 1 1 4
  1 1 0 0 0 1 1 1 1 1 0 0 1 1 2 0 0 0 0 1 0 1 4
  1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 0 0 0 1 1 1 1 2 4
  1 1 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 0 0 1 0 1 0 4
  1 2 1 1 2 1 2 0 1 1 1 1 1 0 1 1 1 1 1 2 1 0 1 1 1 4
  1 1 1 1 1 0 0 2 1 1 1 1 2 1 1 0 0 1 1 2 1 1 1 2 0 1 4
  1 1 1 1 1 0 1 2 2 2 1 0 1 1 1 0 1 0 1 2 0 1 1 1 1 1 1 4
  2 1 1 1 1 -1 0 2 2 1 1 1 1 2 1 0 1 0 1 1 1 1 1 1 1 0 2 1 4
  1 2 1 1 2 0 1 2 2 2 0 1 2 1 1 0 0 0 1 2 1 1 2 2 1 1 2 2 2 4
  1 1 1 1 1 1 1 1 2 2 1 1 1 0 1 1 0 0 1 1 1 1 1 1 1 1 1 2 1 2 4
  1 1 2 1 0 0 0 2 1 0 2 1 1 1 1 0 1 0 1 1 1 1 0 1 1 0 1 2 1 1 1 4
  

• DIVISORS (elementary divisors)
  1^32
  

• MINIMAL_NORM
  4
  

• KISSING_NUMBER
  146880
  

• GROUP_ORDER
  2^7 3^3 17
  

• GROUP_GENERATORS
  5
  32
  -1 2 0 2 0 0 2 0 1 -2 -2 -2 -3 -2 -1 0 -1 2 1 -2 -1 2 0 1 0 0 1 0 2 0 0 1
  0 3 -1 1 0 0 2 0 1 -2 -1 -3 -3 -3 -1 -1 -1 2 2 -3 -3 4 -1 1 0 1 1 -1 2 1 0 2
  0 2 -1 0 0 0 1 0 0 0 -1 -1 -1 -1 0 -1 0 2 1 -1 -2 1 -1 1 0 0 0 -1 1 0 1 1
  -1 1 1 3 3 1 4 1 -4 -3 -4 -3 -3 -2 -1 -1 -1 3 1 -3 -3 3 1 0 -2 1 0 0 5 -1 2 3
  -1 1 1 4 1 1 5 0 -3 -5 -6 -3 -5 -3 -2 -1 0 4 2 -3 -3 5 0 1 -1 1 1 1 5 0 2 3
  1 1 -1 -3 -1 -1 -3 0 3 3 2 1 1 1 1 0 1 0 -1 1 1 -2 -1 1 1 -1 0 -1 -3 0 -1 -1
  0 1 0 -1 -1 -1 -2 0 3 1 1 0 0 0 0 1 0 0 0 0 1 -1 0 1 1 -1 0 0 -2 0 -1 -1
  1 2 -1 0 0 0 -2 -1 3 -1 2 -2 -1 -1 -1 0 -1 0 0 -2 0 1 0 0 0 1 1 0 -1 2 -1 0
  0 1 0 1 0 0 1 0 0 -1 -2 -1 -2 -1 -1 0 0 2 0 -1 -1 1 0 1 0 0 0 0 1 0 1 1
  0 0 1 1 1 0 2 0 -2 -1 -2 -1 -2 -1 -1 0 0 2 0 -1 -1 1 1 0 -1 0 0 0 2 0 1 2
  1 1 -1 0 1 0 0 0 0 0 0 -1 0 -1 0 0 -1 1 0 -1 -1 0 0 0 -1 0 0 0 1 0 0 1
  -1 2 0 3 1 1 5 0 -3 -4 -5 -3 -4 -3 -1 -2 0 4 2 -3 -4 5 -1 1 -1 1 1 0 5 0 2 3
  0 2 0 1 2 1 2 0 -1 -4 -4 -2 -3 -2 -1 -2 1 3 2 -3 -3 4 0 1 -1 1 1 0 2 0 2 2
  0 0 0 0 1 0 2 1 -2 1 -1 0 0 0 0 0 -1 1 0 0 -2 -1 0 0 -1 0 -1 -1 2 -1 1 2
  -1 0 0 2 -1 0 4 0 -1 -2 -3 0 -3 -2 -1 0 -1 2 1 -1 -1 2 0 1 0 0 1 1 3 0 0 1
  0 0 0 0 0 0 2 0 0 -2 -3 0 -2 -1 0 -1 1 2 1 -1 -1 2 -1 1 0 0 1 0 1 0 1 1
  1 0 0 -1 1 -1 -1 1 0 2 1 0 1 0 0 1 -1 0 -1 0 0 -2 1 0 -1 0 -1 -1 0 -1 0 1
  0 1 0 2 2 1 4 0 -3 -4 -4 -2 -3 -2 -1 -2 0 3 2 -3 -3 4 0 0 -2 1 1 1 4 0 2 2
  0 2 0 2 2 1 2 0 -1 -3 -2 -3 -3 -2 -1 -1 -1 2 1 -3 -2 3 0 0 -1 1 1 0 3 0 1 2
  1 1 -1 1 1 0 2 0 -1 -1 0 -2 -2 -2 -1 0 -2 1 1 -2 -2 2 0 0 -1 1 0 0 2 1 0 2
  0 4 -1 1 1 1 0 -1 3 -4 -1 -4 -3 -3 -1 -2 0 2 2 -4 -2 5 -1 1 0 1 2 0 1 1 0 1
  0 0 0 0 1 0 3 0 -2 -1 -2 0 -1 -1 0 -1 0 2 1 -1 -2 1 0 0 -1 0 0 0 2 0 1 2
  -1 1 0 1 -1 0 3 0 0 -2 -3 0 -3 -2 -1 0 0 2 1 -1 -1 2 0 1 0 0 1 1 2 0 0 1
  -1 1 0 2 0 1 2 0 0 -3 -3 -1 -3 -2 -1 0 0 2 1 -1 -1 2 0 1 0 0 1 1 2 0 0 1
  -1 1 1 4 0 1 6 0 -3 -5 -7 -2 -5 -3 -2 -1 0 4 2 -3 -3 5 0 1 -1 1 2 1 5 0 2 3
  1 2 -1 0 1 0 2 1 -1 -1 -1 -2 -2 -2 -1 -1 -1 2 1 -2 -3 3 -1 1 -1 1 0 -1 2 0 1 2
  0 1 0 2 2 1 3 0 -3 -3 -4 -2 -3 -2 -1 -1 0 3 1 -2 -3 3 0 1 -2 1 0 0 4 0 2 3
  2 0 -1 -1 -1 -1 -2 -1 2 2 4 0 1 0 -1 2 -2 -1 -1 0 1 -2 1 -1 0 0 0 0 -2 2 -2 0
  0 1 0 3 1 1 4 0 -2 -4 -5 -2 -4 -3 -2 -1 0 3 1 -2 -3 4 0 1 -1 1 1 0 4 0 2 3
  -1 2 0 3 0 1 3 -1 0 -5 -4 -3 -5 -3 -2 -1 0 3 2 -3 -2 5 0 1 0 1 2 1 3 1 1 2
  0 2 -1 1 -1 1 0 -2 3 -4 -2 -2 -3 -2 -1 -1 1 2 1 -2 0 4 -1 1 1 0 2 1 0 2 0 0
  1 2 -1 0 1 0 0 0 0 1 1 -2 0 -1 0 0 -2 1 0 -2 -2 0 0 0 -1 1 0 -1 1 0 0 2
  
  32
  1 0 -1 -3 1 -1 -5 0 2 4 4 1 4 2 2 1 0 -2 -2 2 2 -4 0 0 0 -1 -2 -1 -3 -1 -1 -1
  0 -1 0 0 0 0 0 -1 0 -1 -1 1 0 0 0 0 1 0 0 1 1 0 0 0 0 -1 0 1 0 0 0 0
  0 1 -1 -2 -1 -1 -2 -1 3 1 1 1 1 0 1 0 1 0 0 1 1 -1 -1 1 1 -1 0 0 -2 0 -1 -1
  -1 -1 0 0 -1 0 -1 0 1 1 1 1 1 1 1 1 0 -1 -1 2 2 -2 0 0 1 -1 -1 0 -1 0 -1 -1
  1 -2 0 -2 -1 -1 -4 0 2 3 4 2 3 2 1 2 0 -3 -2 3 3 -4 0 -1 1 -1 -1 0 -4 1 -2 -2
  0 -1 0 -1 0 0 -1 -1 0 0 -1 2 1 1 1 0 2 0 0 1 1 -1 0 0 0 -1 0 1 -1 0 0 -1
  2 -2 -1 -4 1 -1 -5 0 1 5 5 2 5 3 2 1 0 -3 -2 3 2 -5 0 -1 0 -1 -2 -1 -4 0 -1 -1
  0 1 -1 -1 0 0 -1 0 1 1 1 0 1 0 1 -1 0 0 0 0 0 0 -1 0 0 0 -1 -1 0 0 0 0
  0 1 -1 -1 0 0 -3 -1 3 0 2 -1 1 0 1 0 0 -1 0 0 1 0 -1 0 1 0 0 0 -2 1 -1 -1
  -1 0 0 2 0 1 1 -1 0 -3 -1 -1 -1 -1 0 0 0 0 1 -1 0 2 0 -1 0 0 1 1 1 1 0 0
  0 -1 0 -3 1 -1 -2 1 0 3 2 2 3 2 2 0 1 -1 -1 2 1 -3 0 0 0 -1 -2 -1 -2 -1 0 -1
  -1 0 0 0 -2 0 -1 -1 3 -2 -1 1 -1 0 0 0 2 0 0 1 2 1 -1 1 2 -1 1 1 -2 1 -1 -2
  0 0 -1 -1 -1 0 -1 0 2 1 1 1 1 0 1 0 0 -1 0 1 1 -1 -1 0 1 -1 0 0 -1 0 -1 -1
  -1 1 0 1 0 0 -2 -1 3 -1 2 -2 -1 -1 0 1 -1 -1 0 -1 2 1 0 0 1 0 1 1 -1 1 -2 -1
  0 1 -1 0 2 1 2 1 -2 -2 -3 -1 -1 -1 0 -2 1 2 1 -1 -3 3 -1 1 -1 1 -1 -1 3 -1 2 2
  2 0 -1 -2 2 0 -4 0 2 1 3 0 2 1 1 0 0 -2 -1 0 1 -1 0 -1 0 0 0 0 -3 0 -1 -1
  1 -1 0 -1 3 0 0 1 -3 2 1 0 2 1 1 0 -1 0 -1 0 -1 -2 1 -1 -2 0 -2 -1 1 -1 1 2
  1 -1 -1 -4 -1 -2 -5 1 3 6 7 3 5 3 2 2 -1 -4 -2 3 3 -6 0 -1 1 -1 -2 -1 -5 0 -3 -3
  -1 0 0 0 -1 0 -3 -1 3 0 1 1 1 1 1 1 1 -1 -1 1 3 -2 0 0 1 -1 0 1 -2 0 -1 -2
  -1 0 0 1 0 0 1 0 0 -2 -1 0 -1 -1 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0
  1 -1 -1 -4 -1 -1 -6 -1 4 4 5 3 5 3 2 1 1 -3 -2 3 4 -5 0 -1 1 -2 -1 0 -5 0 -2 -3
  -1 2 -1 1 0 1 0 -1 3 -4 0 -2 -2 -2 0 -1 0 0 2 -2 0 4 -1 0 1 0 2 1 0 1 -1 -1
  -2 1 0 3 1 2 5 0 -2 -6 -6 -2 -4 -3 -1 -2 1 3 3 -3 -3 6 -1 1 -1 1 1 1 5 0 2 2
  -1 0 0 -1 -1 0 -1 0 2 0 -1 1 0 0 1 0 2 0 0 1 1 0 -1 1 1 -1 0 0 -1 0 0 -1
  0 -1 1 1 1 0 2 1 -3 0 -2 0 0 0 0 0 0 1 0 0 -1 0 0 0 -1 0 -1 0 2 -1 1 1
  0 -1 0 0 0 0 0 0 0 -1 -1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
  -1 0 0 1 0 0 1 1 0 -1 -1 0 -1 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0
  -1 1 0 2 1 1 4 0 -3 -3 -3 -2 -2 -2 0 -2 0 2 2 -2 -3 4 -1 0 -1 1 0 0 4 0 2 2
  0 1 0 0 1 0 -1 0 1 -1 0 -1 0 -1 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0
  -1 0 0 1 0 1 2 0 -1 -2 -3 0 -1 -1 0 -1 1 1 1 0 -1 2 -1 0 0 0 0 0 2 0 1 1
  -1 0 0 0 1 1 1 0 -1 -2 -3 0 0 0 1 -2 2 1 1 0 -1 2 -1 0 0 0 0 0 1 -1 2 0
  -2 2 0 2 0 1 3 -1 0 -4 -4 -2 -3 -2 0 -2 1 3 2 -2 -1 4 -1 1 0 0 1 1 3 0 1 1
  
  32
  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0
  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 -1 0 0 -1 0 1 0 0 0 -1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
  1 2 -2 -1 -2 -1 -2 -1 5 1 4 -1 0 -1 0 1 -2 -1 0 -1 1 0 -1 0 1 0 1 0 -2 2 -3 -1
  0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 0 1 0 0 -1 -1 1 -1 2 -1 0 0 -1 1 -1 -1 0 -1 1 0 1 -1 0 0 1 1 -1 1 -1 -1
  0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 -1 -1 1 0 0 2 1 0 0 0 0 1 -1 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0
  0 1 0 1 0 0 0 0 1 -1 0 -1 -1 -1 0 0 0 0 0 -1 0 1 0 0 0 0 1 0 0 0 0 0
  1 1 -1 -2 0 0 -1 0 1 1 1 0 1 0 1 -1 1 0 0 0 -1 0 -1 0 0 0 0 -1 -1 0 0 0
  2 -2 0 -2 0 -1 -3 0 1 3 3 2 3 2 0 2 0 -2 -2 2 2 -4 1 -1 0 -1 -1 0 -3 0 -1 -1
  0 1 0 -1 0 0 -3 -1 3 0 1 0 1 1 1 0 1 -1 0 0 2 -1 0 0 1 -1 1 1 -3 0 -1 -2
  1 1 -1 -1 -1 0 -2 -1 3 0 2 0 0 0 0 0 0 -1 0 0 1 0 -1 0 1 0 1 0 -2 1 -1 -1
  2 0 -2 -3 -2 -1 -4 -1 4 3 4 2 3 1 1 1 0 -2 -1 2 2 -3 -1 0 1 -1 0 0 -4 1 -2 -2
  0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 -1 0 0 -1 0 1 0 0 -1 -1 1 -1 -1 -1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0
  1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 -1 1 2 0 0 2 0 -1 -2 -2 0 -2 -1 -1 1 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 0
  1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 0 -2 0 -1 -2 0 1 3 2 1 2 1 1 1 0 -1 -1 1 1 -3 0 0 0 -1 0 0 -2 -1 -1 -1
  0 1 0 1 0 0 2 0 0 -1 -1 -1 -2 -1 -1 0 -1 1 1 -1 -1 1 0 0 0 0 1 0 1 0 0 1
  -1 1 0 1 -1 0 -1 -1 3 -1 0 -1 -1 0 0 1 0 0 0 0 2 0 0 0 1 -1 1 1 -1 0 -1 -1
  2 -1 0 -1 0 -1 -1 0 -1 3 2 1 2 1 0 1 -1 -1 -1 1 0 -3 1 -1 -1 0 -1 -1 -1 0 0 1
  1 -2 0 0 0 0 1 0 -1 0 0 1 0 0 0 0 0 -1 0 1 0 0 0 -1 0 0 0 0 0 1 0 0
  1 -1 0 -1 -1 -1 -3 -1 3 1 3 1 1 1 0 2 0 -2 -1 1 3 -2 1 -1 1 -1 1 1 -4 1 -2 -2
  0 0 1 1 0 -1 -1 0 0 2 3 -1 1 1 0 2 -2 -2 -1 0 1 -2 1 -1 0 0 0 0 -1 0 -1 -1
  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0
  0 0 0 1 -2 0 0 -1 2 -1 0 0 -1 0 -1 1 0 0 0 0 1 0 0 0 1 0 1 1 -1 1 -1 -1
  0 0 0 0 -1 -1 1 0 0 1 1 0 0 0 0 1 -1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0
  1 0 0 -1 0 -1 -5 -1 3 3 5 0 3 2 1 2 -1 -3 -2 1 3 -4 1 -1 1 -1 0 0 -4 0 -2 -2
  
  32
  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 1 0 0 -1 -1 0 0 1 1 1 0 0 0 0 1 -1 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0
  0 1 0 0 0 0 0 0 1 -1 0 -1 -1 -1 0 0 0 0 1 -1 0 1 0 0 0 0 1 0 0 0 0 0
  0 -1 1 -1 -2 -1 -1 0 1 1 -1 2 0 1 0 1 2 0 -1 2 2 -2 0 1 1 -1 0 0 -2 0 0 -1
  0 0 0 1 0 0 2 0 -2 0 -2 0 0 0 0 0 0 1 0 0 -1 0 0 0 -1 0 0 0 2 -1 1 1
  1 -1 0 -3 -1 -1 -4 0 2 4 3 2 3 3 1 1 1 -2 -2 3 3 -4 0 0 1 -1 -1 -1 -4 0 -1 -2
  -2 2 1 4 3 2 7 1 -5 -6 -8 -3 -5 -3 -1 -3 1 5 3 -4 -5 6 0 1 -2 1 1 0 7 -2 4 4
  -1 1 1 2 -1 0 3 0 -1 -2 -3 -1 -3 -1 -1 0 0 2 1 -1 -1 2 0 1 0 0 1 0 2 0 1 1
  -2 1 1 3 -1 1 4 -1 -1 -5 -6 -1 -4 -2 -1 -1 2 3 2 -2 -1 4 0 1 0 0 2 1 3 0 2 1
  0 0 0 0 -1 -1 0 0 1 1 1 0 0 0 0 1 -1 0 0 0 1 -1 0 0 0 0 0 0 0 0 -1 0
  0 0 1 0 -1 -1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0
  -2 1 1 2 1 1 4 1 -3 -2 -5 -1 -3 -1 0 -1 1 3 1 -1 -2 2 0 1 -1 0 0 0 4 -2 2 2
  0 1 0 0 0 0 0 0 1 0 1 -1 0 0 0 0 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 0 -2 0 -1 -1 0 0 3 1 1 2 1 1 0 0 0 0 1 0 -2 0 0 0 -1 -1 -1 -1 -1 0 0
  0 -2 1 -1 -1 -1 0 1 -2 4 -1 3 2 2 1 1 1 0 -2 3 1 -4 0 1 0 -1 -2 -1 0 -2 1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
  -1 -1 1 1 0 0 5 1 -4 -1 -5 1 -2 -1 0 -1 1 3 1 0 -2 1 0 1 -1 0 0 0 4 -2 2 2
  0 1 0 1 0 0 0 0 1 -1 0 -1 -1 -1 0 0 0 0 0 -1 0 1 0 0 0 0 1 0 0 0 0 0
  -1 1 1 2 -1 0 3 0 0 -2 -3 -1 -3 -2 -1 0 0 2 1 -1 -1 2 0 1 0 0 1 0 2 0 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -2 1 1 2 -1 0 3 0 -1 -1 -3 -1 -2 -1 0 0 0 2 1 -1 -1 1 0 1 0 0 0 0 3 -1 1 1
  -2 0 2 4 1 1 6 0 -4 -4 -6 -2 -4 -2 -1 -1 0 3 2 -2 -2 4 1 0 -1 0 1 1 5 -1 2 2
  -1 1 0 1 -1 0 -1 -1 3 -1 0 -1 -1 0 0 1 0 0 0 0 2 0 0 0 1 -1 1 1 -1 0 -1 -1
  0 -1 1 0 1 0 2 1 -3 -1 -4 1 -1 0 0 -1 2 2 0 0 -1 1 0 1 -1 0 -1 0 2 -1 2 1
  0 -1 1 -1 -2 -1 -1 0 1 2 1 2 1 1 0 1 1 -1 -1 2 2 -2 0 0 1 -1 0 0 -2 0 -1 -2
  -2 1 1 3 0 1 5 0 -2 -4 -6 -1 -4 -2 -1 -1 1 4 2 -2 -2 3 0 1 -1 0 1 1 4 -1 2 2
  -2 2 1 3 0 1 3 -1 0 -5 -5 -2 -4 -2 -1 -1 1 3 2 -3 -1 4 0 1 0 0 2 1 3 0 1 1
  -1 1 1 4 0 1 6 0 -3 -5 -6 -2 -5 -3 -2 -1 0 4 2 -3 -3 5 0 1 -1 1 1 1 5 0 2 3
  -1 1 1 2 1 1 5 0 -3 -4 -7 -1 -4 -2 -1 -2 2 4 2 -2 -3 4 0 1 -1 0 1 0 4 -1 3 3
  -1 0 1 2 -1 0 3 0 -1 -2 -4 0 -3 -1 -1 0 1 2 1 -1 -1 2 0 1 0 0 1 0 2 0 1 1
  -1 2 0 1 1 0 1 0 0 -1 0 -2 -1 -1 0 0 -1 1 1 -2 -1 1 0 0 -1 0 0 0 2 0 0 1
  
  32
  -1 0 0 2 -2 0 2 0 1 0 0 0 -2 -1 -1 1 -2 0 0 0 1 0 0 0 1 0 1 1 1 0 -2 0
  -3 0 2 4 1 1 5 1 -4 -2 -5 -1 -3 -1 0 0 -1 2 1 -1 -1 1 1 0 -1 0 0 1 5 -2 1 2
  -2 0 2 3 0 0 4 1 -3 -1 -5 0 -3 -1 -1 1 0 3 0 -1 -1 0 1 1 -1 0 0 1 4 -2 1 2
  -1 2 0 4 0 1 5 -1 0 -6 -5 -3 -6 -4 -2 -1 -1 3 3 -4 -2 6 0 1 0 1 3 2 4 0 0 2
  -1 0 1 2 1 1 2 0 -1 -3 -5 -1 -3 -1 0 -1 1 2 1 -1 0 2 0 1 0 0 1 1 2 -1 1 1
  -2 -2 2 2 2 1 7 2 -8 -1 -7 2 -1 0 0 -1 1 3 1 1 -3 0 1 0 -2 -1 -1 0 6 -4 4 3
  -1 -1 1 2 1 1 2 1 -2 -1 -2 0 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 1 2 -1 0 0
  -1 0 0 2 -3 0 1 -1 2 -1 0 0 -2 -1 -1 1 -1 0 0 0 2 1 0 0 1 0 1 2 0 1 -2 -1
  0 1 -1 1 0 1 2 0 1 -3 -3 -1 -3 -2 -1 -1 0 2 1 -2 -1 3 -1 1 0 1 1 1 2 0 0 1
  -1 0 0 3 1 2 7 0 -4 -6 -8 -1 -5 -3 -1 -3 1 4 3 -2 -3 6 -1 1 -1 1 1 1 6 -1 3 3
  0 0 0 0 -1 -1 -2 0 2 2 2 1 1 1 0 2 -1 -1 -1 1 2 -3 1 0 1 -1 0 1 -2 -1 -2 -1
  -2 1 1 3 1 1 5 0 -3 -4 -7 -1 -4 -2 -1 -1 1 4 2 -2 -2 3 1 1 -1 0 1 1 5 -2 2 3
  -3 0 2 4 -1 1 5 -1 -2 -5 -6 -1 -5 -2 -1 -1 1 3 2 -2 0 4 0 1 0 0 2 3 4 0 1 0
  0 1 -2 1 -2 1 0 -1 3 -2 -1 0 -2 -1 -1 0 0 1 0 0 1 1 -1 1 1 0 1 1 0 1 -1 0
  0 0 -1 -1 -1 -1 -3 0 4 2 5 1 2 1 0 2 -2 -3 -1 1 3 -3 1 -1 1 -1 0 1 -3 0 -3 -2
  0 -2 0 -3 -1 -1 -3 1 0 5 2 4 4 4 2 1 1 -2 -2 5 3 -6 0 0 1 -2 -2 -1 -3 -2 0 -2
  0 1 -1 1 -2 0 -2 -1 4 0 3 -1 0 0 0 1 -2 -2 0 0 2 0 -1 0 2 0 1 1 -2 1 -3 -2
  0 -1 1 0 0 -1 0 1 -1 2 0 1 0 1 0 1 0 0 -1 1 1 -2 1 0 0 -1 0 0 -1 -1 0 0
  -1 -1 1 3 -2 0 6 0 -3 -2 -6 1 -4 -2 -1 0 0 3 1 0 -1 2 0 1 0 0 1 1 4 -1 1 2
  -1 0 1 2 1 0 2 1 -1 -1 -2 -1 -2 -1 0 1 -1 1 0 -1 0 0 1 0 -1 0 0 1 2 -1 0 1
  -3 -2 3 5 -1 1 6 0 -5 -3 -6 0 -4 -1 -1 0 0 2 1 0 0 2 1 0 0 0 1 2 5 -1 1 1
  -1 0 0 2 0 1 4 0 -3 -3 -5 0 -3 -1 -1 -1 1 3 1 0 -1 2 0 1 -1 0 0 1 4 -1 2 2
  0 0 -1 0 1 1 2 0 -1 -1 0 0 0 -1 0 -1 -1 0 1 -1 -1 1 0 -1 -1 0 0 1 2 0 0 1
  -2 -1 1 3 -1 1 4 -2 -1 -5 -5 1 -3 -2 -1 0 1 2 2 -1 1 2 1 0 0 -1 2 4 3 0 0 0
  1 1 -1 -4 -1 -1 -7 0 5 5 6 1 4 3 2 0 0 -3 -2 2 3 -4 -1 0 2 -1 -1 -1 -6 0 -2 -3
  -2 -1 2 2 1 0 2 1 -2 0 -2 0 -1 0 1 1 -1 0 0 0 1 -1 1 0 0 -1 0 1 2 -2 0 0
  -3 0 1 4 -1 1 4 -1 0 -5 -4 -1 -4 -2 -1 0 0 2 2 -2 1 3 1 0 0 0 2 3 3 0 0 0
  0 1 -1 0 -1 0 -1 0 3 -1 0 0 -1 -1 0 0 0 0 0 0 1 1 -1 1 1 0 0 1 -1 0 -1 -1
  0 1 -2 -1 -3 0 -3 -2 6 0 3 0 0 0 0 0 0 -1 0 0 3 0 -1 0 2 0 1 1 -3 2 -3 -2
  -1 0 0 1 0 1 1 -1 1 -3 -3 0 -2 -1 0 -1 1 1 1 -1 1 2 0 0 0 0 1 2 1 0 0 0
  0 -1 0 -2 1 0 0 1 -1 1 -1 2 1 1 1 -1 1 0 0 1 0 -1 0 0 0 0 -1 0 0 -2 1 0
  -1 2 0 2 -2 0 -1 -1 3 -2 -1 -1 -2 -1 -1 1 0 1 0 -1 1 1 0 1 1 0 1 2 0 0 -1 -1
  
  

• ORBITS
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 (4896x)
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 (4896x)
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 (14688x)
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 (4896x)
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 (14688x)
  0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (14688x)
  0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 (14688x)
  

• PROPERTIES
  INTEGRAL = 1
  MODULAR = 15
  

• REFERENCES
  G. Nebe, Finite quaternionic matrix groups,
  Representation Theory 2, 106-223 (April 1998)
  

• NOTES
  

• URL (links to other sites for this lattice)
  All the quaternionic matrix groups
  

• LAST_LINE
  
  
  

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  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe