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 13:13:53 CEST 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

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

• NAME
  SL2(17)SS3.2
  

• DIMENSION
  32
  

• GRAM (floating point or integer Gram matrix)
  32 0
  44
  13 44
  16 2 44
  22 4 10 44
  14 -2 14 18 44
  2 12 13 8 14 44
  14 14 14 22 14 -2 44
  8 22 18 4 2 18 7 44
  18 -2 9 22 14 -6 11 5 44
  22 16 8 19 5 9 11 18 10 44
  18 18 9 14 14 11 6 19 7 22 44
  4 11 10 8 19 22 16 12 8 11 2 44
  11 14 -1 18 8 8 18 4 12 7 0 22 44
  14 14 8 -5 1 -1 3 9 2 7 8 5 -2 44
  8 2 5 13 22 6 11 6 14 3 9 14 18 -13 44
  7 15 -2 4 -1 -3 18 -7 15 5 -4 10 11 14 -8 44
  9 11 18 7 6 18 14 11 1 14 14 16 -2 13 -7 14 44
  13 14 16 19 7 10 18 9 8 22 15 10 7 7 -2 7 14 44
  19 6 19 13 15 6 15 10 4 10 7 9 0 2 10 1 7 1 44
  8 9 22 2 11 16 5 22 1 12 14 18 -1 7 2 -5 22 6 10 44
  10 22 10 -5 5 4 9 22 -4 13 22 4 -5 9 -4 4 14 8 16 19 44
  -2 14 13 5 -5 22 6 19 4 11 7 13 0 -2 -7 8 22 18 5 18 11 44
  3 5 11 13 22 11 13 7 3 -2 6 11 6 -1 19 -4 -5 5 9 14 7 6 44
  8 22 7 5 5 6 14 15 7 14 9 10 9 9 5 22 18 -2 12 10 13 14 7 44
  22 18 6 22 13 11 11 12 4 22 13 12 8 3 14 -3 7 15 15 11 8 2 16 9 44
  14 19 -5 14 13 2 22 6 11 4 3 18 19 13 3 22 5 5 8 8 10 7 18 19 10 44
  10 22 4 10 16 11 19 14 -3 18 16 14 11 6 -2 8 2 9 9 11 18 7 13 15 6 22 44
  -5 2 14 10 22 19 13 4 3 8 5 22 3 -6 9 4 3 16 8 4 2 14 22 7 8 4 18 44
  14 22 2 14 3 8 11 18 4 13 13 6 11 14 7 4 -2 8 5 2 4 9 14 13 10 22 22 10 44
  10 4 10 16 9 22 5 10 10 19 14 18 5 -6 2 6 22 19 16 13 14 22 -2 5 6 2 4 10 -5 44
  7 7 9 1 11 0 13 -6 6 6 -7 22 18 13 7 14 3 4 -1 10 -6 -1 9 14 1 13 14 14 5 -4 44
  19 12 19 22 22 12 22 11 8 9 5 18 12 4 9 5 5 10 22 9 8 -2 18 6 22 13 18 13 4 8 10 44
  

• DIVISORS (elementary divisors)
  1^4 17^28
  

• MINIMAL_NORM
  44
  

• GROUP_ORDER
  2^7 * 3^3 * 17
  

• GROUP_GENERATORS
  3
  32
  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
  -1 -1 -1 0 0 0 -3 5 1 -1 1 0 0 -4 -2 3 5 2 4 -4 -1 -2 4 -3 1 -1 2 -3 0 -2 4 -2
  0 0 0 0 1 0 1 -1 -1 0 0 0 0 1 0 0 -2 0 -1 1 0 1 -1 1 0 0 -1 0 0 1 -1 1
  1 -3 -3 2 -1 1 -3 5 1 -3 1 3 -1 -4 -2 3 4 4 4 -3 1 -2 4 -1 0 -3 2 -4 0 -4 4 -2
  0 0 2 0 -1 0 2 -5 -1 1 -1 -1 0 4 3 -2 -4 -2 -4 3 1 2 -4 2 0 2 -1 3 0 2 -4 3
  0 2 3 0 1 0 4 -7 -2 3 -1 -2 0 5 3 -3 -7 -4 -6 4 1 4 -6 3 -1 3 -4 4 0 3 -5 4
  0 -2 -2 1 0 1 -2 5 1 -2 1 3 -1 -4 -3 3 4 3 4 -4 0 -2 5 -2 1 -3 2 -5 0 -3 4 -3
  0 0 0 1 1 0 0 0 -1 0 0 0 0 0 0 1 -1 0 0 0 0 1 0 0 0 -1 0 -1 0 0 0 0
  0 -1 0 0 1 1 2 -2 0 0 0 1 0 1 -1 -1 -3 0 -1 1 1 1 -1 2 0 -1 -1 -1 1 0 -1 1
  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 0 0 1 -2 -2 -3 1 -1 0 -1 -2 1 1 3 0 3 0 0 0 -1 0 0 -1 -1 2 2 3 -2 0 -1 1
  -1 -1 0 0 3 1 1 1 0 0 1 3 -1 -3 -4 2 -1 1 1 -2 1 0 2 0 1 -3 -2 -5 3 -1 2 -1
  -1 -1 0 0 3 2 2 1 0 0 2 3 -1 -3 -5 2 -2 0 1 -2 1 0 2 0 1 -3 -3 -5 3 -1 3 -1
  0 -1 -1 0 0 0 -3 5 1 -2 0 1 0 -4 -2 3 5 3 4 -3 -1 -3 4 -2 1 -2 3 -3 0 -2 3 -3
  -1 -1 1 -1 1 1 2 -2 0 1 1 1 0 0 -2 0 -3 -1 -1 0 1 1 0 1 1 -1 -2 -2 2 1 0 1
  -1 1 2 -1 1 1 3 -3 0 2 0 -1 0 2 0 -2 -3 -2 -2 1 0 1 -2 1 0 2 -2 1 0 1 -2 1
  2 0 -2 1 -1 -1 -3 3 0 -1 -1 0 0 -1 1 1 4 2 2 -1 -1 -1 2 -1 -1 0 2 1 -2 -2 0 -1
  0 -1 -1 0 -1 1 -1 1 1 -1 0 0 0 -1 0 0 2 2 1 -1 0 -1 1 0 0 0 1 -1 0 -1 1 0
  -1 2 4 0 0 0 4 -7 -2 3 -1 -3 0 6 4 -4 -7 -5 -6 4 1 4 -7 2 0 5 -3 5 -1 4 -5 4
  0 -2 -2 0 1 -1 -3 5 0 -2 1 2 0 -4 -2 4 4 3 4 -3 -1 -1 4 -2 1 -3 2 -4 1 -2 3 -2
  -1 1 2 -1 0 -2 -1 0 -1 1 0 -3 1 1 2 0 1 -2 -1 0 -2 1 -1 -2 1 3 1 2 -1 2 -1 1
  0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 -1 0 0 0 0
  -2 -3 0 -1 1 0 -2 4 1 -2 2 2 0 -4 -3 4 3 2 3 -4 0 -1 4 -2 3 -3 2 -6 2 -1 4 -2
  0 0 0 1 0 0 -1 1 0 0 0 0 0 0 0 1 1 0 1 -1 0 0 1 -1 0 0 1 0 -1 -1 0 -1
  0 -1 -1 1 -2 0 -3 2 1 -1 0 0 0 -1 1 1 3 2 2 -1 0 -1 1 -1 0 0 2 0 -1 -2 1 0
  -1 -3 -2 0 1 1 -3 7 2 -3 2 4 -1 -7 -5 5 6 4 6 -6 0 -3 7 -3 2 -5 3 -8 2 -4 6 -4
  -1 -1 0 1 1 0 -1 3 0 -1 1 2 -1 -3 -2 3 2 1 2 -3 0 -1 3 -2 1 -2 1 -4 1 -1 3 -2
  -1 1 3 0 0 0 3 -6 -1 2 -1 -2 0 5 3 -3 -5 -3 -5 3 1 3 -5 2 0 3 -2 3 0 3 -4 3
  -1 -3 -2 0 1 1 -3 7 2 -3 2 3 -1 -7 -5 5 6 4 6 -6 0 -3 7 -3 2 -5 3 -8 2 -3 7 -4
  0 2 3 0 1 0 4 -7 -2 3 -1 -2 0 5 3 -4 -7 -4 -6 4 1 4 -6 3 -1 4 -4 4 0 3 -5 4
  -1 -3 -3 0 2 1 -3 8 2 -3 2 5 -1 -8 -7 6 6 5 7 -6 0 -4 8 -3 2 -6 2 -9 3 -4 7 -5
  -1 -2 -1 1 1 1 -1 3 0 -1 1 2 -1 -3 -2 3 1 2 2 -2 1 -1 2 -1 1 -2 0 -4 1 -2 3 -1
  32
  -3 -1 3 -3 2 1 4 -3 0 1 2 0 0 0 -2 0 -4 -2 -2 0 0 1 -1 1 3 0 -2 -3 3 3 0 1
  -1 -2 0 -2 1 -1 -2 4 0 -1 2 0 1 -3 -2 3 3 1 2 -3 -1 -1 3 -2 2 -1 1 -3 1 0 3 -1
  -1 -3 -3 -1 0 0 -4 7 2 -3 2 2 0 -7 -4 5 7 5 6 -4 -1 -4 6 -3 2 -4 3 -6 2 -3 6 -3
  -1 -2 -1 -1 0 0 -2 4 1 -2 2 1 0 -4 -3 3 4 2 4 -3 -1 -2 4 -2 2 -2 2 -4 1 -1 4 -2
  -1 0 1 -1 0 1 2 -2 0 1 1 0 0 0 -1 -1 -2 -1 -1 1 0 0 -1 1 0 1 -2 0 1 1 0 1
  0 1 1 -1 -1 0 0 -1 0 1 0 -2 1 1 1 -1 0 -1 -1 1 -1 0 -1 0 0 2 0 2 -1 1 -1 1
  -1 -5 -4 0 2 0 -6 13 2 -5 4 6 -1 -12 -9 9 10 7 10 -9 -1 -6 12 -5 3 -8 4 -12 3 -5 11 -7
  0 -3 -2 -1 0 0 -4 7 1 -3 2 2 0 -6 -3 5 6 4 5 -4 -1 -3 5 -3 2 -3 3 -5 1 -3 5 -3
  -1 0 2 -2 0 0 2 -4 0 1 0 -2 1 2 1 -2 -2 -2 -2 2 0 1 -3 1 1 2 -1 2 1 2 -2 2
  -2 -2 1 -2 0 0 -2 4 1 -1 2 0 0 -4 -2 3 4 1 3 -4 -1 -2 3 -3 3 0 2 -4 1 0 4 -2
  -1 0 2 -1 1 0 2 -2 -1 1 1 0 0 1 0 0 -3 -2 -2 1 0 1 -2 1 1 1 -2 0 1 2 -1 1
  0 0 1 -1 -1 0 0 -1 0 1 0 -2 1 1 1 -1 0 -1 -1 1 -1 0 -1 0 0 2 0 2 -1 1 -1 1
  -1 1 3 -1 1 0 3 -5 -2 3 0 -3 1 4 2 -2 -5 -4 -4 3 0 3 -4 1 0 3 -3 3 0 3 -3 3
  -2 -2 0 -2 3 1 1 3 1 -1 2 2 0 -4 -5 3 0 1 2 -3 0 -1 3 -1 3 -3 -1 -6 3 0 4 -2
  -1 0 2 -1 1 0 2 -3 -1 2 1 0 0 1 0 -1 -3 -2 -2 1 0 2 -2 1 0 1 -2 0 1 1 -1 2
  -2 -1 1 -2 2 0 0 1 1 0 1 0 1 -2 -3 1 1 0 1 -2 0 -1 2 -1 2 -1 0 -3 2 1 2 -1
  -1 -2 -1 -1 2 0 -2 6 1 -2 2 2 0 -6 -5 4 4 3 4 -4 -1 -3 5 -2 2 -3 1 -6 2 -1 5 -3
  0 -2 -2 0 -1 0 -3 5 1 -2 1 1 0 -4 -2 3 5 3 4 -3 0 -3 4 -2 1 -2 2 -3 0 -2 4 -2
  -1 -1 0 -1 -1 0 -1 1 1 -1 1 0 0 -1 0 1 2 1 1 -1 -1 -1 1 -1 1 0 2 -1 0 0 1 0
  -1 -1 1 -1 0 1 1 -1 0 0 1 -1 0 0 0 0 -2 0 -1 1 0 0 -2 1 1 1 -1 0 1 1 0 1
  0 -1 0 0 -1 0 -1 1 0 -1 0 0 0 0 1 1 1 1 0 0 0 -1 0 0 0 0 1 0 0 0 0 0
  1 -3 -4 0 -1 0 -6 9 2 -4 1 2 0 -7 -3 5 9 6 7 -5 -1 -5 7 -3 1 -4 5 -5 0 -4 6 -4
  0 -4 -4 1 -1 1 -5 8 2 -4 2 4 -1 -7 -4 5 7 6 7 -5 0 -4 7 -2 1 -5 4 -7 1 -5 7 -4
  -2 -4 -2 -2 2 0 -5 9 2 -3 3 3 0 -9 -6 6 8 5 7 -7 -1 -4 8 -4 3 -4 3 -9 3 -3 8 -4
  -1 -3 -1 -1 -1 0 -3 5 1 -2 2 1 0 -4 -2 3 5 3 4 -4 -1 -2 4 -2 2 -1 3 -4 0 -2 4 -2
  -1 -3 -1 -1 1 1 -1 4 1 -2 2 2 0 -4 -4 3 2 2 3 -3 0 -2 4 -1 2 -3 1 -5 2 -1 4 -2
  -1 -2 -1 -1 0 0 -3 6 1 -2 2 1 0 -5 -3 4 5 2 4 -4 -1 -3 5 -3 2 -2 2 -4 1 -1 5 -3
  1 -3 -5 1 -3 0 -8 10 3 -4 1 3 0 -8 -3 5 12 7 9 -6 -1 -6 9 -4 0 -4 6 -5 -1 -6 7 -5
  -1 -4 -3 -1 1 0 -5 10 2 -4 3 4 0 -9 -6 7 8 5 8 -7 -1 -4 9 -4 3 -6 4 -9 2 -4 8 -5
  0 3 4 -1 -2 0 4 -9 -1 3 -2 -5 1 8 6 -6 -6 -5 -7 6 0 3 -8 3 -1 6 -2 8 -2 5 -7 5
  -2 -2 0 -2 2 1 0 2 1 0 2 1 0 -4 -4 2 1 1 2 -3 0 -1 3 -1 2 -2 -1 -5 3 0 4 -1
  -1 -2 -1 -1 0 0 -2 4 1 -2 2 1 0 -4 -3 3 4 2 3 -3 -1 -2 4 -2 2 -2 2 -4 1 -1 4 -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
  1 1 0 1 0 0 0 0 -1 0 0 1 -1 0 0 0 -1 0 0 0 0 0 0 0 -1 0 -1 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 1 1 0 -2 -1 1 -4 -1 1 -2 -4 1 5 5 -3 -2 -2 -3 4 0 2 -5 1 -1 4 0 6 -2 2 -4 3
  0 -4 -4 0 0 -1 -7 11 2 -4 2 3 0 -9 -5 7 11 6 9 -7 -1 -5 9 -5 2 -5 5 -7 1 -5 8 -5
  0 1 2 -1 -1 -1 0 -2 -1 1 -1 -3 1 3 3 -1 -1 -2 -2 2 -1 1 -3 0 0 3 0 4 -1 2 -3 2
  0 0 1 1 -1 -1 0 -1 -1 0 0 -1 0 2 2 -1 -1 -1 -1 1 0 1 -2 0 0 2 0 2 -1 1 -1 1
  0 -1 0 0 1 1 0 3 0 -1 1 2 -1 -3 -3 2 1 1 2 -3 0 -1 3 -1 1 -2 0 -4 1 -1 3 -2
  0 -2 -1 -1 0 1 0 1 1 -1 1 1 0 -2 -2 1 1 2 2 -1 0 -1 2 0 1 -2 1 -3 1 -1 2 -1
  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 -1 3 0 -1 1 2 -1 -3 -2 3 2 1 2 -3 0 -1 3 -2 1 -2 1 -4 1 -1 3 -2
  0 1 2 -1 -1 -1 1 -3 -1 1 0 -2 1 3 2 -2 -2 -2 -2 2 -1 1 -3 1 0 3 -1 4 -1 2 -3 2
  2 3 2 1 -4 -1 2 -8 -2 3 -3 -5 1 9 8 -6 -5 -4 -6 7 0 3 -8 3 -3 7 -2 11 -4 3 -8 5
  0 -1 -1 -1 1 0 -2 5 1 -1 2 2 0 -5 -4 3 4 2 4 -4 -1 -2 5 -3 1 -2 1 -4 1 -2 4 -3
  0 -2 -2 0 -1 0 -3 5 1 -2 1 1 0 -4 -2 3 5 3 4 -3 0 -3 4 -2 1 -2 2 -3 0 -2 4 -2
  1 0 0 1 -1 0 0 -2 -1 0 0 0 0 2 2 -1 -2 0 -1 2 0 1 -2 1 -1 1 0 2 -1 0 -2 1
  0 2 4 -1 0 -2 2 -5 -2 2 -1 -3 1 5 4 -3 -4 -4 -5 3 -1 3 -5 1 0 4 -1 5 -1 4 -5 3
  0 -1 -1 0 1 -1 -2 4 0 -2 1 1 0 -3 -2 3 3 2 3 -2 -1 -1 3 -2 1 -2 1 -3 1 -1 3 -2
  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 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 1 2 0 0 2 -1 0 1 2 -1 -2 -2 2 0 0 1 -2 0 0 2 -1 0 -2 -1 -3 1 -1 2 -1
  0 2 3 0 1 0 4 -6 -2 2 -1 -1 0 5 2 -3 -7 -3 -5 4 0 3 -5 3 -1 2 -3 3 0 3 -5 3
  0 -2 -3 1 0 0 -4 7 1 -2 1 2 0 -5 -3 4 6 4 6 -4 0 -3 5 -3 0 -3 2 -4 0 -4 5 -3
  2 -1 -2 2 -1 0 -3 4 0 -2 0 3 -1 -3 -1 2 3 3 3 -2 0 -2 3 -1 -1 -2 2 -2 -1 -3 2 -2
  0 -1 -1 -1 2 0 0 3 0 -1 1 1 0 -3 -3 2 1 1 2 -2 0 -1 2 -1 1 -2 -1 -3 2 0 3 -1
  2 -1 -3 2 -2 -1 -4 5 0 -2 0 1 0 -2 0 2 5 3 4 -2 -1 -2 3 -2 -1 -1 3 0 -2 -3 2 -2
  1 0 -1 2 -1 0 -2 2 0 -1 0 1 -1 -1 0 1 2 1 2 -1 0 -1 1 -1 -1 0 1 0 -1 -2 1 -1
  -1 -1 0 0 1 0 -1 2 0 -1 1 1 0 -2 -2 2 1 1 2 -1 0 -1 1 -1 1 -1 0 -2 1 -1 2 -1
  1 2 1 1 -1 0 1 -2 -1 1 -1 -2 0 3 2 -2 -2 -2 -2 2 0 1 -3 0 -1 3 -1 4 -2 1 -2 1
  0 1 2 -1 -1 -1 1 -4 -1 1 -1 -3 1 4 4 -2 -2 -2 -3 3 -1 2 -4 1 0 3 0 4 -1 2 -4 3
  1 0 -1 1 -2 0 -2 1 1 -1 0 1 0 -1 0 0 2 2 2 0 0 -2 1 0 -1 0 1 1 -1 -2 0 -1
  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
  

• PROPERTIES
  INTEGRAL = 1
  

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

• NOTES
  The dual lattice has kissing number 233 376 and minimal norm 6
  and can be constructed as a Mordell Weil lattice.
  

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

• LAST_LINE
  
  
  

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  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe