The Lattice SL2(9)q8d8.Alt5.2

An entry from the Catalogue of Lattices, which is a joint project of
Gabriele Nebe, University of Ulm (nebe@mathematik.uni-ulm.de) and
Neil J. A. Sloane, AT&T Shannon Labs (njas@research.att.com)

Last modified Tue Oct 30 16:12:34 EST 2001

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
PROPERTIES
REFERENCES
NOTES
URL (links to other sites for this lattice)
LAST_LINE

• NAME
  SL2(9)q8d8.Alt5.2
  
• DIMENSION
  32
  
• GRAM (floating point or integer Gram matrix)
  32 0
  8
  4 8
  4 2 8
  4 4 4 8
  4 2 4 4 8
  1 2 1 0 1 8
  4 4 4 2 2 3 8
  4 4 2 2 4 2 4 8
  4 2 2 2 2 0 3 1 8
  4 0 4 4 4 0 0 0 2 8
  2 0 2 1 4 2 1 1 2 3 8
  2 2 4 3 2 2 3 1 2 1 4 8
  2 1 3 1 4 1 1 2 2 2 4 3 8
  1 1 0 0 1 4 2 2 1 1 4 2 1 8
  2 1 4 2 1 3 1 0 0 3 3 4 3 2 8
  2 2 1 0 2 4 1 3 1 1 4 2 3 4 2 8
  2 4 2 4 2 0 2 4 1 2 0 1 0 0 1 0 8
  1 2 3 2 2 4 2 1 1 1 2 4 1 2 2 2 0 8
  1 2 1 0 1 4 3 2 1 0 2 3 2 2 2 3 0 4 8
  2 2 2 2 4 2 4 4 1 2 3 2 1 4 0 1 2 2 2 8
  1 2 3 2 2 4 2 1 0 1 2 3 2 2 3 3 0 4 4 2 8
  0 2 2 2 2 4 2 2 1 0 2 3 1 2 1 3 0 4 4 2 4 8
  3 4 1 3 1 2 2 1 3 1 0 2 0 1 1 2 1 2 0 0 2 2 8
  3 4 1 3 1 0 1 2 3 1 1 1 1 2 2 2 2 0 0 1 2 0 4 8
  0 2 2 2 1 4 1 1 0 1 2 3 1 2 4 3 2 4 4 0 4 4 0 0 8
  2 4 2 4 2 0 4 2 1 2 1 2 0 1 0 0 4 0 0 4 0 0 2 1 0 8
  2 3 2 4 3 2 1 2 2 1 2 4 2 0 3 2 2 2 2 1 2 2 3 3 2 1 8
  2 4 0 2 2 2 1 3 3 0 2 2 1 2 1 4 3 2 2 1 2 2 4 4 2 1 4 8
  4 4 0 4 2 0 0 2 3 2 1 1 0 1 0 2 2 2 0 0 2 2 4 4 2 0 2 4 8
  2 4 0 2 2 2 1 3 2 0 1 1 1 1 1 2 3 0 0 1 2 2 4 4 2 1 2 4 4 8
  3 4 1 3 1 2 2 1 2 1 1 1 0 0 1 2 1 2 2 0 4 2 4 4 2 2 1 4 4 4 8
  4 2 2 2 2 0 2 2 4 2 2 2 2 1 2 1 2 1 0 2 1 0 1 2 1 0 2 3 4 3 1 8
  
• DIVISORS (elementary divisors)
  1^16 6^16
  
• MINIMAL_NORM
  8
  
• KISSING_NUMBER
  7200
  
• GROUP_ORDER
  2^12 * 3^3 * 5^2
  
• GROUP_GENERATORS
  4
  32
  -9 0 10 2 1 7 -7 4 2 -4 2 1 -2 -1 0 -1 -2 -6 7 2 -4 -6 4 -1 -1 1 -3 -2 7 -3 2 2
  0 -1 1 0 0 1 -1 0 0 -1 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 1 0 0 1 0 0 0
  -7 -2 12 1 0 6 -7 1 2 -7 1 -1 0 0 1 0 0 -6 7 5 -5 -6 4 -3 -1 1 -1 -3 10 -2 3 0
  -4 0 4 1 0 3 -3 2 2 -2 1 0 -1 -1 1 0 -1 -2 3 1 -1 -3 1 -1 -1 1 -1 -1 4 -1 0 0
  -7 -1 9 2 0 7 -6 3 2 -4 2 0 -1 -2 0 -1 -2 -5 6 2 -3 -5 3 0 -1 2 -3 -1 7 -2 0 1
  -1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 -1 -1 1 0 0 -1 0 0 0 0 -1 1 1 0 -1 0
  -5 0 6 2 0 4 -4 2 1 -3 2 0 -1 -1 0 0 -1 -4 4 2 -2 -4 3 -1 0 0 -2 -1 4 -2 1 1
  -6 0 6 2 0 6 -4 3 1 -2 2 1 -1 -2 0 -1 -2 -4 4 1 -2 -4 2 0 -1 1 -3 0 5 -2 0 1
  -5 -1 8 0 1 4 -5 1 1 -4 1 0 -1 0 0 0 0 -4 5 2 -3 -4 3 -1 -1 1 -1 -2 6 -2 2 1
  -7 1 6 2 1 5 -5 4 2 -2 2 1 -2 -1 0 -1 -2 -4 5 0 -2 -4 3 0 -1 1 -3 -2 4 -2 0 2
  -4 0 4 2 0 3 -2 2 1 -1 1 0 -1 -1 0 0 -2 -2 3 0 -1 -3 1 0 -1 1 -2 0 3 0 -1 0
  -3 -1 5 1 0 2 -2 0 1 -3 0 -1 0 0 1 1 0 -2 3 2 -2 -3 1 -2 -1 0 0 -1 5 0 1 -1
  -4 -2 9 1 0 5 -5 1 1 -5 1 -1 0 0 0 -1 -1 -4 5 2 -3 -4 2 -1 -1 2 -1 -1 7 -1 1 0
  -2 1 -1 2 0 1 1 2 0 2 1 1 -1 -1 -1 0 -2 0 0 -2 1 -1 0 1 0 0 -2 1 -1 0 -2 1
  -3 -1 5 1 0 2 -2 0 1 -3 0 -1 0 1 1 0 0 -2 3 2 -2 -3 1 -2 -1 0 0 -1 5 0 1 -1
  -1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 -1 0 1 -1 0 -1 -1 0 -1 1 -1 1 1 1 -1 0
  -2 1 -1 1 0 1 0 2 1 1 1 1 -1 -1 1 0 -1 0 0 -1 1 -1 0 0 -1 0 -1 0 0 0 -1 0
  -1 -2 5 0 -1 2 -2 -1 0 -3 0 -1 1 0 0 0 0 -2 3 2 -2 -2 1 -1 0 1 0 0 5 0 0 -1
  1 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 -1 1 -1 0 -1 0
  -6 1 5 3 0 6 -4 4 1 -1 3 1 -2 -3 -1 -1 -3 -4 4 0 -1 -4 3 1 0 1 -4 0 3 -2 -2 2
  1 -1 1 1 -1 0 0 -1 0 -1 0 -1 1 0 0 0 0 0 1 1 0 -1 0 -1 0 0 0 1 1 1 -1 -1
  0 -2 3 0 0 1 -1 -2 0 -3 -1 -1 1 0 1 1 1 -1 2 2 -1 -1 0 -1 -1 1 0 0 4 0 0 -1
  -1 0 1 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 1 0 0 0
  0 0 0 0 0 0 0 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
  3 -1 -2 0 -1 -2 2 -2 0 0 -1 -1 1 1 1 1 1 2 -1 0 1 1 -2 -1 -1 0 1 1 0 2 -1 -2
  -2 2 -2 2 0 1 0 3 1 2 2 1 -2 -2 0 0 -2 0 0 -2 2 -1 0 1 0 0 -2 0 -2 0 -2 1
  -2 -1 4 0 0 2 -2 0 1 -2 0 -1 0 0 1 0 0 -1 2 1 -1 -2 0 -1 -1 1 0 0 4 0 0 -1
  -2 -1 3 0 0 2 -1 0 0 -1 0 0 0 0 0 0 0 -1 2 0 -1 -2 0 0 -1 1 0 0 3 0 0 0
  -1 -1 2 0 0 1 -1 0 0 -1 0 0 0 0 0 0 0 0 2 0 -1 -1 0 0 -1 1 0 0 2 0 0 0
  -1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 -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 1 0 0 -1 0 0 0 0 0 0 0 0 0 0
  -8 -2 13 1 0 7 -7 2 1 -6 2 -1 -1 0 0 -1 -1 -6 8 3 -5 -6 4 -2 -2 2 -1 -2 10 -2 2 1
  32
  -8 -1 11 1 1 7 -6 2 1 -5 2 0 -1 -1 0 -1 -1 -7 7 3 -5 -5 4 -1 -1 1 -2 -2 9 -3 2 1
  0 0 0 0 0 0 0 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
  -3 0 3 1 0 2 -1 1 1 -1 1 0 -1 -1 1 0 -1 -2 2 1 -1 -2 0 -1 -1 0 -1 0 4 0 0 -1
  -1 1 -1 1 0 0 1 1 1 1 1 0 -1 -1 1 0 -1 0 0 -1 1 0 -1 0 -1 0 -1 1 0 1 -2 -1
  -3 0 3 1 0 2 -1 1 1 -1 1 0 -1 -1 1 0 -1 -2 2 1 -1 -2 1 -1 -1 0 -1 0 3 0 0 -1
  0 1 -2 0 1 0 0 1 0 1 0 1 -1 -1 0 0 0 0 -1 -1 1 1 0 1 0 0 -1 0 -2 -1 0 1
  -4 0 5 0 1 4 -4 2 1 -2 1 1 -1 -1 0 -1 -1 -4 3 1 -2 -2 2 0 0 1 -2 -1 4 -2 1 1
  -5 -1 8 0 1 5 -5 1 1 -4 1 0 -1 0 0 -1 0 -5 5 2 -3 -3 3 -1 -1 1 -1 -2 6 -2 2 1
  -1 -1 3 -1 1 2 -2 0 0 -2 0 0 0 0 0 0 0 -2 2 1 -2 -1 1 0 0 1 0 -1 3 -1 1 0
  -4 0 5 1 0 3 -2 1 1 -2 1 0 -1 -1 1 0 -1 -3 3 2 -2 -3 1 -1 -1 0 -1 0 5 -1 0 -1
  -1 0 2 0 0 1 -1 0 0 -1 0 0 0 0 1 0 0 -1 1 1 -1 -1 0 -1 -1 0 0 0 2 0 1 -1
  2 1 -4 0 0 -2 2 0 0 2 0 0 0 0 1 0 0 2 -2 -2 2 2 -2 0 -1 0 0 1 -2 1 -1 -1
  2 0 -2 0 0 -1 2 -1 -1 1 0 0 0 0 0 0 0 1 -1 -1 1 1 -1 0 0 0 0 1 -1 1 -1 -1
  0 2 -3 0 1 0 0 1 0 2 0 2 -1 -1 0 0 0 0 -1 -1 1 1 0 1 0 -1 -1 0 -3 -1 0 1
  -1 1 -1 1 0 0 1 1 0 1 1 0 -1 -1 1 0 -1 0 0 -1 1 0 -1 0 -1 0 -1 1 0 0 -1 0
  -2 0 2 1 1 2 -2 1 0 -1 0 1 -1 0 0 0 0 -2 2 0 -1 -1 1 0 -1 0 -1 -1 1 -1 1 1
  -1 -1 4 0 0 2 -2 -1 1 -3 0 -1 0 0 1 0 0 -2 2 2 -1 -1 0 -1 -1 1 0 0 4 0 0 -1
  2 0 -3 -1 0 -2 2 -1 0 1 -1 0 0 0 1 1 1 2 -2 -1 1 2 -2 0 -1 0 1 0 -1 1 0 -1
  0 1 -2 0 1 0 0 1 0 1 0 1 -1 0 0 0 0 0 -1 -2 1 1 0 1 0 0 -1 0 -2 -1 0 1
  -2 1 2 0 0 2 -2 2 1 0 1 1 -1 -1 0 -1 -1 -2 1 0 0 -1 1 0 0 0 -1 0 1 -1 0 0
  2 2 -6 1 0 -2 3 1 0 4 0 1 -1 -1 0 0 -1 2 -3 -3 3 2 -2 1 0 -1 -1 2 -5 1 -2 0
  3 2 -7 0 0 -3 3 1 0 4 0 1 -1 0 0 0 0 3 -4 -3 3 3 -2 1 0 -1 0 1 -6 1 -1 0
  1 0 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 2 -7 0 1 -3 4 0 0 4 -1 1 -1 0 1 1 0 3 -4 -3 3 3 -3 1 -1 -1 0 1 -5 1 -1 0
  0 0 1 0 0 0 -1 0 1 -1 0 0 0 0 1 0 0 -1 0 1 0 0 0 -1 0 0 0 0 1 0 0 -1
  1 -1 -1 0 0 -1 1 0 0 0 0 -1 0 0 1 0 0 1 0 -1 1 1 -1 0 -1 1 0 1 0 1 -1 -1
  0 -1 1 0 0 1 -1 0 0 -1 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 -1 1 0 0 1 0 0 0
  -1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -1 0 0 0 -1 0 0 0 1 0 0 0
  1 1 -2 0 0 -1 1 0 0 1 0 0 0 0 0 0 0 0 -1 0 1 1 0 0 0 -1 0 0 -2 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
  -3 -1 5 0 0 4 -2 1 0 -2 1 0 0 -1 0 -1 -1 -3 3 1 -2 -2 1 0 -1 1 -1 0 5 -1 0 0
  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
  2 0 -2 0 0 -1 1 0 0 1 0 0 0 0 0 0 0 1 -1 -1 1 1 -1 0 0 0 0 1 -1 1 -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
  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 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
  -1 0 2 1 -1 1 -1 1 0 0 1 0 0 0 -1 -1 -1 -1 1 0 0 -1 1 0 0 0 -1 1 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 1 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 0 0 0 0 0 0 0 0 0
  2 0 -2 0 0 -1 2 -1 -1 1 0 0 0 0 0 0 0 1 -1 -1 1 1 -1 0 0 0 0 1 -1 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 0
  -1 1 0 1 -1 1 0 2 0 2 2 0 -1 -1 -1 -1 -2 0 0 -2 1 0 0 1 0 1 -1 1 -1 0 -2 1
  -1 1 -1 1 0 1 0 2 0 2 1 1 -1 -1 -1 -1 -2 0 0 -2 1 0 0 1 0 1 -1 1 -1 0 -2 1
  -4 2 2 2 0 3 -2 3 1 1 2 1 -2 -1 0 -1 -2 -2 2 -1 0 -2 1 0 -1 0 -2 0 1 -1 -1 1
  -1 -1 4 0 -1 1 -2 0 0 -2 1 -1 0 0 0 0 0 -1 2 1 -1 -1 1 -1 -1 1 0 0 3 0 0 0
  0 1 0 1 -1 0 0 1 0 1 1 0 0 0 -1 -1 -1 0 0 -1 1 0 0 0 0 0 0 1 -1 0 -1 0
  -1 0 2 2 -1 2 -2 2 0 0 2 0 -1 -1 -1 -1 -2 -1 2 -1 0 -1 1 1 0 1 -2 1 0 0 -2 1
  0 0 0 0 1 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
  -2 -1 4 1 -1 3 -2 1 0 -1 1 0 0 -1 -1 -1 -1 -2 2 1 -1 -2 1 0 0 1 -1 1 3 0 -1 0
  0 1 -2 1 -1 0 1 2 0 3 1 1 -1 -1 -1 -1 -2 1 -1 -2 2 0 -1 1 0 0 -1 2 -2 1 -2 0
  0 0 1 -1 0 0 -1 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
  -1 1 -1 1 0 0 0 2 0 2 1 1 -1 0 -1 -1 -1 0 0 -2 1 0 0 1 0 0 -1 1 -2 0 -1 1
  2 0 -3 1 -1 -2 2 0 0 2 0 0 0 0 0 0 -1 2 -2 -1 2 1 -2 0 0 0 0 2 -2 2 -2 -1
  3 -2 0 -1 0 -1 1 -2 -1 -1 -1 -1 1 1 0 0 1 1 0 0 0 1 -1 0 0 1 1 1 1 1 -1 -1
  4 1 -6 0 0 -3 3 0 -1 3 0 0 0 0 0 0 0 3 -3 -3 3 3 -2 1 0 0 0 2 -5 1 -2 0
  0 0 0 1 -1 0 0 1 0 1 1 0 0 0 -1 -1 -1 0 0 -1 1 0 0 0 0 0 0 1 -1 1 -1 0
  -2 -1 4 -1 1 2 -2 0 0 -2 0 0 0 0 0 0 0 -2 2 1 -2 -1 1 0 0 1 0 -1 4 -1 1 0
  3 1 -4 0 0 -2 2 0 -1 3 0 0 0 0 -1 -1 -1 2 -2 -2 2 2 -1 1 1 0 0 2 -4 1 -2 0
  4 0 -4 0 0 -2 2 -1 -1 2 0 0 0 0 -1 0 0 2 -2 -2 2 2 -1 1 1 0 0 2 -4 1 -2 0
  2 0 -2 0 0 -1 1 0 0 1 0 0 0 0 0 0 0 1 -1 -1 1 1 -1 0 0 0 0 1 -2 1 -1 0
  6 0 -7 -1 0 -4 4 -2 -1 3 -1 0 1 1 0 0 1 4 -4 -3 3 4 -3 1 0 0 1 2 -5 2 -2 -1
  4 1 -7 0 0 -3 4 0 -1 4 0 1 0 0 -1 0 0 3 -4 -3 3 3 -2 2 1 -1 0 2 -6 1 -2 0
  2 1 -2 0 0 -1 1 -1 0 1 0 0 0 0 0 0 0 1 -1 -1 1 1 -1 0 0 0 0 1 -2 1 -1 0
  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 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
  1 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 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
  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
  -3 -2 7 -1 1 3 -3 -1 0 -4 0 -1 0 1 0 0 1 -3 4 2 -3 -3 2 -1 -1 1 1 -2 6 -1 2 0
  -1 0 2 -1 1 1 -1 0 0 -1 0 0 0 0 0 0 0 -1 1 1 -1 -1 1 0 0 0 0 -1 2 -1 1 0
  -1 0 1 0 1 1 -1 0 0 -1 0 0 0 0 0 0 0 -1 1 1 -1 -1 1 0 0 0 0 -1 1 -1 1 1
  3 1 -5 0 0 -2 3 0 -1 3 0 1 0 0 -1 0 0 2 -3 -2 2 2 -1 1 1 -1 0 1 -4 0 -1 0
  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
  -2 -1 4 0 0 2 -2 0 0 -2 0 0 0 0 0 0 0 -3 3 2 -2 -2 2 -1 0 0 0 -1 4 -1 1 0
  -2 -1 5 0 0 2 -2 0 0 -3 1 -1 0 0 0 0 0 -3 3 2 -2 -2 2 -1 0 0 0 -1 4 -1 1 0
  2 1 -4 0 0 -2 2 0 0 2 0 0 0 0 0 0 0 1 -2 -1 2 1 0 0 1 -1 0 1 -3 0 -1 0
  -3 -1 5 -1 1 2 -3 0 0 -3 0 0 0 1 0 0 1 -3 3 2 -3 -2 3 -1 0 0 1 -3 4 -2 3 1
  0 -1 3 -1 0 0 -1 -1 0 -2 0 -1 0 1 0 0 1 -1 2 1 -1 -1 1 -1 0 0 1 -1 2 0 1 0
  0 0 -1 0 1 -1 1 -1 0 0 -1 0 0 1 1 1 1 0 0 0 0 0 0 -1 -1 -1 1 -1 0 0 1 0
  1 0 0 0 0 0 0 -1 0 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
  -3 -2 7 0 0 3 -3 0 0 -4 1 -1 0 0 0 0 0 -3 4 2 -3 -3 2 -1 -1 1 0 -1 6 -1 1 0
  -1 0 1 0 1 0 0 -1 0 -1 0 0 0 0 0 1 1 -1 1 1 -1 -1 1 0 0 -1 0 -1 1 -1 1 0
  -3 -1 5 -1 1 3 -3 0 0 -3 0 0 0 0 0 0 0 -3 3 2 -3 -2 2 0 0 1 0 -2 5 -2 2 1
  1 -1 0 -1 1 -1 0 -1 0 -1 -1 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 -1 0 0 1 0
  -2 -1 3 0 1 2 -1 0 0 -2 0 0 0 0 0 0 0 -2 2 1 -2 -2 1 0 0 0 0 -1 3 -1 1 0
  3 -1 0 -1 0 -2 1 -2 -1 -1 -1 -1 1 2 0 0 1 1 -1 0 0 1 -1 -1 0 0 2 0 0 1 1 -1
  4 1 -5 -1 1 -3 2 -1 -1 2 -1 1 0 1 -1 0 1 2 -3 -2 2 3 -1 1 1 -1 1 0 -5 0 0 1
  -5 -1 7 1 1 4 -4 1 1 -4 1 0 -1 0 0 0 0 -4 5 2 -3 -4 3 -1 -1 0 -1 -2 5 -2 2 1
  0 1 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
  3 -1 -1 -1 0 -2 2 -3 -1 -1 -1 -1 1 1 0 1 2 1 -1 1 0 1 -1 -1 0 -1 2 0 0 1 1 -1
  3 0 -4 0 1 -3 3 -2 -1 1 -1 0 0 1 0 1 1 2 -2 -1 1 2 -1 0 0 -1 1 0 -3 1 0 0
  1 -1 0 1 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
  -1 -1 3 0 1 2 -2 0 0 -2 0 0 0 1 -1 -1 0 -2 2 0 -1 -1 1 0 0 1 0 -1 2 -1 1 1
  0 1 -1 1 1 0 0 1 0 1 0 1 -1 0 -1 0 -1 0 0 -2 1 0 0 1 0 0 -1 0 -2 0 -1 1
  0 -1 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 1 0 0 0
  
• 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
  
  

INDEX FILE | ABBREVIATIONS