The Lattice Q(A_6^(2),1,1,1)

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 Sun Sep 15 10:36:13 EDT 2002

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
GRAM MATRIX
MINIMUM
KISSING NUMBER
GROUP ORDER
GROUP GENERATORS
MODULAR = 6
NOTES
LAST LINE

• NAME
  Q(A_6^(2),1,1,1)
  
• GRAM MATRIX
  12 0
  4
  -2 4
  -2 2 4
  -2 1 2 4
  1 1 1 -1 4
  1 -2 0 -1 -1 4
  1 0 0 0 1 0 4
  0 1 0 0 1 -1 2 4
  0 0 0 0 1 0 2 2 4
  0 0 0 1 0 0 2 1 2 4
  0 0 1 1 0 0 1 -1 -1 1 4
  0 1 0 0 0 0 1 2 0 1 -1 4
  
• MINIMUM
  4
  
• KISSING NUMBER
  84
  
• GROUP ORDER
  2^6 * 3^1 * 7^1 = 1344
  
• GROUP GENERATORS
  3
  12
  0 0 0 0 0 0 0 0 0 0 0 1
  0 0 0 0 0 0 0 0 1 -1 1 0
  0 0 0 0 0 0 0 1 0 0 0 -1
  0 0 0 0 0 0 0 1 -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 -1 0
  1 1 0 0 0 0 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
  1 0 1 -1 -1 -1 0 0 0 0 0 0
  0 0 0 0 0 -1 0 0 0 0 0 0
  0 0 1 -1 0 0 0 0 0 0 0 0
  12
  -1 -1 0 0 1 0 0 0 0 0 0 0
  0 0 0 0 -1 0 0 0 0 0 0 0
  0 1 -1 1 0 1 0 0 0 0 0 0
  0 1 -1 0 0 1 0 0 0 0 0 0
  -1 0 0 0 0 0 0 0 0 0 0 0
  0 0 -1 1 1 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 -1 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 0 -1 0
  0 0 0 0 0 0 0 -1 1 0 0 1
  0 0 0 0 0 0 0 0 -1 1 -1 -1
  12
  1 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 1 -1 -1 -1 0 0 0 0 0 0
  -1 0 0 -1 0 0 0 0 0 0 0 0
  1 1 0 0 -1 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 1 0 -1 0 -1 0
  0 0 0 0 0 0 0 0 0 0 0 1
  0 0 0 0 0 0 0 0 -1 1 -1 0
  0 0 0 0 0 0 0 0 0 0 -1 0
  0 0 0 0 0 0 0 0 0 -1 0 0
  0 0 0 0 0 0 0 1 0 0 0 0
  
• MODULAR = 6
  
• NOTES
  Extremal strongly 6-modular lattice
  
• LAST LINE
  
  

INDEX FILE | ABBREVIATIONS