The Lattice M6,2

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 Thu Jun 28 23:56:33 EDT 2001

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
GRAM
DIVISORS
MINIMAL_NORM
KISSING_NUMBER
GROUP_ORDER
GROUP_NAME
GROUP_GENERATORS
NOTES
REFERENCES
PROPERTIES
LAST_LINE

• NAME
  M6,2
  
• DIMENSION
  6
  
• GRAM
  6 6
  3 -1 -1 1 1 0
  -1 3 -1 -1 0 1
  -1 -1 3 0 -1 -1
  1 -1 0 3 -1 1
  1 0 -1 -1 3 -1
  0 1 -1 1 -1 3
  
• DIVISORS
  1 1 1 5 5 5
  
• MINIMAL_NORM
  3
  
• KISSING_NUMBER
  20
  
• GROUP_ORDER
  240
  
• GROUP_NAME
  C2 x S5
  
• GROUP_GENERATORS
  2
  6
  0 0 0 -1 0 0
  0 0 0 0 -1 0
  -1 0 0 1 1 0
  0 0 0 0 0 -1
  0 -1 0 -1 0 1
  0 0 -1 0 -1 -1
  6
  -1 0 0 0 0 0
  0 0 0 1 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 1
  
• NOTES
  Called F_15 by Plesken & Pohst, Q_6(4)^{+2} in LDL II (see references)
  The "shorter" associate of Q8(1).
  
• REFERENCES
  E. M. Rains and N. J. A. Sloane,
  The Shadow Theory of Modular and Unimodular Lattices,
  J. Number Theory, 73 (1998), pp. 359-389;
  http://www.research.att.com/~njas/doc/shad.pdf or shad.ps
  Plesken & Pohst, Math. Comp. 31 (1977), 552-573.
  Conway-Sloane, "Low-Dimensional Lattices II: Subgroups of GL(n,Z)",
  Proc. Royal Soc. London, A 419 (1988), 29-68.
  
• PROPERTIES
  INTEGRAL=1
  MODULAR=5
  
• LAST_LINE
  

INDEX FILE | ABBREVIATIONS

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