The Lattice C2 x G(2,3)

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

Last modified Tue Jan 13 19:20:41 EST 1998

INDEX FILE | ABBREVIATIONS

Contents of this file

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

• NAME
  C2 x G(2,3)
  
• DIMENSION
  14
  
• GRAM
  14 14
  4 1 1 1 1 1 1 1 1 1 1 1 1 1
  1 4 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1
  1 1 4 1 -1 1 1 -1 -1 -1 -1 1 1 -1
  1 -1 1 4 1 -1 1 1 -1 -1 -1 -1 1 1
  1 1 -1 1 4 1 -1 1 1 -1 -1 -1 -1 1
  1 1 1 -1 1 4 1 -1 1 1 -1 -1 -1 -1
  1 -1 1 1 -1 1 4 1 -1 1 1 -1 -1 -1
  1 -1 -1 1 1 -1 1 4 1 -1 1 1 -1 -1
  1 -1 -1 -1 1 1 -1 1 4 1 -1 1 1 -1
  1 -1 -1 -1 -1 1 1 -1 1 4 1 -1 1 1
  1 1 -1 -1 -1 -1 1 1 -1 1 4 1 -1 1
  1 1 1 -1 -1 -1 -1 1 1 -1 1 4 1 -1
  1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 4 1
  1 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 4
  
• DIVISORS
  1 1 1 1 1 1 1 3 3 3 3 3 3 3
  
• MINIMAL_NORM
  4
  
• KISSING_NUMBER
  756
  
• GROUP_ORDER
  8491392
  
• GROUP_NAME
  C2 x G(2,3)
  
• GROUP_GENERATORS
  2
  14
  1 0 0 0 0 -1 -1 0 -1 1 -1 0 -1 -1
  0 1 0 1 0 -1 0 -1 1 1 0 0 -1 -1
  0 0 -1 1 0 1 -1 0 -1 1 0 1 0 -1
  1 0 0 -1 0 0 -1 1 -1 0 0 -1 1 -1
  1 0 1 0 -1 -1 -1 0 1 0 0 -1 -1 0
  0 0 0 1 -1 0 -1 0 0 1 0 0 -1 0
  0 0 -1 0 0 0 0 0 -1 0 0 0 1 -1
  0 -1 1 -1 1 -1 0 0 0 0 0 0 0 0
  0 -1 1 0 0 0 -1 0 0 0 0 0 -1 1
  0 0 0 0 0 0 0 0 -1 0 0 0 0 0
  0 0 0 0 1 -1 1 -1 0 0 0 0 0 -1
  0 -1 0 0 1 0 0 -1 0 0 0 1 -1 0
  0 0 0 0 0 1 -1 1 -1 0 0 0 0 0
  1 1 0 0 0 -1 0 0 0 0 0 -1 0 -1
  14
  -1 0 -1 0 0 1 1 0 0 -1 0 1 1 1
  -1 0 1 -1 1 0 1 1 0 0 0 0 1 1
  -1 0 0 0 0 0 1 0 1 0 0 0 0 1
  0 -1 0 0 0 0 0 -1 0 0 0 1 -1 1
  0 0 0 -1 1 0 0 0 -1 0 0 0 1 0
  0 1 -1 0 0 0 1 0 0 0 -1 0 1 0
  0 0 -1 1 -1 1 0 0 0 0 -1 1 -1 1
  0 0 -1 0 0 1 0 0 -1 0 0 1 0 0
  0 1 -1 0 0 0 0 0 0 0 0 0 1 -1
  1 0 -1 0 -1 0 0 0 0 -1 -1 0 0 0
  0 0 0 0 -1 1 0 1 0 -1 0 0 0 1
  -1 0 0 0 0 1 0 1 0 0 1 0 1 0
  0 -1 0 0 0 0 0 -1 1 -1 1 0 0 0
  0 -1 1 -1 0 0 0 0 0 -1 0 0 0 1
  
• PROPERTIES
  INTEGRAL=1
  MODULAR=3
  
• REFERENCES
  ATLAS of Finite Groups, page 60.
  Conway-Sloane, On lattices equivalent to their duals, J. Number Theory,
  48 (1994), 373-382, esp. p. 381.
  
• LAST_LINE
  

INDEX FILE | ABBREVIATIONS

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