The Lattice C2 x L(3,3):C2

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)

INDEX FILE | ABBREVIATIONS

Contents of this file

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

• NAME
  C2 x L(3,3):C2
  
• DIMENSION
  13
  
• GRAM
  13
  5 3 2 1 -1 -3 -3 -3 -3 -1 1 2 3
  3 5 3 2 1 -1 -3 -3 -3 -3 -1 1 2
  2 3 5 3 2 1 -1 -3 -3 -3 -3 -1 1
  1 2 3 5 3 2 1 -1 -3 -3 -3 -3 -1
  -1 1 2 3 5 3 2 1 -1 -3 -3 -3 -3
  -3 -1 1 2 3 5 3 2 1 -1 -3 -3 -3
  -3 -3 -1 1 2 3 5 3 2 1 -1 -3 -3
  -3 -3 -3 -1 1 2 3 5 3 2 1 -1 -3
  -3 -3 -3 -3 -1 1 2 3 5 3 2 1 -1
  -1 -3 -3 -3 -3 -1 1 2 3 5 3 2 1
  1 -1 -3 -3 -3 -3 -1 1 2 3 5 3 2
  2 1 -1 -3 -3 -3 -3 -1 1 2 3 5 3
  3 2 1 -1 -3 -3 -3 -3 -1 1 2 3 5
  
• DIVISORS
  1 1 1 1 1 1 3 3 3 3 3 3 3
  
• MINIMAL_NORM
  3
  
• KISSING_NUMBER
  52
  
• GROUP_ORDER
  22464
  
• GROUP_NAME
  C2 x L(3,3):C2
  
• GROUP_GENERATORS
  2
  13
  0 0 0 0 0 0 0 0 0 0 0 0 1
  0 0 0 0 0 0 0 0 0 0 0 1 0
  0 0 0 1 0 -1 0 0 1 0 -1 1 0
  0 0 0 1 0 0 0 -1 0 1 0 1 -1
  0 0 -1 1 0 0 0 -1 0 0 0 1 -1
  0 0 0 1 0 0 0 0 0 0 0 1 -1
  0 0 0 1 -1 0 0 0 0 0 0 0 -1
  0 0 -1 0 0 1 0 0 -1 0 0 0 0
  0 0 0 0 0 0 -1 1 0 0 0 -1 0
  0 0 0 0 0 0 0 1 0 0 0 -1 1
  0 0 0 -1 0 0 0 1 -1 0 0 -1 1
  0 1 0 -1 0 0 0 1 0 0 0 -1 1
  -1 0 1 0 0 -1 0 1 0 0 0 0 1
  13
  -1 -1 0 0 0 0 0 1 -1 -1 0 1 1
  0 0 0 -1 0 1 0 1 -1 0 0 0 1
  0 0 -1 0 0 1 0 0 0 0 0 0 1
  -1 1 0 0 0 0 0 0 0 1 0 0 0
  0 1 0 0 0 0 -1 0 1 1 0 -1 0
  0 1 0 0 0 0 0 -1 1 1 0 -1 0
  0 1 0 0 0 -1 0 -1 1 1 0 -1 -1
  0 1 1 0 -1 -1 0 0 1 0 0 -1 -1
  1 0 0 0 0 -1 0 0 1 0 -1 -1 0
  0 0 0 0 0 -1 1 0 0 -1 0 0 0
  0 -1 1 0 0 -1 0 1 0 -1 0 0 0
  0 -1 0 0 0 0 0 1 -1 -1 0 0 1
  0 -1 0 0 0 0 1 1 -1 -1 0 1 1
  
• NOTES
  Called F_2(iii) by Plesken, Q'_13(4)^{+2} in LDL II (see references)
  
• REFERENCES
  Plesken, J. Algebra, vol. 97 (1985) pp. 286-312
  Conway-Sloane, "Low-Dimensional Lattices II: Subgroups of GL(n,Z)",
  Proc. Royal Soc. London, A 419 (1988), 29-68.
  
• LAST_LINE
  

INDEX FILE | ABBREVIATIONS

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