The Lattice A2xA4#

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
  A2xA4#
  
• DIMENSION
  8
  
• GRAM
  8
  8 -2 -2 -2 -4 1 1 1
  -2 8 -2 -2 1 -4 1 1
  -2 -2 8 -2 1 1 -4 1
  -2 -2 -2 8 1 1 1 -4
  -4 1 1 1 8 -2 -2 -2
  1 -4 1 1 -2 8 -2 -2
  1 1 -4 1 -2 -2 8 -2
  1 1 1 -4 -2 -2 -2 8
  
• DIVISORS
  1 1 5 5 15 15 15 15
  
• MINIMAL_NORM
  8
  
• KISSING_NUMBER
  30
  
• GROUP_ORDER
  1440
  
• GROUP_NAME
  C2 x S5 x S3
  
• GROUP_GENERATORS
  3
  8
  0 0 0 0 1 1 1 1
  0 0 0 0 -1 0 0 0
  0 0 0 0 0 -1 0 0
  0 0 0 0 0 0 -1 0
  -1 -1 -1 -1 -1 -1 -1 -1
  1 0 0 0 1 0 0 0
  0 1 0 0 0 1 0 0
  0 0 1 0 0 0 1 0
  8
  0 0 0 0 1 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 1
  1 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 1 0 0 0 0
  8
  0 1 0 0 0 0 0 0
  1 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 1 0 0
  0 0 0 0 1 0 0 0
  0 0 0 0 0 0 1 0
  0 0 0 0 0 0 0 1
  
• NOTES
  Called F_18 by Plesken & Pohst, (A4 tensor A2)^{+25} in LDL II (see references)
  
• REFERENCES
  Plesken & Pohst, Math. Comp. 34 (1980), 259-275.
  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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