An entry from the Catalogue of Lattices, which is a joint project of
Gabriele Nebe, RWTH Aachen University (nebe@math.rwth-aachen.de) and
Neil J. A. Sloane (njasloane@gmail.com)

Last modified Fri Jul 18 13:16:09 CEST 2014

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
  M8,3
  

• DIMENSION
  8
  

• GRAM
  8
  8 -4 -1 2 2 -4 -1 2
  -4 8 2 -4 -1 2 -1 -1
  -1 2 8 -4 -4 2 2 -1
  2 -4 -4 8 2 -1 -1 -1
  2 -1 -4 2 8 -4 2 -1
  -4 2 2 -1 -4 8 -1 2
  -1 -1 2 -1 2 -1 8 -4
  2 -1 -1 -1 -1 2 -4 8
  

• DIVISORS
  1 3 3 3 3 21 21 21
  

• MINIMAL_NORM
  8
  

• KISSING_NUMBER
  42
  

• GROUP_ORDER
  672
  

• GROUP_NAME
  C2 x PGL(2,7)
  

• GROUP_GENERATORS
  2
  8
  0 0 0 0 0 0 0 1
  0 0 0 0 0 0 1 0
  1 1 -1 0 -1 0 1 0
  0 0 1 0 1 0 -1 0
  -1 0 1 1 0 -1 0 1
  1 0 0 0 0 1 0 -1
  0 0 0 0 -1 -1 0 0
  0 0 0 0 0 1 0 0
  8
  -1 -1 1 0 1 0 -1 0
  0 0 -1 0 -1 0 1 0
  0 0 0 0 0 0 0 -1
  0 0 0 0 0 0 -1 0
  -1 0 0 0 0 -1 0 1
  1 0 -1 -1 0 1 0 -1
  0 0 0 0 0 -1 0 0
  0 0 0 0 1 1 0 0
  

• NOTES
  Called F_23 by Plesken & Pohst, Q_8(3)^{+3} 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
  

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  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe