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 Wed Feb 15 13:57:52 CET 2012

INDEX FILE | ABBREVIATIONS

Contents of this file

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

• NAME
  Q1766
  

• DIMENSION
  17
  

• DET
  722204136308736
  

• DIVISORS
  1 6 6 6 6 6 6 6 6 12 12 12 12 12 12 12 12
  

• MINIMAL_NORM
  17
  

• KISSING_NUMBER
  240
  

• GRAM
  17 17
  17 -1 -1 -1 -7 -1 -7 5 5 5 5 -7 -1 -7 -1 -1 -1
  -1 17 -1 -1 -1 -7 -1 -7 5 5 5 5 -7 -1 -7 -1 -1
  -1 -1 17 -1 -1 -1 -7 -1 -7 5 5 5 5 -7 -1 -7 -1
  -1 -1 -1 17 -1 -1 -1 -7 -1 -7 5 5 5 5 -7 -1 -7
  -7 -1 -1 -1 17 -1 -1 -1 -7 -1 -7 5 5 5 5 -7 -1
  -1 -7 -1 -1 -1 17 -1 -1 -1 -7 -1 -7 5 5 5 5 -7
  -7 -1 -7 -1 -1 -1 17 -1 -1 -1 -7 -1 -7 5 5 5 5
  5 -7 -1 -7 -1 -1 -1 17 -1 -1 -1 -7 -1 -7 5 5 5
  5 5 -7 -1 -7 -1 -1 -1 17 -1 -1 -1 -7 -1 -7 5 5
  5 5 5 -7 -1 -7 -1 -1 -1 17 -1 -1 -1 -7 -1 -7 5
  5 5 5 5 -7 -1 -7 -1 -1 -1 17 -1 -1 -1 -7 -1 -7
  -7 5 5 5 5 -7 -1 -7 -1 -1 -1 17 -1 -1 -1 -7 -1
  -1 -7 5 5 5 5 -7 -1 -7 -1 -1 -1 17 -1 -1 -1 -7
  -7 -1 -7 5 5 5 5 -7 -1 -7 -1 -1 -1 17 -1 -1 -1
  -1 -7 -1 -7 5 5 5 5 -7 -1 -7 -1 -1 -1 17 -1 -1
  -1 -1 -7 -1 -7 5 5 5 5 -7 -1 -7 -1 -1 -1 17 -1
  -1 -1 -1 -7 -1 -7 5 5 5 5 -7 -1 -7 -1 -1 -1 17
  

• PROPERTIES
  INTEGRAL=1
  

• NOTES
  Called F_6(vi) by Plesken, Q_17(6)^{+6} 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.
  

• THETA_SERIES
  0 1
  1 0
  2 0
  3 0
  4 0
  5 0
  6 0
  7 0
  8 0
  9 0
  10 0
  11 0
  12 0
  13 0
  14 0
  15 0
  16 0
  17 240
  18 0
  19 0
  20 1020
  21 816
  21 0
  23 0
  24 2040
  25 0
  26 0
  27 0
  28 0
  29 17952
  30 0
  

• GROUP_ORDER
  32640
  

• GROUP_NAME
  C2 x L(2,16):C4
  

• LAST_LINE
  

  ---

  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe