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 13:26:50 CEST 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
MINIMAL_NORM
KISSING_NUMBER
DETERMINANT
DIVISORS
PROPERTIES
NOTES
GRAM
GROUP_GENERATORS
LAST_LINE

• NAME
  Sp4(4)xC_3
  

• DIMENSION
  36
  

• MINIMAL_NORM
  6
  

• KISSING_NUMBER
  720
  

• DETERMINANT
  387420489
  

• DIVISORS
  1^18 3^18
  

• PROPERTIES
  INTEGRAL=1
  MODULAR=3
  

• NOTES
  Found by G. Nebe Feb. 1998.
  

• GRAM
  36 0
  8
  3 8
  -3 2 8
  -3 0 -1 8
  3 4 0 2 8
  3 4 1 -3 1 8
  2 -1 -4 -2 -2 -1 8
  -1 2 -1 2 0 -2 -1 8
  -1 -3 1 1 1 -1 0 -3 8
  -4 -4 -2 1 -5 -2 2 -1 1 10
  3 4 1 -1 3 2 -2 0 -3 -5 8
  -3 -2 3 0 0 1 -2 -2 4 0 0 8
  3 -2 -1 -1 -1 -2 0 1 1 -3 2 1 10
  0 -1 2 0 -2 2 -1 -2 1 -2 1 2 1 8
  0 3 2 -1 2 4 -3 -1 -2 -1 1 -1 -3 -2 8
  -2 2 3 2 3 -2 -1 0 2 0 0 2 -2 -1 0 8
  -4 -1 1 2 0 -2 0 1 -1 -1 1 2 0 -1 0 1 8
  3 -2 -1 -5 -1 -1 4 -1 0 0 -1 0 3 -2 -1 -2 -2 10
  -3 -2 2 -1 -2 1 1 -1 1 2 -2 4 -2 1 0 0 3 1 8
  3 -1 -3 1 3 1 1 -2 4 0 -2 1 1 -1 0 0 -3 2 0 8
  -4 -4 3 -1 -4 -4 1 -2 0 2 -2 1 1 0 0 0 2 3 2 -3 10
  2 0 0 -4 -3 2 0 -1 -2 -1 1 -2 2 0 2 -4 -1 1 -2 -2 2 8
  3 0 -4 0 3 2 2 -2 2 0 -1 -1 -1 -1 0 0 -1 -1 -1 4 -5 -1 8
  -4 1 1 1 -1 -1 1 3 -1 0 -1 1 -2 -1 0 1 4 -2 1 -3 1 0 -1 8
  -4 1 3 3 1 -1 -4 2 1 1 -2 2 -2 -1 1 4 0 -3 -1 0 0 -2 -1 2 8
  2 3 -2 -1 1 4 -1 1 -4 -2 2 -3 -1 0 4 -3 0 -3 -2 -1 -4 3 3 2 0 10
  3 4 2 -1 2 1 -2 1 -3 -2 2 -2 0 -1 2 1 -3 2 -2 -1 -1 1 -2 -2 1 1 8
  0 -2 -3 2 0 -4 0 2 1 0 1 0 4 -1 -4 0 0 -1 -3 1 -1 -1 0 0 1 0 -2 8
  -4 0 0 4 -1 -3 1 1 1 2 0 1 0 -2 -2 1 3 -3 -1 -1 2 -1 -1 4 2 -1 -3 3 10
  2 3 2 -1 0 0 0 1 -1 0 0 -3 0 0 -1 1 -4 1 -2 0 0 0 -2 -2 1 -1 3 0 0 8
  -3 -1 -1 2 1 -1 -2 2 1 2 -2 2 -3 -2 1 2 1 -3 1 1 -1 -1 1 3 3 1 -2 1 1 -2 8
  1 -2 1 -2 0 -1 -2 -2 0 -2 0 0 1 2 0 1 -2 1 -2 0 2 2 -1 -2 1 -1 2 0 -4 0 0 8
  -4 0 4 2 -1 0 -4 -1 2 2 0 2 -3 2 1 3 0 -4 0 -2 1 0 -2 0 4 -2 0 -1 1 0 1 1 8
  1 2 3 -2 2 0 0 0 2 -4 3 2 3 0 0 2 1 2 -1 -1 1 0 -2 1 0 -2 0 1 0 0 -2 0 0 8
  1 2 0 2 1 -1 2 2 0 -3 2 0 3 2 -3 1 1 -1 -1 -1 0 -1 0 1 -1 -1 -1 1 3 1 -2 -2 -1 2 8
  -1 -3 0 -3 -4 -2 0 0 0 2 -2 -1 2 -1 -1 -2 -1 1 -1 -2 3 4 -2 0 0 0 -1 2 0 1 0 2 0 0 -2 8
  

• GROUP_GENERATORS
  2
  36 36
  -2 3 -4 -3 -1 -1 -3 -2 2 0 0 -1 0 1 0 0 1 0 0 0 1 0 0 1 1 -1 1 1 -1 0 0 -1 -1 -1 1 -1
  -6 5 -7 -4 -1 -1 -5 -4 3 -1 0 -4 1 2 -1 1 0 1 1 0 0 1 -1 1 2 -2 1 0 -1 -1 0 -2 -2 -1 1 -1
  0 1 1 2 -3 -2 1 1 -1 -1 0 3 -1 -1 1 -1 0 0 -1 1 0 -1 2 -1 -2 1 0 -1 0 1 0 1 1 1 0 1
  -2 -3 0 -2 4 5 -1 -2 0 0 0 -7 2 1 -3 3 -1 1 1 0 -1 1 -4 1 2 -1 0 0 1 -3 1 -2 -1 -1 0 0
  -5 1 -5 -4 1 3 -4 -4 2 -1 0 -7 2 1 -3 2 0 1 1 0 0 0 -3 1 2 -1 1 0 0 -2 1 -2 -1 -1 1 -1
  -3 2 -4 0 -2 0 -2 -2 2 -1 1 -1 0 0 0 0 0 1 1 -1 0 0 1 1 1 -1 1 0 -1 1 0 0 -1 0 1 0
  3 -3 2 1 1 2 1 1 0 1 1 0 0 0 1 0 0 0 0 -1 0 0 0 1 1 -1 0 1 0 0 0 0 0 -1 0 0
  -2 0 -1 -1 2 -1 0 -1 0 0 0 -1 1 0 -1 1 -2 -1 1 0 -1 2 -2 0 1 0 -1 -1 0 -1 -1 -1 -1 0 -1 -1
  0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  2 4 0 0 0 -4 1 2 0 1 -1 4 -1 2 3 -2 1 0 0 -1 0 1 2 -1 0 -1 -1 1 0 1 -1 1 0 0 -1 0
  -3 4 -4 -4 -2 -3 -3 -2 1 -1 -1 0 0 0 -1 -1 1 -1 -1 2 1 -1 0 0 0 0 1 -1 -1 0 0 -1 0 0 1 -1
  3 -4 4 3 -1 1 3 2 -2 0 1 2 -1 -2 0 -1 0 -1 -1 1 0 -1 1 0 -1 1 0 -1 0 1 0 1 1 1 0 1
  3 -1 2 0 -2 -3 1 2 -2 0 0 5 -2 -2 0 -1 0 -3 -2 3 2 -1 1 0 -2 2 0 -1 -1 1 -1 0 1 1 0 0
  0 -3 1 2 -1 4 0 -1 0 -1 1 -2 0 -2 -1 1 0 1 0 0 0 -1 0 1 0 0 1 0 0 0 1 0 0 0 1 1
  -3 1 -2 0 0 1 -1 -1 1 -1 0 -2 1 0 -1 1 -1 1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 4 -3 -2 -1 -1 -3 -1 2 0 0 -2 0 2 0 0 1 1 0 0 1 0 0 0 1 -1 0 0 0 -1 0 -1 -1 -1 0 0
  4 -5 5 3 0 1 3 3 -2 0 1 2 -1 -2 -1 0 -1 -1 -1 1 0 -1 0 -1 -1 2 -1 -2 1 0 0 1 1 1 -1 1
  3 -3 4 1 1 0 4 2 -2 1 0 3 0 -1 2 -2 0 -2 -1 0 0 -1 1 0 -1 0 0 1 0 1 0 1 2 0 0 0
  5 -8 7 6 1 3 6 3 -2 0 2 2 0 -3 1 0 -2 0 0 -2 -2 0 0 0 0 1 -2 -1 1 1 0 2 1 0 -1 1
  -3 -1 -3 -3 4 4 -2 -4 1 0 0 -7 3 1 -2 2 -1 1 2 -2 -1 1 -4 2 3 -2 0 1 0 -2 1 -2 -1 -2 1 -1
  7 -6 9 5 0 1 6 5 -4 1 0 5 -1 -2 2 -1 0 -1 -2 1 0 -2 2 -1 -3 2 -1 0 1 1 0 2 3 1 -1 2
  1 5 -1 0 -4 -6 -1 1 0 0 -1 6 -2 0 2 -2 1 -1 -1 1 1 -1 3 -1 -2 1 0 0 -1 2 -1 1 0 1 0 0
  -3 4 -7 -3 -2 0 -5 -3 4 -1 1 -3 0 1 -1 1 1 1 1 -1 1 0 -1 1 2 -1 1 0 -1 0 0 -1 -2 -1 1 -1
  -2 -3 0 1 1 3 0 -1 0 -1 1 -3 1 -1 -2 2 -2 0 1 0 -1 1 -2 0 1 0 0 -1 0 -1 0 -1 -1 0 0 0
  -4 4 -4 -2 1 0 -3 -2 1 0 -1 -3 1 2 -1 1 0 1 1 0 0 1 -1 0 0 -1 0 0 0 -1 0 -1 -1 0 0 0
  -6 3 -7 -2 -1 1 -5 -4 3 -2 0 -4 1 0 -2 2 -1 1 2 -1 0 1 -1 1 1 -1 1 0 -1 0 0 -1 -2 0 1 -1
  1 -1 2 1 -1 0 1 1 0 0 0 1 -1 0 1 0 0 0 -1 0 0 0 1 0 -1 0 0 1 0 0 0 0 0 0 0 0
  -1 1 -1 -3 3 -1 -1 -1 -1 1 -2 -1 1 1 -1 0 0 -1 0 1 0 1 -2 0 0 0 0 0 0 -1 0 -1 0 0 0 -1
  0 0 1 -1 0 -1 0 0 -1 0 0 0 0 0 -1 0 0 -1 -1 2 0 0 -1 0 0 0 0 -1 -1 -1 0 -1 0 0 0 0
  -5 10 -7 -5 -1 -5 -5 -4 2 0 -2 -1 1 3 1 -1 1 1 1 0 0 1 0 0 1 -2 0 1 -1 -1 0 -1 -1 -1 1 -1
  -3 5 -5 -3 1 -2 -4 -3 2 0 -1 -3 1 2 -1 1 0 1 2 -1 -1 2 -2 0 2 -1 -1 0 0 -1 -1 -1 -2 -1 0 -1
  3 -5 4 3 1 4 2 1 -1 0 0 -1 0 -1 0 1 0 1 0 -1 0 -1 0 0 -1 1 0 1 1 0 1 0 1 0 0 1
  -3 6 -3 -2 -1 -3 -2 -1 1 0 -1 0 0 2 1 -1 1 1 0 0 0 0 1 -1 0 -1 0 0 0 0 0 0 -1 0 0 0
  -2 4 -2 -2 -2 -4 -1 1 -1 0 -1 4 -1 0 0 -2 1 -2 -2 3 2 -1 2 -1 -2 1 1 -1 -1 1 -1 0 1 1 0 0
  -1 0 -1 -1 -2 0 -1 -1 0 -1 1 0 0 -1 -1 0 0 -1 -1 2 1 -1 0 1 0 0 1 -1 -1 0 0 -1 0 0 0 0
  3 3 2 2 -2 -5 1 3 -2 1 -2 7 -2 0 2 -2 1 -1 -1 1 1 0 3 -2 -3 2 -1 0 0 2 -1 2 1 2 -1 0
  36 36
  2 -1 3 1 0 -2 4 2 -3 0 -1 5 0 -1 1 -2 0 -2 -2 1 0 -1 1 -1 -2 1 0 -1 0 1 0 1 2 1 -1 0
  -2 5 -2 -2 -1 -4 -1 0 0 0 -1 3 0 0 0 -1 0 -1 -1 1 1 0 0 -1 -1 1 -1 -1 -1 0 -1 0 0 0 0 -1
  1 -4 1 2 0 4 -1 -1 2 0 2 -4 0 -1 -1 3 -1 2 1 -2 -1 1 -2 1 2 0 -1 0 0 -1 0 -1 -2 -1 1 0
  -1 0 0 0 0 -2 1 1 0 0 1 2 -1 0 1 -1 0 -1 0 1 0 1 1 0 0 0 0 0 -1 1 -1 0 0 0 0 0
  -1 4 -1 -1 -2 -5 1 1 0 0 0 5 -1 0 1 -2 1 -2 -2 2 1 0 1 -1 -1 1 0 -1 -2 1 -1 0 0 0 0 0
  -5 5 -6 -5 2 0 -5 -4 1 0 -2 -4 2 2 -2 2 0 1 1 0 0 1 -3 0 1 -1 0 0 0 -2 0 -2 -1 -1 1 -1
  1 4 2 0 0 -4 2 3 -2 1 -2 5 0 1 1 -3 1 -1 -1 1 1 -1 3 -2 -3 1 0 0 1 1 0 2 2 1 -2 0
  -3 5 -5 -2 -3 -4 -3 -1 1 -1 0 2 -1 0 0 -1 0 -1 0 1 1 0 1 0 0 0 0 -1 -1 1 -1 0 -1 1 0 -1
  2 -6 4 4 1 2 4 2 -1 0 2 1 0 -1 1 1 -1 0 0 -1 -1 1 1 0 0 0 0 0 0 1 0 0 0 0 -1 1
  2 -1 2 1 2 1 1 2 -1 1 -1 0 0 2 2 0 0 1 1 -1 0 0 2 0 -1 -1 0 2 2 0 0 1 1 0 -1 1
  -4 7 -3 -3 -3 -4 -2 -2 1 -1 -1 2 0 -1 -1 -2 1 -1 -2 2 1 -1 0 -1 -1 1 0 -1 -2 0 0 0 0 0 1 -1
  -4 4 -4 -1 -2 0 -4 -3 3 -1 1 -3 0 0 -2 2 0 2 1 0 0 1 -1 0 1 0 0 0 -1 -1 0 -1 -2 -1 1 0
  3 -3 2 3 -5 -1 2 1 0 -2 2 4 -2 -4 0 -1 0 -1 -2 1 0 -2 1 0 -1 2 0 -2 -1 2 0 1 1 1 0 0
  -4 0 -3 -3 3 2 -3 -4 1 0 0 -6 2 1 -2 2 -1 1 2 -1 -2 2 -3 1 3 -2 0 0 0 -2 0 -2 -2 -1 1 -1
  -1 1 -3 -2 0 2 -3 -1 2 0 0 -3 0 1 -1 2 1 1 0 0 1 0 -2 0 1 0 0 0 0 -1 0 -1 -1 -1 1 0
  -1 -1 1 1 1 1 1 0 1 0 1 -2 1 0 0 1 -1 1 1 -1 -1 1 -1 0 1 0 -1 0 0 -1 0 0 -1 -1 0 0
  -3 8 -5 -3 -3 -4 -5 -2 3 0 -1 0 -1 1 -1 -1 2 1 0 1 1 0 0 -1 0 1 0 0 -1 0 0 0 -1 0 1 -1
  2 3 1 2 -4 -2 1 3 0 0 0 5 -2 0 1 -2 2 0 -2 1 2 -2 4 -1 -3 1 1 0 0 2 0 2 1 1 -1 1
  -2 4 -2 -1 0 0 -3 -1 1 1 -1 -2 0 2 -1 1 1 2 1 0 0 1 0 -1 0 0 0 1 1 -1 0 0 -1 0 0 0
  1 -4 3 2 1 1 4 2 -2 0 1 2 0 0 1 0 0 -1 -1 1 0 0 1 0 -1 0 1 0 0 1 0 0 1 0 -1 1
  4 -6 5 4 -1 5 2 2 1 0 2 -2 -1 -2 -1 1 0 1 0 -1 0 -1 0 0 0 1 0 0 1 0 1 1 0 0 0 1
  3 -5 2 2 0 3 1 0 -1 -1 0 -1 0 -2 -1 1 -1 0 0 -1 0 -1 -1 0 0 1 0 -1 1 0 1 0 1 1 0 0
  -1 3 -3 -3 1 -3 -1 -1 -1 0 -2 1 1 2 1 -1 1 -1 0 1 0 0 0 0 0 -1 1 0 0 0 0 -1 1 0 0 0
  -2 9 -5 -3 -3 -6 -5 -1 2 0 -1 2 -1 1 -1 -1 1 0 0 1 2 0 1 -1 0 1 -1 -1 -1 0 -1 0 -1 0 0 -1
  -2 0 -4 0 -1 1 -3 -2 3 -1 2 -3 0 0 0 2 -1 1 2 -1 0 1 -1 2 2 -1 0 0 -1 0 -1 -1 -2 -1 1 0
  -2 7 -7 -5 -2 -5 -5 -3 1 -1 -2 1 0 1 0 -1 1 -1 0 1 1 -1 -1 0 1 0 0 -1 -1 0 -1 -1 0 0 1 -1
  2 1 0 1 -1 -2 1 1 0 0 0 3 -1 0 2 -1 0 0 0 -1 0 0 1 0 0 0 -1 0 0 1 -1 1 0 0 0 0
  3 -5 6 5 -2 0 6 3 -2 -1 2 5 -1 -4 1 -2 -1 -2 -2 1 0 -2 2 0 -2 2 0 -1 -1 2 0 2 2 1 -1 1
  1 -1 2 1 -2 -1 1 1 0 -1 1 2 -1 -2 0 -1 0 -1 -1 1 1 -1 1 0 -1 1 0 0 -1 1 0 0 1 0 0 0
  4 -10 7 4 3 4 6 2 -3 0 1 0 1 -2 1 1 -3 -1 0 -2 -2 0 -1 1 0 0 -1 0 1 0 0 0 1 0 -1 0
  -1 -1 -1 0 0 1 -1 -1 0 -1 0 -2 0 0 -1 2 -1 0 1 0 0 1 -1 0 1 0 0 0 0 -1 0 -1 -1 0 0 0
  1 -8 2 1 4 7 1 -2 0 0 1 -7 2 -1 -2 3 -2 1 2 -2 -2 1 -4 2 3 -1 0 0 1 -2 1 -1 -1 -1 1 0
  -3 -1 -2 0 2 3 -2 -2 2 0 1 -5 1 1 0 2 -1 2 2 -2 -1 2 -1 1 2 -2 0 1 0 -1 0 -1 -2 -1 1 0
  0 5 1 2 -5 -5 1 3 1 0 1 7 -2 -2 0 -2 1 -1 -3 2 2 -1 3 -2 -3 3 -1 -2 -2 2 -1 2 0 1 -1 0
  -2 4 -2 -2 -3 -6 -1 0 0 -1 0 4 -1 -1 0 -2 0 -2 -1 2 0 0 1 -1 -1 1 0 -2 -1 1 -1 0 0 1 0 -1
  7 -9 6 5 -1 5 3 2 -1 0 2 -1 -1 -3 0 1 -1 0 0 -1 0 -2 0 1 0 1 0 0 1 0 1 1 1 1 0 1
  

• LAST_LINE
  

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  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe