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 13:14:07 CEST 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
GRAM (floating point or integer Gram matrix)
DIVISORS (elementary divisors)
MINIMAL_NORM
KISSING_NUMBER
GROUP_ORDER
GROUP_GENERATORS
PROPERTIES
REFERENCES
NOTES
URL (links to other sites for this lattice)
LAST_LINE

• NAME
  SL2(9)SL2(5).2
  

• DIMENSION
  32
  

• GRAM (floating point or integer Gram matrix)
  32 0
  6
  3 6
  1 2 6
  1 2 1 6
  2 3 3 3 6
  1 3 3 2 3 6
  2 3 3 1 2 3 6
  2 2 1 1 1 1 3 6
  0 1 2 2 1 3 2 2 6
  1 1 3 3 2 1 1 1 1 6
  2 3 2 1 2 2 3 2 1 1 6
  3 2 2 1 1 1 3 3 3 1 2 6
  1 1 2 3 2 1 1 1 1 3 1 1 6
  2 1 1 3 2 1 2 2 1 3 2 2 3 6
  1 2 3 1 3 2 2 1 1 1 3 1 3 1 6
  1 3 2 2 3 3 2 1 2 1 3 1 1 1 3 6
  1 2 2 3 1 3 1 1 3 3 1 1 2 2 1 1 6
  1 2 1 2 2 2 1 2 2 1 1 1 1 1 1 3 2 6
  2 1 1 1 1 1 1 3 1 1 3 2 1 2 2 2 1 3 6
  1 1 1 1 1 1 2 3 1 1 1 1 2 1 2 2 1 3 3 6
  1 1 3 1 1 2 2 3 2 3 1 1 1 1 1 1 2 2 2 3 6
  1 3 3 1 3 2 3 2 1 2 3 1 2 3 3 2 1 1 1 1 1 6
  1 1 2 3 3 1 1 2 1 2 1 1 2 2 2 1 1 3 2 2 3 2 6
  3 3 1 2 2 2 1 3 1 1 2 2 1 1 1 1 2 3 3 2 2 1 3 6
  2 1 2 2 1 2 3 3 2 3 1 3 2 3 1 1 3 1 2 1 2 1 1 1 6
  1 2 3 1 2 3 3 1 1 2 3 1 1 1 3 3 2 1 2 3 2 2 1 1 2 6
  1 1 1 2 2 3 2 3 3 1 1 1 1 1 1 1 3 3 2 3 3 1 3 3 2 2 6
  3 3 1 2 2 2 1 1 3 1 1 3 1 1 1 2 2 2 1 1 1 1 1 3 1 1 2 6
  1 2 1 3 1 2 1 1 2 2 1 1 3 2 2 3 3 3 1 2 1 1 1 2 2 1 1 2 6
  3 3 1 2 2 2 1 2 1 1 1 2 1 1 1 2 1 1 2 1 1 1 1 3 2 1 1 3 2 6
  3 3 1 2 2 2 1 1 1 1 2 2 1 1 1 1 2 1 2 1 1 1 1 3 1 1 2 3 1 3 6
  1 2 1 1 1 1 3 3 1 1 2 3 1 2 1 1 0 1 2 1 1 2 1 2 3 1 1 2 1 1 2 6
  

• DIVISORS (elementary divisors)
  1^24 10^8
  

• MINIMAL_NORM
  6
  

• KISSING_NUMBER
  4800
  

• GROUP_ORDER
  2^7 * 3^3 * 5^2
  

• GROUP_GENERATORS
  2
  32
  -2 -1 -1 0 1 0 1 1 -2 -1 0 1 1 -1 -1 0 0 0 1 -2 1 1 0 0 1 1 -1 2 1 -1 1 -2
  -2 0 -1 0 1 0 1 0 -2 -1 0 1 1 -1 -1 0 0 -1 2 -1 1 1 0 0 1 0 0 2 1 -1 0 -2
  0 -1 -1 -1 1 1 1 1 -1 0 0 0 0 -1 -1 0 2 -1 1 0 -1 0 2 -1 -1 0 -1 1 1 0 0 0
  -1 1 0 1 0 0 -1 -1 -1 -1 0 1 0 -1 -1 0 -2 -1 1 0 1 2 -1 1 3 0 1 1 1 -2 0 -2
  -2 1 0 0 0 0 0 0 -1 -1 0 0 0 0 -1 0 -2 -1 1 0 0 1 0 1 3 0 0 2 1 -2 1 -3
  -1 1 0 2 0 -1 -1 -2 -1 -2 0 1 0 0 0 0 -2 0 0 0 2 2 -2 2 3 0 1 0 0 -1 0 -2
  0 -2 -2 -1 2 0 2 1 -2 -1 -1 1 2 -2 -2 1 3 -1 2 -2 1 1 1 -1 -2 1 -1 1 1 0 0 0
  0 -1 -1 -1 1 1 0 1 -1 0 1 0 1 -1 -1 0 1 0 0 0 0 0 1 -1 0 0 -1 1 0 0 0 0
  1 1 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 -1 1
  0 -1 -1 0 0 1 0 0 -1 0 0 1 0 -1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
  0 -1 -1 0 1 0 0 0 -1 -1 0 1 1 -1 -1 0 1 0 1 -1 1 1 0 -1 -1 1 0 0 1 0 0 0
  0 -1 -1 -1 1 0 1 1 -1 0 0 0 1 -1 -1 0 1 0 1 -2 0 0 1 -1 -1 1 0 1 1 0 0 0
  0 0 0 -1 0 1 0 1 -1 0 0 0 0 -1 -1 0 1 -1 1 0 -1 0 2 -2 0 0 0 1 1 0 0 0
  0 -1 -1 0 0 0 0 0 -1 -1 0 1 1 -1 -1 1 1 0 0 -1 1 1 0 0 0 1 0 0 0 0 0 0
  0 0 0 -1 0 1 0 1 -1 0 0 0 0 0 -1 0 1 -1 1 0 -1 0 2 -2 -1 0 0 1 1 0 0 0
  0 0 0 1 0 0 -1 -1 -1 -1 0 1 0 0 0 0 0 0 0 0 1 1 -1 0 0 0 1 0 0 0 -1 0
  -1 1 0 1 0 0 -1 -1 -1 -1 0 1 0 0 0 0 -1 0 0 0 1 1 -1 1 2 0 1 0 0 -1 0 -1
  -1 0 0 1 0 0 -1 0 -1 -1 0 0 0 0 0 0 -1 0 0 0 1 1 -1 1 2 0 0 1 0 -1 0 -1
  0 0 0 1 0 0 -2 0 0 -1 1 0 0 0 0 -1 -1 1 -1 0 1 1 -1 0 1 1 0 0 0 0 0 0
  0 0 0 0 0 1 -1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 1 0 0 0 0
  0 -1 -2 0 1 1 0 0 -1 0 0 1 0 -1 0 0 1 0 0 0 1 1 0 0 0 0 -1 0 0 0 0 0
  0 -1 -1 -1 0 1 1 1 -1 0 0 0 1 -1 -1 1 2 -1 1 0 -1 0 2 -1 -1 0 -1 1 0 0 0 0
  -1 0 -1 0 0 1 0 1 -1 0 0 0 0 -1 -1 0 -1 -1 1 0 0 1 1 0 2 0 -1 2 1 -2 1 -2
  -2 1 0 1 0 0 -1 0 -1 -1 1 0 0 0 0 -1 -3 0 0 0 1 1 -1 1 4 0 0 2 1 -2 1 -3
  0 -1 -1 0 1 0 0 0 -1 -1 0 1 1 -1 -1 0 1 0 0 -1 1 1 0 0 0 1 0 0 0 0 0 0
  0 0 0 1 0 0 -1 -1 -1 -1 0 1 0 0 0 0 0 0 0 0 1 1 -1 0 0 0 1 0 0 0 0 0
  -1 1 0 1 0 0 -1 0 -1 -1 0 0 0 0 0 0 -2 0 0 0 1 1 -1 1 3 0 0 1 0 -2 1 -2
  -1 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 -1 1 -1 0 0 0 0 1 0 1 1 1 -1 0 -1
  0 0 0 1 0 0 -1 -1 -1 -1 0 1 0 0 0 0 0 0 0 0 1 1 -1 0 1 0 1 0 0 0 -1 0
  -1 1 0 1 0 0 -1 -1 0 -1 1 0 0 0 0 -1 -2 0 0 0 1 1 -1 1 3 0 0 1 0 -1 0 -2
  -2 1 0 1 0 0 0 0 -1 -1 0 0 0 0 0 -1 -3 0 1 -1 1 1 -1 1 3 1 0 2 1 -2 1 -3
  0 -1 -1 -1 1 0 1 1 -1 0 0 0 1 -1 -1 0 1 -1 1 -1 0 0 1 -1 -1 1 0 1 1 0 0 0
  32
  0 1 0 1 0 -1 -1 -1 1 -1 0 0 0 1 0 0 -1 1 -1 0 1 0 -1 1 1 1 0 -1 -1 0 0 0
  0 1 1 1 -1 0 -1 0 1 0 1 -1 -1 1 1 -1 -1 1 -1 1 -1 -1 0 0 1 0 0 0 -1 0 0 0
  1 -1 0 -1 0 1 1 2 0 1 0 -1 0 0 0 0 2 0 0 0 -2 -2 2 -2 -3 0 -1 0 0 1 0 2
  0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 -1 1 0 0 0 0 -1 0 -1 -1 0 0 0 0 1 -1 1
  2 -1 0 -1 0 1 0 1 1 1 1 -1 0 0 0 0 3 0 -1 1 -2 -2 2 -2 -3 0 -1 -1 -1 2 -1 3
  0 0 0 0 0 1 0 1 0 0 1 -1 0 0 0 -1 0 0 0 1 -1 -1 1 -1 0 0 -1 1 0 0 0 0
  0 0 0 1 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 1 1 0 0 -1 0 0 1 -1 0 -1 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0
  0 1 0 0 0 0 0 0 1 0 0 -1 0 1 1 -1 -1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0
  1 -1 0 -1 1 0 1 1 0 1 0 0 0 0 0 0 3 0 0 0 -1 -2 1 -2 -4 0 0 -1 0 2 -1 3
  0 0 0 -1 0 1 1 2 0 1 0 -1 0 0 0 0 1 0 0 0 -2 -2 2 -1 -1 0 -1 1 0 0 0 0
  0 1 0 1 0 -1 -1 -1 1 -1 0 0 0 1 1 0 -1 1 -1 0 1 0 -1 1 1 0 0 -1 -1 0 0 0
  1 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 -1 0 -1 -2 0 0 -1 0 1 -1 2
  1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 -1 0 -1 -2 0 0 -1 0 1 -1 2
  1 -1 0 -1 0 1 1 2 0 1 0 -1 0 0 0 0 2 0 0 0 -2 -2 2 -2 -2 0 -1 0 0 1 0 1
  0 0 0 -1 0 1 1 2 0 1 0 -1 0 0 0 0 1 -1 1 0 -2 -2 2 -1 -1 0 -1 1 0 0 0 0
  0 1 1 1 0 0 -1 0 1 0 1 -1 -1 1 1 -2 -2 1 -1 1 0 -1 -1 0 1 0 0 0 0 0 0 0
  0 2 2 0 -1 0 -2 0 1 0 1 -1 -1 2 1 -1 -2 0 -1 1 -1 -2 0 0 1 0 1 0 0 0 0 0
  0 1 1 -1 0 0 0 1 0 0 0 -1 0 1 0 0 0 0 0 0 -1 -2 1 -1 0 0 0 1 0 0 0 0
  0 0 1 0 0 0 0 0 0 -1 0 0 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0
  0 0 1 -1 0 0 1 1 0 0 0 -1 0 1 0 0 1 0 0 0 -1 -2 1 -1 -2 0 0 0 0 1 0 1
  1 -1 0 -1 0 1 1 2 0 1 0 -1 0 0 0 0 3 0 0 0 -2 -2 2 -2 -3 0 -1 0 0 1 0 2
  0 0 1 -1 0 0 0 1 0 0 1 -1 0 1 0 0 1 0 -1 0 -1 -2 1 -1 -1 0 0 0 0 1 0 1
  0 1 1 0 0 -1 -1 0 1 -1 1 -1 0 1 0 -1 -1 1 -1 0 0 -1 0 0 1 1 0 0 0 0 0 0
  0 0 0 1 1 -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0
  0 -1 0 0 0 1 1 2 -1 0 0 0 0 0 0 0 1 0 0 0 -1 -1 1 -1 -1 0 -1 1 0 0 0 0
  0 1 1 0 0 0 -1 0 1 -1 1 -1 0 1 0 -1 -1 0 -1 1 0 -1 0 0 1 0 0 0 0 0 0 0
  0 1 0 1 0 -1 -1 -1 1 -1 0 0 0 1 1 -1 -1 1 -1 0 1 0 -1 1 1 1 0 -1 -1 0 0 0
  0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 -1 0 0 1 -1 0 -1 0 -1 -1 1 0 0 1 0 0 0
  0 0 0 1 0 -1 0 0 0 -1 0 0 1 0 0 0 0 1 0 -1 1 0 -1 0 0 1 0 0 -1 0 0 0
  0 1 1 0 0 0 -1 0 1 0 1 -1 0 1 0 -1 -1 1 -1 1 -1 -1 0 0 1 0 0 0 -1 0 0 0
  0 0 0 0 1 -1 0 0 0 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  

• PROPERTIES
  INTEGRAL = 1
  

• REFERENCES
  G. Nebe, Finite quaternionic matrix groups,
  Representation Theory 2, 106-223 (April 1998)
  

• NOTES
  

• URL (links to other sites for this lattice)
  All the quaternionic matrix groups
  

• LAST_LINE
  

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  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe