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 13:14:18 CEST 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

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

• NAME
  SL2(5)C5Q24.2
  

• DIMENSION
  32
  

• GRAM (floating point or integer Gram matrix)
  32 0
  12
  1 12
  2 1 12
  2 3 4 12
  1 3 4 2 12
  3 -1 -1 0 3 12
  3 6 1 6 2 2 12
  6 2 2 1 -1 1 2 12
  3 4 2 2 2 -2 4 1 12
  2 4 6 0 2 0 -2 2 2 12
  2 1 2 3 2 2 3 2 3 2 12
  1 6 0 4 5 2 3 0 4 1 -2 12
  3 3 3 6 2 4 6 4 4 1 2 6 12
  2 3 0 2 3 -1 5 2 6 0 6 2 2 12
  6 0 2 3 1 1 0 6 1 4 0 1 3 0 12
  1 3 -1 2 3 6 2 1 1 3 6 2 4 3 0 12
  -1 3 1 3 2 2 6 -1 3 -1 5 1 3 2 -4 2 12
  1 3 1 2 -1 -2 2 1 4 -1 0 3 1 3 -2 0 0 12
  3 -2 4 2 1 -2 -2 3 2 2 1 -3 -1 2 6 -2 -3 0 12
  2 4 3 4 1 0 4 3 3 1 3 2 4 4 0 1 4 4 2 12
  2 2 5 2 3 2 0 6 3 3 1 4 4 1 2 2 2 3 1 6 12
  2 2 6 2 3 -3 -1 0 4 6 2 2 -1 2 2 -1 1 2 4 4 4 12
  2 0 6 2 2 1 3 0 2 3 4 -1 2 4 0 2 2 4 2 5 2 6 12
  -1 4 1 0 6 -3 0 -2 6 1 2 4 0 4 -2 3 2 4 1 1 1 4 1 12
  6 3 1 4 2 1 2 4 4 1 1 3 2 1 3 2 2 3 1 6 6 5 1 3 12
  2 3 4 0 3 0 1 1 6 4 6 1 3 3 2 2 4 2 0 2 3 2 2 4 1 12
  4 4 4 6 2 2 6 1 5 4 2 4 6 1 2 4 3 4 -1 2 2 3 4 2 4 1 12
  5 3 4 -1 1 -1 2 4 4 4 -1 3 2 3 3 -3 -2 3 2 4 4 6 4 0 3 3 0 12
  6 0 2 2 -2 0 4 6 1 -2 1 -2 2 3 0 -2 2 4 3 6 3 0 2 -2 4 -1 1 4 12
  3 2 1 4 2 0 0 4 1 0 1 3 2 1 2 2 0 4 3 6 6 2 2 2 6 0 0 2 3 12
  3 2 2 -1 1 1 2 3 2 0 3 -2 -2 2 -3 -1 4 0 3 3 2 2 0 1 2 1 -2 3 6 1 12
  0 0 4 3 3 2 0 1 0 2 6 1 3 3 0 3 3 1 -1 2 3 2 4 1 0 6 -1 1 -1 3 1 12
  

• GROUP_ORDER
  2^6 * 3^2 * 5^2
  

• GROUP_GENERATORS
  3
  32
  -2 -1 -2 0 -1 0 2 1 -2 0 -1 2 -1 0 -3 -1 -3 -3 2 -1 0 1 1 0 1 5 3 -1 2 1 0 0
  -1 0 -2 0 -1 0 1 0 -2 0 -1 1 0 1 -1 -1 -2 -2 1 -1 1 1 1 0 0 3 2 -1 1 1 1 0
  -1 0 0 -1 0 -1 0 -1 0 0 0 1 1 0 1 0 0 0 0 -1 0 0 1 -1 1 0 0 -1 1 0 1 0
  -1 0 -1 0 0 -1 -1 0 -1 -1 0 1 0 0 0 0 0 -1 1 0 0 -1 1 0 0 1 2 1 0 0 1 0
  0 0 1 -2 0 -1 1 -1 0 0 1 1 1 0 1 0 0 1 0 -1 0 0 0 -1 1 -1 -1 -1 0 0 1 0
  0 0 -1 0 0 0 1 1 0 0 0 1 -1 -1 -2 0 -1 -1 2 0 0 0 0 0 0 1 1 0 1 -1 -1 1
  -2 0 -2 0 -1 0 1 1 -2 -1 -1 2 -1 0 -2 0 -2 -3 2 -1 0 1 1 0 0 4 3 0 2 1 0 0
  -1 0 -1 0 0 -1 0 0 -1 0 0 1 0 0 -1 0 -1 -1 1 -1 0 0 1 -1 1 2 1 0 1 0 0 0
  -1 -1 -1 -1 -1 0 3 0 -1 1 0 2 0 0 -1 -1 -2 -1 1 -1 0 1 1 0 1 2 0 -2 1 1 0 0
  -1 0 -2 0 -1 0 1 0 -1 0 -1 2 -1 0 -2 -1 -2 -3 2 -1 1 0 2 0 1 3 2 -1 2 0 0 1
  -1 -1 -1 0 -1 0 2 1 -1 0 -1 2 -1 0 -2 0 -2 -2 1 0 0 1 1 0 0 3 1 -1 1 0 0 0
  0 0 -1 -1 0 -1 1 -1 -1 1 1 1 1 0 0 -1 -1 0 1 -1 1 -1 1 0 1 0 0 -1 0 0 1 0
  -1 0 -1 -1 0 -1 1 0 -1 0 0 2 0 0 -1 0 -1 -1 2 -1 0 0 1 -1 1 2 1 -1 1 0 0 0
  -1 -1 -1 0 -1 0 2 1 -1 0 -1 2 -1 0 -2 0 -2 -2 1 -1 0 1 1 0 0 3 1 -1 1 1 0 0
  -1 0 -1 0 0 0 0 0 -1 0 0 1 0 0 -1 -1 -1 -1 1 -1 0 0 1 0 1 2 1 0 1 0 0 0
  -1 0 -1 0 -1 0 1 1 -1 -1 -1 2 -2 0 -2 0 -2 -3 2 0 0 0 1 0 0 3 3 0 1 0 0 1
  -1 0 -1 0 -1 0 0 1 -1 -1 0 2 -1 0 -1 0 -1 -2 1 0 0 0 1 0 0 2 2 0 1 0 0 0
  -2 0 -2 0 -1 0 1 0 -1 0 0 1 -1 0 -1 -1 -2 -3 1 -1 1 0 1 1 0 2 3 0 2 1 0 1
  0 0 1 0 0 0 -1 0 1 0 0 0 0 0 1 0 1 1 -1 0 -1 0 0 0 0 -1 -1 0 0 0 0 0
  -2 0 -1 0 -1 0 0 0 -1 -1 -1 1 0 1 0 0 -2 -2 0 -1 0 1 1 0 0 3 2 -1 2 1 1 0
  -1 0 0 -1 0 -1 0 -1 0 0 1 1 1 0 1 0 -1 0 0 -1 0 0 1 -1 1 0 0 -1 1 0 1 0
  -1 0 0 -1 -1 0 0 -1 -1 0 0 1 1 1 0 -1 -1 -1 0 -1 0 0 1 0 1 1 1 -1 1 1 1 0
  -2 0 -1 -1 -1 0 1 0 -1 -1 -1 2 -1 0 -1 0 -2 -3 1 -1 0 1 1 0 0 3 3 -1 3 1 0 1
  -1 0 0 -1 -1 0 1 0 -1 0 0 1 0 1 0 -1 -1 -1 0 -1 0 0 1 0 1 1 1 -1 0 1 1 0
  -2 0 -1 0 -1 0 0 0 -2 -1 0 1 0 1 -1 -1 -2 -2 1 -1 0 0 1 0 1 3 3 0 1 1 1 0
  -1 -1 -1 -1 -1 0 3 0 -1 1 0 2 0 0 -1 -1 -2 -1 1 -1 1 1 1 0 1 2 0 -2 1 0 0 0
  -3 0 -3 0 -1 0 1 1 -2 -1 -1 3 -2 0 -3 -1 -3 -5 3 -1 0 0 2 0 1 5 5 0 3 1 0 1
  -1 0 -1 -1 -1 0 2 -1 -1 1 0 1 1 0 -1 -1 -2 -1 1 -2 1 1 1 0 1 2 0 -2 2 1 0 0
  -2 0 -2 1 -1 0 0 1 -1 -1 -1 1 -1 0 -2 0 -2 -3 1 -1 0 1 1 0 0 4 3 0 2 1 0 0
  0 0 1 -1 0 -1 0 -1 0 0 1 0 1 0 2 0 0 1 -1 0 0 0 0 0 0 -1 -1 -1 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 0 0 0 0
  1 0 1 -1 0 -1 0 -1 0 0 1 0 1 0 1 0 1 1 0 0 1 -1 0 0 0 -2 -1 0 -1 -1 0 0
  32
  -2 -1 -2 1 -1 1 2 2 -1 0 -2 2 -2 0 -3 0 -3 -3 1 -1 0 2 1 0 0 5 2 -1 2 1 0 0
  -1 0 -2 1 -1 0 0 1 -1 -1 0 1 -2 -1 -2 0 -1 -3 2 0 1 -1 1 1 0 2 3 2 1 0 -1 1
  -1 0 -1 0 -1 1 1 1 -1 -1 -1 1 -2 0 -2 0 -2 -3 1 0 0 1 0 1 -1 3 3 0 2 1 -1 1
  -2 0 -3 1 -1 1 1 1 -1 -1 -1 1 -2 0 -2 -1 -3 -4 1 0 1 1 1 1 -1 4 4 0 2 1 0 1
  0 -1 -1 0 0 0 2 1 0 1 0 1 -1 -1 -2 0 -1 -1 1 0 0 1 0 0 0 1 0 -1 1 0 -1 1
  0 -1 -1 0 0 0 2 1 1 1 -1 1 -1 -1 -2 0 -1 -1 1 0 0 1 0 0 0 1 0 -1 1 0 -1 1
  -2 0 -2 0 -1 0 1 0 -1 -1 -1 1 -1 0 -1 0 -2 -3 1 -1 1 1 1 0 0 3 3 0 2 1 0 1
  -1 0 0 0 0 0 0 1 0 -1 -1 1 -1 0 -1 1 -1 -1 0 0 -1 1 0 -1 0 2 1 0 1 1 0 0
  -2 0 -2 1 -1 1 0 1 -1 -1 -1 1 -1 0 -2 0 -2 -3 1 -1 0 1 1 0 0 4 3 0 2 1 0 0
  -1 0 -2 1 -1 1 1 2 -1 -1 -1 2 -3 -1 -4 0 -2 -4 3 0 0 0 1 1 0 4 3 1 2 0 -2 1
  -2 0 -2 1 0 0 0 1 -1 -1 -1 1 -1 0 -2 0 -2 -3 1 -1 0 1 1 0 0 4 3 0 2 1 0 0
  -1 0 -2 1 -1 1 1 1 0 0 0 1 -2 -1 -2 -1 -2 -3 1 0 1 0 1 1 0 2 2 0 2 0 -1 1
  -2 0 -1 0 -1 1 1 1 0 -1 -1 1 -2 0 -2 0 -2 -3 1 0 0 1 0 0 0 3 3 0 2 1 -1 1
  -2 0 -2 1 0 0 0 1 -1 -1 -1 1 -1 0 -2 0 -2 -3 1 -1 0 1 1 -1 0 4 3 0 2 1 0 0
  -2 -1 -2 1 -1 1 2 2 -1 0 -2 2 -2 0 -3 0 -3 -3 1 0 -1 2 1 0 0 5 2 -1 2 1 0 0
  -1 0 -2 1 0 0 0 2 0 -1 -1 1 -2 -1 -3 0 -1 -3 2 0 0 0 1 0 0 3 3 1 1 0 -1 1
  -1 0 -1 -1 0 -1 1 -1 0 0 1 1 0 -1 0 0 -1 -1 1 -1 1 -1 1 0 1 0 1 0 1 0 0 1
  0 0 -1 0 0 0 1 0 0 0 0 0 0 -1 0 0 -1 0 0 0 1 1 0 0 -1 1 0 -1 1 0 0 0
  -1 0 -1 1 0 1 0 1 0 0 -1 0 -1 0 -1 0 -1 -1 0 0 -1 1 0 0 -1 2 1 0 1 1 0 0
  -1 0 -1 0 0 0 1 1 0 0 0 1 -1 -1 -1 0 -1 -1 1 0 0 0 0 0 0 1 1 0 1 0 -1 1
  0 0 -1 0 0 0 1 1 0 0 0 1 -1 -1 -2 0 -1 -1 1 0 0 0 0 0 0 1 1 0 1 0 -1 1
  0 0 -1 1 0 1 1 1 0 0 0 0 -1 -1 -1 0 -1 -1 0 0 0 1 0 1 -1 1 0 0 1 0 -1 0
  -1 0 -1 0 0 0 1 1 0 -1 -1 1 -2 -1 -1 1 -1 -2 1 0 0 1 0 0 -1 2 2 0 2 0 -1 1
  0 0 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 -1 -1 0 0 0 2 1 0 1 0 1 0 -1 -1 0 -1 0 0 0 0 1 0 0 0 1 -1 -1 0 0 0 0
  -2 -1 -2 0 -1 0 2 1 -2 0 -1 2 -1 0 -3 0 -3 -3 2 -1 0 1 1 0 1 5 3 -1 2 1 0 0
  -1 0 -2 1 -1 1 1 1 0 -1 -1 1 -2 -1 -2 0 -2 -3 1 0 1 1 1 1 -1 3 2 0 2 0 -1 1
  -1 0 -1 0 -1 1 2 1 -1 0 -1 1 -1 0 -2 0 -2 -2 1 -1 0 2 0 0 0 3 1 -1 2 1 -1 0
  -1 0 0 -1 0 0 1 0 0 0 0 1 0 0 0 0 -1 0 0 -1 0 1 0 -1 0 1 0 -1 1 1 0 0
  -1 0 -1 0 0 0 1 1 0 0 0 1 -1 -1 -1 0 -1 -1 1 0 0 0 0 0 0 1 1 0 1 0 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 0 0
  -1 -1 -1 0 0 0 2 1 -1 0 -1 1 -1 0 -2 0 -2 -2 1 0 0 1 0 0 0 3 2 -1 1 1 0 0
  32
  -2 0 -2 1 -1 1 1 1 -1 0 -1 1 -1 0 -2 -1 -2 -3 1 -1 0 1 1 1 0 3 2 0 2 1 0 0
  -1 0 -1 1 0 1 0 1 0 0 -1 0 -1 0 -1 0 -1 -1 0 0 0 1 0 0 -1 2 1 0 1 1 0 0
  -1 0 0 0 0 0 0 1 0 -1 -1 1 -1 0 -1 1 -1 -1 1 0 -1 1 0 -1 0 2 1 0 1 0 0 0
  -1 1 0 0 0 0 -1 0 0 -1 0 0 -1 0 0 0 0 -1 1 0 0 -1 0 0 0 0 2 1 1 0 0 1
  0 0 -1 1 0 0 0 1 -1 0 -1 0 0 0 -2 0 -1 -1 1 0 0 1 0 0 0 2 1 0 0 0 0 0
  1 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0 1 1 0 0 0 1 -1 0 0 -1 -1 0 -1 0 0 0
  -1 0 -1 0 0 0 1 1 0 0 0 1 -1 -1 -1 0 -1 -1 1 0 0 0 0 0 0 1 1 0 1 0 0 1
  0 0 1 0 0 1 0 0 0 0 -1 -1 1 1 1 0 0 1 -2 0 -1 2 -1 0 -1 0 -1 -1 0 1 1 -1
  0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0
  -1 0 1 0 0 0 -1 0 0 -1 -1 0 0 1 1 1 0 0 -1 0 -1 1 0 -1 0 1 0 0 0 1 1 -1
  1 1 2 -1 0 0 0 -1 1 0 1 -1 1 0 2 0 1 2 -1 0 0 0 -1 0 0 -3 -2 0 -1 0 0 0
  0 0 -1 2 0 1 -1 1 0 0 -1 -1 -1 0 -1 0 0 -1 0 1 0 0 0 1 -1 1 1 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 0 0 0 0 0 0 0 1 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 0 0 0
  -1 0 0 0 0 0 -1 0 -1 -1 -1 0 0 1 0 0 0 -1 0 0 -1 0 0 0 0 1 2 1 0 1 1 0
  1 1 2 -1 0 0 -1 -1 1 0 1 -1 1 0 2 0 2 2 -1 0 0 0 -1 0 0 -3 -2 0 -1 0 0 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
  -1 0 -1 0 0 1 1 0 0 1 0 0 0 0 0 -1 -1 0 0 0 0 1 0 0 0 1 0 -1 1 0 0 0
  -1 0 0 -1 0 0 1 0 -1 0 -1 1 0 1 -1 0 -1 -1 1 -1 -1 1 0 -1 1 2 1 -1 1 1 0 0
  -1 0 -1 0 -1 1 1 1 -1 0 -1 1 -1 1 -2 -1 -2 -2 1 0 0 1 0 0 0 3 2 -1 1 1 0 0
  1 0 1 1 0 1 -1 1 0 0 -1 -1 0 1 0 0 1 1 -1 1 -1 1 -1 0 -1 0 -1 0 -1 0 0 -1
  -2 0 -1 1 -1 1 0 2 -1 -1 -2 1 -2 1 -2 0 -2 -3 1 0 -1 1 1 0 0 4 3 0 1 1 0 0
  -1 0 0 -1 0 0 1 1 0 0 0 1 0 0 -1 0 -1 0 1 0 -1 1 0 -1 1 1 0 -1 0 0 0 0
  0 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
  -1 0 -1 1 -1 1 0 1 -1 0 -1 0 -1 1 -1 -1 -1 -2 0 0 0 1 0 1 -1 2 2 0 1 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 0 0 1 0 0 0 0
  -1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
  -2 -1 -2 1 -1 1 2 2 -1 0 -2 2 -2 0 -3 0 -3 -3 1 0 -1 2 1 0 0 5 2 -1 2 1 0 0
  -2 0 -2 0 -1 1 2 1 -1 0 -1 2 -1 0 -2 -1 -3 -3 1 -1 0 2 1 0 0 4 2 -2 3 1 0 0
  0 0 1 0 0 1 0 0 0 1 0 -1 1 1 0 -1 0 1 -1 0 -1 1 -1 0 0 0 -1 -1 0 1 0 -1
  -1 0 -1 0 -1 1 2 1 -1 0 -1 1 -1 0 -2 0 -2 -2 1 -1 0 2 0 0 0 3 1 -1 2 1 -1 0
  0 1 0 0 0 0 -1 0 0 -1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 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