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 Di 9. Jun 19:14:44 CEST 2020

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DET
BASIS
GRAM
DIVISORS
MINIMAL_NORM
MINVECS
KISSING_NUMBER
DENSITY
HERMITE_NUMBER
GROUP_ORDER
GROUP_NAME
GROUP_GENERATORS
REFERENCES
LAST_LINE (required)

• NAME
  Fi_{22}-invariant lattice I
  

• DIMENSION
  78
  

• DET
  2^{312}
  

• BASIS
  78 78
  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 9
  0 2 0 0 0 2 0 0 0 2 0 2 0 0 0 2 0 0 0 0 0 6 0 0 0 2 0 2 0 0 0 2 0 0 0 0 0 6 0 2 0 0 0 0 2 0 2 2 2 0 0 0 2 0 4 0 0 6 4 4 0 2 2 2 0 0 6 2 2 2 6 0 4 2 6 4 0 14
  0 0 2 0 0 2 0 0 0 0 0 2 0 2 0 2 0 2 2 2 2 6 0 0 0 0 0 2 0 2 0 2 0 2 2 2 2 6 0 0 0 0 0 0 0 0 0 0 2 2 0 0 2 2 6 2 2 6 6 6 0 2 0 0 0 0 4 0 0 0 6 0 4 2 4 4 0 6
  0 0 0 2 0 2 0 0 0 0 0 2 0 2 0 2 2 0 0 0 2 2 0 0 0 0 0 2 0 2 0 2 2 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 4 0 0 0 6 6 0 0 0 0 0 0 6 2 6 6 2 0 6 0 4 4 0 12
  0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 2 2 0 0 2 6 0 0 0 0 0 0 0 0 0 0 2 2 0 0 2 6 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 4 0 0 4 6 2 0 0 0 0 0 4 4 0 6 2 6 6 4 0 0 0 0 0
  0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 4 0 0 4 0 0 0 0 0 0 4 0 0 4 4 4 4 0 4 0 0 4 12
  0 0 0 0 0 0 2 0 0 2 0 2 0 2 0 0 0 0 2 2 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 2 0 0 2 2 2 2 2 2 0 6 0 2 2 2 6 2 0 0 2 2 2 2 0 0 0 2 2 0 6 4 0 0 4
  0 0 0 0 0 0 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 0 2 2 0 0 2 2 2 6 2 0 2 0 0 6 4 2 2 0 0 0 2 6 4 0 4 4 2 4 4 6 6 6 6 4
  0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 2 0 2 0 2 2 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 2 2 2 2 2 2 2 2 0 6 4 2 0 2 2 2 2 4 6 0 2 0 0 0 6 4 2 6 4 6
  0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 4 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 0 4 0 0 0 0 0 0 0 4 0 0 0 0 0 4 4 0 4 0 4 0
  0 0 0 0 0 0 0 0 0 0 2 2 0 0 0 2 2 0 2 0 2 4 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 0 0 6 0 2 2 0 2 4 4 2 2 0 0 0 0 2 4 0 0 0 4 6 4 0 4 4 0 10
  0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 4 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 4 0 0 4 4 0 4 0 0 2 2 2 2 2 6 2 2 2 6 2 2 2 6 0 0 6 10
  0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 2 2 0 0 2 0 6 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 2 4 0 2 6 4 0 6 2 4 2 2 2 2 0 2 0 2 4 6 6 2 2 0 0 0 2 14
  0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 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 4 0 0 0 0 0 0 4 0 0 0 0 0 0 4 4 0 4 4 4 4 0 4 4 4 0 12
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 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 2 2 2 2 2 2 2 0 4 4 0 2 0 2 0 0 2 0 2 4 4 2 2 4 4 0 0 2 10
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 4 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 4 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 4 4 4 4 8
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 4 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 4 0 0 0 4 0 0 4 4 0 0 0 0 0 4 0 0 0 4 0 4 0 4 0 0 4 4
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 4 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 4 0 0 4 0 0 4 0 4 2 2 2 2 2 2 2 2 2 2 2 6 6 6 0 0 6 10
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 4 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 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 4 4 4 4 4 4 12
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 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 4 4 0 4 0 4 0 0 0 0 0 0 0 0 4 0 4 0 0 4 4 4 4 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 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 4 4 0 4 0 4 2 2 2 2 2 6 2 2 6 2 6 6 6 2 0 0 2 6
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 2 0 2 0 0 0 0 2 2 0 4 0 2 0 2 0 2 2 0 0 2 2 2 0 4 2 0 2 4 2 2 4 4 2 2 0 2 0 4 6 0 6 6 6 2 4 6 4 6 4 14
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 0 2 2 2 2 2 2 0 4 2 0 6 0 0 6 0 6 0 2 2 2 0 4 2 2 2 2 6 4 0 6 6 2 4 10
  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 2 0 0 0 0 0 2 0 2 0 2 2 4 0 0 0 0 0 2 2 0 0 2 2 2 2 2 2 2 6 6 0 6 2 4 0 2 2 2 0 6 0 2 4 2 0 4 6 0 2 4 0 2
  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 4 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 4 0 4 0 0 0 4 4 4 0 0 12
  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 2 0 0 0 2 2 0 2 0 2 4 0 0 0 0 0 0 0 0 0 0 2 0 2 4 0 2 0 2 2 4 6 0 0 2 0 0 2 0 0 0 4 0 4 2 4 4 4 4 6 4
  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 4 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 4 4 4 2 2 2 2 2 6 6 2 2 2 6 2 6 6 0 0 2 6
  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 2 2 0 2 2 0 0 2 0 6 0 0 0 0 0 0 0 0 0 0 0 2 0 6 0 2 0 2 0 6 0 6 2 2 2 2 2 0 6 0 2 4 6 6 2 4 0 0 6 10
  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 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 4 0 0 0 0 0 0 4 0 0 4 0 4 0 0 0 4 4 4 8
  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 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 0 4 0 4 2 2 0 2 2 0 2 0 4 4 2 2 4 4 0 0 2 8
  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 4 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 4 0 0 4 4 0 0 0 0 0 0 0 0 4 4 4 0 0 0 4 4 4 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 4 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 4 0 0 0 0 0 0 0 0 0 4 0 0 4 0 0 4 0 4 0 0 4 12
  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 4 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 4 0 0 4 0 4 2 2 2 2 2 2 2 2 6 6 2 6 6 6 0 0 6 2
  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 4 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 4 4 4 4 4 4 4
  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 0 4 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0 4 0 4 0 0 4 4 4 4 8
  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 0 0 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 0 4 4 0 2 2 2 2 2 6 2 2 6 2 6 6 6 2 0 0 2 6
  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 0 0 0 8 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 0 0 0 0 0 8
  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 0 0 0 0 2 2 0 0 0 2 2 2 0 0 2 2 0 0 0 0 2 6 2 2 4 4 0 0 2 2 2 2 0 0 4 0 4 4 0 0 0 6 4 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 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 4 4 4 2 2 2 2 2 2 6 2 2 2 6 6 2 2 0 4 2 14
  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 0 0 0 0 0 0 2 2 0 2 0 0 2 2 0 0 2 2 0 0 6 2 0 0 6 6 2 2 2 2 2 2 6 2 6 6 0 0 4 4 0 6 2 14
  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 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 4 0 0 0 0 0 0 0 0 0 0 0 4 0 0 4 0 4 0 8
  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 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 4 4 0 2 2 2 2 2 2 2 4 4 0 0 4 4 2 2 0 10
  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 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 4 4 0 4 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 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 4 0 0 0 4 0 4 4 0 0 0 0 0 0 4 0 0 0 0 0 4 0 0 4 0 4 12
  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 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 4 0 0 4 0 0 4 0 4 2 2 2 2 2 6 2 2 2 2 2 6 2 2 4 0 6 14
  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 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 4 0 0 0 4 0 0 4 4 0 0 0 0 0 0 0 0 0 0 0 0 4 4 0 4 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 4 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 0 4 0 8
  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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 4 0 0 4 4 0 4 0 4 2 2 2 2 2 6 2 2 2 6 2 2 6 2 4 4 2 6
  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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 0 0 0 0 0 4 4 0 0 0 0 0 0 4 0 0 0 4 4 4 0 4 4 4 0 4
  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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 0 0 4 4 0 0 4 4 0 0 0 0 0 0 0 0 0 0 4 4 4 4 0 0 0 8
  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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 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 8
  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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 0 0 0 4 4 2 2 2 2 2 2 2 2 6 2 6 2 2 6 4 4 6 10
  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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 0 0 4 4 0 0 0 0 0 0 0 0 4 0 4 0 0 4 4 4 4 8
  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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
  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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
  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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 4 4 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 2 2
  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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
  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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
  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 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 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
  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 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 4 0 0 0 0 0 0 0 4 4 4 4 4 4 0 0 4 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 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 4 0 0 0 0 4 0 4 0 4 0 4 0 0 0 4 8
  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 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 4 0 0 4 0 0 0 4 0 4 4 0 0 0 4 8
  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 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 4 0 4 4 0 0 0 0 0 4 4 0 0 0 12
  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 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 4 4 4 0 0 4 4 0 4 0 0 0 4 4
  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 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 8 0 0 0 0 0 0 0 0 0 0 0 8
  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 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 8 0 0 0 0 0 0 0 0 0 0 8
  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 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 4 4 0 0 4 0 4 0 0 4 12
  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 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 8 0 0 0 0 0 0 0 0 8
  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 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 0 8 0 0 0 0 0 0 0 8
  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 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 0 0 8 0 0 0 0 0 0 8
  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 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 0 0 0 8 0 0 0 0 0 8
  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 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 0 0 0 0 8 0 0 0 0 8
  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 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 0 0 0 0 0 8 0 0 0 8
  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 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 0 0 0 0 0 0 8 0 0 8
  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 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 0 0 0 0 0 0 0 8 0 8
  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 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 0 0 0 0 0 0 0 0 8 8
  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 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 0 0 0 0 0 0 0 0 0 16
  
  

• GRAM
  78 78
  158 224 160 192 80 160 112 144 144 32 160 160 208 160 160 112 80 160 144 48 128 80 240 192 112 144 112 128 176 112 144 48 144 96 80 112 128 80 64 192 208 96 160 32 144 192 32 96 128 80 112 80 160 112 80 80 64 80 80 80 32 96 96 128 64 80 80 128 80 80 80 80 80 80 80 80 80 144
  224 576 416 416 240 288 240 304 320 96 336 288 400 320 272 224 128 304 256 160 272 160 480 400 240 304 240 304 352 224 256 144 208 208 160 256 272 160 128 400 400 176 288 80 240 336 80 176 272 176 208 112 336 224 144 112 144 160 144 144 64 192 144 224 128 112 160 192 128 128 160 112 144 128 160 144 112 224
  160 416 448 320 256 192 224 256 272 80 272 192 304 208 208 160 112 224 160 176 224 96 352 304 240 176 224 240 272 160 208 144 112 176 144 192 224 96 144 272 272 128 192 96 144 208 96 112 208 144 176 48 240 176 96 64 128 96 96 96 48 112 64 112 80 48 80 80 48 48 96 48 80 64 80 80 48 96
  192 416 320 480 224 256 176 272 256 48 288 240 352 304 256 192 144 256 208 112 240 112 432 288 208 240 208 256 288 208 240 160 192 208 128 192 240 112 112 336 432 144 288 64 192 288 96 160 256 144 208 112 304 208 128 96 128 96 144 144 80 176 144 192 128 96 144 176 144 144 112 96 144 96 128 128 96 192
  80 240 256 224 352 192 128 224 176 96 208 160 224 176 160 96 128 192 80 112 240 48 240 192 208 112 176 224 224 128 144 128 112 224 96 112 256 48 128 192 176 48 112 80 96 160 64 48 160 128 128 32 160 80 32 0 112 32 48 16 96 80 64 48 80 32 32 48 48 16 48 48 32 0 0 0 0 0
  160 288 192 256 192 352 128 224 176 64 224 288 320 288 240 176 192 256 224 96 224 128 368 256 144 208 192 224 288 208 192 128 272 192 144 192 240 128 112 272 288 160 208 64 240 288 64 128 192 160 192 128 256 192 96 128 96 96 128 96 96 144 160 176 112 128 96 208 128 128 128 128 96 128 96 96 128 192
  112 240 224 176 128 128 256 224 176 64 176 176 208 160 144 128 112 192 128 128 160 64 240 256 144 112 112 160 176 80 144 64 96 144 96 96 128 32 96 192 208 80 160 64 112 192 64 96 160 112 144 48 192 112 80 32 96 48 48 80 48 48 48 96 48 48 48 80 32 32 48 48 32 80 64 32 32 64
  144 304 256 272 224 224 224 448 320 144 272 288 272 272 240 208 176 288 208 176 240 48 400 336 240 192 256 272 288 192 208 160 176 272 176 192 240 32 176 272 304 112 224 96 208 304 112 128 288 224 160 80 288 176 48 32 144 80 64 48 128 112 128 128 128 80 64 128 64 64 48 64 64 80 80 80 80 64
  144 320 272 256 176 176 176 320 352 112 240 240 256 208 224 176 128 256 192 144 224 80 336 256 224 192 208 240 240 144 192 96 144 192 144 160 208 48 144 256 304 112 224 80 176 240 112 128 240 144 144 64 240 160 64 64 128 96 80 64 64 128 112 160 112 80 96 112 64 48 48 48 96 80 64 96 80 96
  32 96 80 48 96 64 64 144 112 128 96 96 80 64 64 80 64 112 96 64 112 32 80 96 96 64 80 80 80 48 48 32 48 96 80 48 96 0 48 64 32 0 32 32 80 112 16 16 96 64 32 0 64 32 0 0 48 32 0 0 48 32 64 32 48 32 0 32 0 0 0 32 32 0 32 0 32 0
  160 336 272 288 208 224 176 272 240 96 352 224 304 272 224 208 144 256 224 96 224 112 336 272 176 192 192 224 272 176 176 96 176 160 128 160 208 80 112 304 272 128 192 80 224 288 80 144 224 176 192 128 224 160 96 80 112 112 112 96 64 128 128 160 96 96 112 144 80 80 112 128 112 80 112 112 80 160
  160 288 192 240 160 288 176 288 240 96 224 384 352 256 256 192 192 320 224 128 272 112 368 304 192 208 176 256 304 160 224 96 240 256 160 160 256 80 112 288 320 128 224 80 224 336 64 144 272 160 176 112 272 160 112 112 128 112 80 80 112 144 176 192 144 128 96 192 96 128 96 96 96 128 80 80 128 160
  208 400 304 352 224 320 208 272 256 80 304 352 512 304 320 208 192 336 224 160 320 160 416 352 240 224 192 256 352 192 272 128 240 240 128 192 288 112 144 368 384 160 272 80 256 368 64 160 288 176 240 144 304 208 160 144 144 160 128 144 96 176 176 192 128 128 112 208 144 160 160 128 128 112 112 112 128 224
  160 320 208 304 176 288 160 272 208 64 272 256 304 352 224 192 160 240 240 96 208 128 384 272 128 224 176 224 256 208 176 112 224 160 128 192 208 96 96 304 320 160 224 64 224 288 64 144 208 192 176 128 272 192 96 96 96 96 128 96 80 144 144 192 112 128 128 192 128 128 128 128 96 128 128 128 96 192
  160 272 208 256 160 240 144 240 224 64 224 256 320 224 288 160 144 256 192 96 224 96 320 240 176 192 176 208 240 144 208 80 192 192 112 160 224 80 96 256 288 128 224 64 192 256 64 128 208 144 176 96 240 160 96 96 112 112 112 80 96 128 144 160 96 96 80 176 112 112 96 96 112 112 80 80 96 160
  112 224 160 192 96 176 128 208 176 80 208 192 208 192 160 224 112 224 208 96 144 96 240 208 112 144 144 128 176 128 128 64 160 144 144 128 128 64 64 192 208 96 144 80 160 224 64 144 160 112 144 96 192 128 96 64 48 64 64 64 64 96 112 128 64 64 64 144 64 64 64 96 96 96 96 96 96 128
  80 128 112 144 128 192 112 176 128 64 144 192 192 160 144 112 192 176 128 80 144 64 208 160 112 80 112 144 176 96 112 96 144 144 96 80 128 32 96 144 176 80 128 48 144 176 80 64 144 112 128 64 144 112 32 64 80 32 64 64 64 48 96 80 64 64 32 96 32 64 32 64 32 64 32 32 64 64
  160 304 224 256 192 256 192 288 256 112 256 320 336 240 256 224 176 384 240 128 288 112 352 320 192 208 192 272 336 144 240 80 224 288 160 160 256 80 112 320 320 112 224 96 208 352 80 160 256 144 208 112 288 160 112 80 144 112 80 112 128 160 176 192 128 96 96 208 96 96 96 128 128 128 80 80 128 160
  144 256 160 208 80 224 128 208 192 96 224 224 224 240 192 208 128 240 288 80 176 128 288 224 112 208 144 160 192 160 144 48 208 128 160 160 160 96 64 240 240 128 176 64 208 272 48 144 176 128 144 96 224 160 96 96 64 96 96 96 64 128 160 192 96 128 96 192 96 96 96 128 128 128 128 128 128 192
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• REFERENCES
  Bernd Schroeder, Konstruktionen und Darstellungen der Fischer-Gruppe Fi22, thesis, University Essen, dissertation.de-Verlag, Berlin, 1999.
  Bernd Schroeder's hompage
  Bernd Schroeder, Invariant lattices of the sporadic simple group Fi22, to appear.
  

• LAST_LINE (required)
  
  
  

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  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe