The Lattice Sp4(4)D8.4
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 13:08:40 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
GRAM
DET
MINIMAL_NORM
KISSING_NUMBER
HERMITE_NUMBER
GROUP_ORDER
GROUP_GENERATORS
PROPERTIES
NOTES
LAST_LINE
-
NAME
Sp4(4)D8.4
-
DIMENSION
36
-
GRAM
36 36
4 -1 1 1 -2 -2 -2 -2 -1 0 -1 1 -2 -2 -1 -1 -1 -2 -1 -1 1 1 -1 -2 1 1 -1 -1 -1 -2 0 1 -2 -1 -1 -2
-1 4 -2 -2 2 2 -1 -1 -1 -1 2 1 1 -1 -1 -1 2 0 2 0 -2 1 -1 -1 -1 -2 0 2 2 1 1 -2 2 2 0 -1
1 -2 4 0 -2 -2 1 1 1 1 -2 0 0 0 1 -1 0 1 -2 -1 2 1 1 0 2 1 -1 0 -1 -1 -1 0 -1 0 1 0
1 -2 0 4 -2 -2 1 1 -1 -1 0 0 -2 -1 1 2 -2 -2 0 1 2 -1 -1 0 0 2 -1 -1 0 -1 -1 2 -2 -2 -1 1
-2 2 -2 -2 5 1 -1 1 0 0 0 -1 1 0 0 0 0 1 2 -1 -1 0 -1 0 0 -2 2 1 0 2 2 -1 2 2 1 -1
-2 2 -2 -2 1 5 -1 -1 1 -1 1 1 1 2 0 -1 2 1 0 1 -2 -1 1 1 -1 -2 0 0 1 2 0 -2 2 0 0 1
-2 -1 1 1 -1 -1 5 1 0 1 0 -1 2 1 1 2 -1 0 -1 1 1 0 0 2 -1 0 0 0 1 -1 -1 0 -1 1 0 1
-2 -1 1 1 1 -1 1 5 0 -1 0 -1 0 0 1 1 -1 1 1 0 2 -1 0 1 1 1 1 1 0 1 -1 0 1 -1 1 1
-1 -1 1 -1 0 1 0 0 4 0 -1 0 1 2 1 -1 1 2 -1 -1 -1 -1 2 1 0 -1 0 -1 -2 0 -1 -1 0 -1 1 2
0 -1 1 -1 0 -1 1 -1 0 4 -1 -2 0 1 0 1 0 1 -1 0 -1 0 1 0 0 0 1 -1 -1 0 1 1 0 2 1 -1
-1 2 -2 0 0 1 0 0 -1 -1 4 1 1 0 -1 1 1 0 2 1 -1 -1 0 0 -1 0 0 1 2 1 0 0 1 0 0 1
1 1 0 0 -1 1 -1 -1 0 -2 1 4 1 0 -1 -2 0 0 0 -1 1 1 0 0 0 -1 -1 1 0 0 0 -1 -1 0 0 1
-2 1 0 -2 1 1 2 0 1 0 1 1 5 1 -1 -1 0 1 0 0 0 1 1 2 -1 -2 1 1 0 1 0 -2 0 1 1 1
-2 -1 0 -1 0 2 1 0 2 1 0 0 1 5 0 1 0 3 -1 0 -1 -1 2 2 -1 0 0 0 -1 1 0 0 0 1 1 3
-1 -1 1 1 0 0 1 1 1 0 -1 -1 -1 0 4 0 1 1 0 0 1 -1 0 1 1 0 -1 -1 1 1 0 1 0 0 1 1
-1 -1 -1 2 0 -1 2 1 -1 1 1 -2 -1 1 0 5 -2 -1 0 2 0 -2 0 0 -1 1 0 0 0 0 0 1 0 0 0 1
-1 2 0 -2 0 2 -1 -1 1 0 1 0 0 0 1 -2 5 2 1 0 -2 0 1 0 0 0 -1 1 2 1 0 -1 2 1 0 0
-2 0 1 -2 1 1 0 1 2 1 0 0 1 3 1 -1 2 5 0 -1 -1 0 2 1 0 0 0 1 0 2 1 0 1 2 2 2
-1 2 -2 0 2 0 -1 1 -1 -1 2 0 0 -1 0 0 1 0 4 0 -1 0 -1 0 -1 0 1 1 1 1 1 0 1 1 0 0
-1 0 -1 1 -1 1 1 0 -1 0 1 -1 0 0 0 2 0 -1 0 4 -1 -1 1 0 -1 1 0 0 1 1 0 0 1 -1 -1 1
1 -2 2 2 -1 -2 1 2 -1 -1 -1 1 0 -1 1 0 -2 -1 -1 -1 5 0 -1 1 2 1 -1 0 0 0 -1 1 -2 -1 0 0
1 1 1 -1 0 -1 0 -1 -1 0 -1 1 1 -1 -1 -2 0 0 0 -1 0 4 -1 -1 0 0 0 1 0 -1 1 -1 -1 2 0 -1
-1 -1 1 -1 -1 1 0 0 2 1 0 0 1 2 0 0 1 2 -1 1 -1 -1 4 1 0 0 0 0 -1 1 0 0 1 -1 1 2
-2 -1 0 0 0 1 2 1 1 0 0 0 2 2 1 0 0 1 0 0 1 -1 1 4 -1 0 0 0 0 1 -1 0 0 0 0 2
1 -1 2 0 0 -1 -1 1 0 0 -1 0 -1 -1 1 -1 0 0 -1 -1 2 0 0 -1 4 1 0 0 0 0 0 1 0 -1 1 -1
1 -2 1 2 -2 -2 0 1 -1 0 0 -1 -2 0 0 1 0 0 0 1 1 0 0 0 1 5 -1 0 0 -1 -1 2 -1 -1 -1 1
-1 0 -1 -1 2 0 0 1 0 1 0 -1 1 0 -1 0 -1 0 1 0 -1 0 0 0 0 -1 4 -1 -1 0 1 0 1 0 0 -1
-1 2 0 -1 1 0 0 1 -1 -1 1 1 1 0 -1 0 1 1 1 0 0 1 0 0 0 0 -1 5 1 1 1 -1 1 2 1 0
-1 2 -1 0 0 1 1 0 -2 -1 2 0 0 -1 1 0 2 0 1 1 0 0 -1 0 0 0 -1 1 5 1 0 0 1 1 -1 -1
-2 1 -1 -1 2 2 -1 1 0 0 1 0 1 1 1 0 1 2 1 1 0 -1 1 1 0 -1 0 1 1 5 1 0 2 1 1 1
0 1 -1 -1 2 0 -1 -1 -1 1 0 0 0 0 0 0 0 1 1 0 -1 1 0 -1 0 -1 1 1 0 1 4 1 0 2 1 -1
1 -2 0 2 -1 -2 0 0 -1 1 0 -1 -2 0 1 1 -1 0 0 0 1 -1 0 0 1 2 0 -1 0 0 1 5 -1 -1 0 0
-2 2 -1 -2 2 2 -1 1 0 0 1 -1 0 0 0 0 2 1 1 1 -2 -1 1 0 0 -1 1 1 1 2 0 -1 5 0 0 0
-1 2 0 -2 2 0 1 -1 -1 2 0 0 1 1 0 0 1 2 1 -1 -1 2 -1 0 -1 -1 0 2 1 1 2 -1 0 6 1 -1
-1 0 1 -1 1 0 0 1 1 1 0 0 1 1 1 0 0 2 0 -1 0 0 1 0 1 -1 0 1 -1 1 1 0 0 1 4 1
-2 -1 0 1 -1 1 1 1 2 -1 1 1 1 3 1 1 0 2 0 1 0 -1 2 2 -1 1 -1 0 -1 1 -1 0 0 -1 1 6
-
DET
1
-
MINIMAL_NORM
4
-
KISSING_NUMBER
42840
-
HERMITE_NUMBER
4
-
GROUP_ORDER
2^13 * 3^2 * 5^2 * 17
-
GROUP_GENERATORS
3
36
1 -2 0 1 -2 3 3 -2 3 0 0 -3 -1 -2 -3 -2 -2 0 3 -2 2 -1 0 -1 0 1 0 1 1 1 2 -1 2 1 1 1
1 1 -1 0 1 -2 0 1 -2 -1 -1 1 0 1 0 1 2 1 -1 1 -1 0 0 1 1 -1 0 -1 -1 0 -1 0 -1 0 0 0
2 0 0 1 -1 2 1 0 2 0 0 -2 0 -1 -2 -1 -1 0 1 0 1 0 0 0 0 0 0 0 1 0 1 0 1 1 1 1
-1 -2 1 0 0 2 1 -1 2 1 1 0 -1 -1 -1 -1 -1 -1 1 -1 1 0 0 -1 -1 1 0 1 1 0 1 0 1 0 0 0
-4 0 -2 -2 1 -5 -6 2 -4 1 0 4 2 2 4 3 2 2 -2 4 -2 2 -1 2 2 -3 -2 -1 -2 -3 -3 1 -2 -1 -2 -2
0 2 2 -1 2 -2 -1 1 -2 -1 -1 2 0 1 1 2 2 -1 -2 0 -2 0 0 1 -1 0 1 -1 0 1 -1 1 -2 -1 0 0
0 0 1 0 1 1 0 -1 0 1 0 1 0 0 1 0 -1 0 0 0 0 0 0 -1 -1 1 1 1 1 0 -1 0 0 -1 0 0
0 2 -2 0 1 -3 -3 3 -1 1 1 2 1 2 2 1 2 0 -3 3 -1 2 0 2 1 -2 -1 -1 -1 -2 -1 1 -1 0 -1 -1
-5 -1 3 -1 0 0 -2 -2 -1 0 1 0 -1 -1 0 0 -1 0 0 0 0 0 -1 0 -1 0 0 0 0 0 0 0 -1 -1 0 0
2 -1 -2 0 -1 1 1 1 1 0 0 -1 1 0 0 -1 -1 0 1 0 0 0 0 -1 1 0 -1 0 0 0 0 0 1 1 0 0
3 4 -1 0 1 -2 2 2 -1 -1 -1 1 0 2 1 0 2 -1 -2 0 -1 -1 1 0 0 1 1 -1 -1 1 0 0 -1 0 0 0
3 1 -1 -1 0 0 2 1 2 0 -1 0 -1 0 -1 0 1 -1 0 0 1 0 0 0 -1 1 1 0 1 1 1 0 0 0 1 1
2 3 -1 -1 1 -2 -1 2 -1 1 -1 2 1 2 3 1 1 -1 -2 1 -1 0 0 0 -1 1 1 0 0 0 -1 0 -1 -1 0 0
3 2 0 0 2 0 0 2 0 0 1 0 0 1 2 0 1 -1 -2 1 0 1 1 0 -1 0 1 0 0 0 -1 1 -1 0 0 0
-6 -1 4 -1 0 0 -4 -2 -2 0 0 2 1 -1 1 2 -1 1 0 0 -1 0 -1 0 -1 0 0 0 0 -1 -1 1 -1 -1 -1 -1
1 0 -2 -1 2 -1 0 2 -1 1 1 2 0 1 2 0 1 0 -1 2 -1 1 1 0 1 -1 -1 0 -1 -1 -2 1 -1 0 -1 -1
-2 1 3 1 -2 0 1 -2 -2 -4 -2 -2 0 -1 -3 0 0 0 0 -3 -1 -3 0 0 0 1 1 -2 0 2 2 -1 0 1 1 1
0 1 0 1 -1 0 -1 1 0 -1 0 -1 1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 1 0 0
-1 2 -1 0 0 -3 -2 1 -3 -1 0 1 1 2 2 1 2 1 -2 1 -1 0 0 1 1 -1 0 -1 -2 -1 -1 0 -1 0 -1 -1
0 0 2 1 1 1 1 -1 -1 -1 0 0 0 0 0 0 0 -1 0 -2 -1 -1 1 -1 -1 1 1 0 0 1 0 0 0 0 0 0
3 2 -2 -1 0 -1 -1 3 2 2 -1 2 1 1 1 1 1 -1 -1 2 0 1 0 1 0 0 0 0 1 -1 0 1 0 0 0 0
3 -2 -1 2 -1 3 2 -1 2 0 0 -3 0 -1 -2 -1 -1 1 2 -1 2 0 0 -1 0 0 0 1 1 0 1 -1 2 1 1 1
2 2 -1 -1 0 -1 1 2 -1 -1 0 0 0 1 1 0 1 -1 -1 0 -1 0 1 0 0 0 0 -1 -1 1 0 0 -1 0 0 0
-1 3 0 -2 1 -3 -4 2 -1 1 0 3 1 2 4 2 1 -1 -3 2 -1 1 0 1 -1 0 1 0 0 -1 -2 1 -2 -1 -1 -1
3 2 -2 -1 0 -1 0 3 1 1 -1 1 1 1 0 1 1 0 0 2 0 1 0 1 1 -1 -1 -1 0 -1 0 1 0 0 0 0
2 0 1 3 -2 3 3 -1 2 -2 0 -4 0 -1 -3 -2 -1 -1 1 -3 1 -2 1 -1 0 1 1 0 1 1 3 -1 2 2 1 1
-2 0 -2 -1 -1 -2 -2 0 -1 1 0 1 1 1 2 1 0 1 0 1 0 1 -1 0 1 -1 -1 0 -1 -1 -1 0 0 -1 -1 -1
3 1 -2 0 2 -2 0 2 -1 -1 1 0 -1 1 0 0 2 1 -2 3 0 1 1 2 1 -2 0 -1 -1 -1 -1 0 -1 1 0 0
2 3 0 1 0 -1 1 1 -1 -1 -2 1 1 1 0 1 1 0 -1 -1 -1 -1 1 0 0 1 1 -1 0 1 0 0 0 0 0 0
0 3 -2 -2 2 -5 -5 5 -1 1 0 5 2 3 4 3 3 -1 -4 4 -2 2 0 2 0 -1 -1 -2 -1 -2 -2 2 -2 0 -1 -2
0 -1 -1 0 0 0 -1 0 -1 0 0 0 1 0 1 1 0 2 1 1 0 1 0 0 1 -1 -1 0 -1 -1 -1 0 0 0 -1 -1
1 1 0 0 -1 1 1 0 2 0 0 0 0 0 0 0 -1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 -1
-2 2 -2 -2 0 -4 -3 2 -3 -1 -1 3 1 1 2 3 2 1 -2 2 -2 1 0 2 2 -2 -1 -2 -2 -1 -2 1 -2 0 -1 -1
1 -1 -1 1 0 0 -1 0 -1 -1 0 -1 1 0 0 0 0 2 0 1 0 0 0 0 1 -1 0 0 0 -1 -1 0 0 1 0 0
3 0 -1 -1 2 0 0 3 -1 1 1 1 1 1 2 0 1 0 -1 2 -1 1 0 0 0 -1 -1 0 -1 -1 -1 1 -1 0 -1 0
1 2 0 -1 1 0 0 2 0 0 0 1 0 1 2 0 1 -2 -2 0 0 0 1 -1 -2 1 1 0 0 0 0 1 -1 0 0 0
36
-1 -1 1 -1 1 0 0 -1 1 1 2 0 -2 0 0 -1 -1 0 0 1 1 1 -1 0 -1 0 0 1 0 0 0 0 0 -1 0 0
2 -3 -2 0 -1 2 4 0 -1 -1 0 -2 0 -1 -1 -2 0 0 2 -2 0 -1 1 -2 1 0 -1 0 -1 1 1 -1 1 1 0 1
-3 2 2 0 1 -2 -4 0 -1 1 0 2 1 1 2 1 0 0 -2 1 -1 0 -1 1 -1 0 0 0 0 -1 -1 1 -1 -1 -1 -1
2 2 0 1 0 0 0 0 2 0 0 -1 -1 1 -1 0 0 0 0 1 1 1 0 1 0 0 1 0 1 0 0 0 0 0 1 0
1 -1 -3 -1 -2 0 1 2 1 0 -2 1 1 -1 -1 1 1 0 1 0 0 0 0 0 1 0 -1 -1 0 0 1 0 1 1 0 0
-1 -1 0 0 0 0 1 -1 -2 -1 1 -1 0 0 1 -1 0 0 0 -1 0 -1 1 -1 0 0 0 0 -1 0 0 -1 0 0 0 0
2 2 0 2 0 0 -1 1 0 0 -1 0 2 1 1 0 0 -1 -1 -1 -1 -1 1 0 0 1 1 0 1 0 0 0 0 1 0 0
-2 3 0 0 -1 -3 -4 1 -1 -1 -3 2 2 1 0 3 2 1 -1 2 -1 0 -1 2 1 -1 0 -2 0 -1 -1 1 -1 0 0 -1
2 2 -1 -1 0 0 0 2 2 1 -1 1 1 0 1 1 0 -1 -1 0 0 0 0 0 -1 1 0 0 1 0 0 1 0 0 0 0
-2 -1 1 1 0 1 -1 -1 0 1 1 0 0 -1 0 0 -1 0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 -1 0
0 -3 1 1 -1 3 3 -3 0 -2 0 -3 -1 -2 -3 -1 -1 1 3 -2 1 -1 0 -1 1 0 0 0 0 1 1 -1 1 1 1 1
0 -1 -1 -1 1 -1 0 0 0 0 2 0 -1 1 1 -1 0 1 0 2 1 1 0 0 0 -1 -1 0 -1 -1 -1 0 0 0 0 -1
3 1 -1 1 0 1 1 1 0 0 -1 0 2 0 1 0 0 0 0 -1 0 -1 1 -1 0 1 0 0 0 0 0 0 1 1 0 0
-4 1 2 0 0 -2 -2 -1 -1 -1 0 1 0 0 0 1 0 0 -1 0 -1 -1 0 1 0 0 0 -1 0 0 0 0 -1 0 0 -1
3 2 -2 0 0 0 -1 3 2 2 -1 1 1 1 1 1 1 -1 -1 1 0 1 0 1 0 0 0 0 1 -1 0 1 0 0 0 0
-1 -1 3 3 -1 3 1 -3 2 -1 0 -3 -1 -2 -4 -1 -2 0 2 -2 1 -1 0 0 0 1 1 0 2 1 2 -1 1 1 1 1
2 -1 0 0 1 1 3 0 -2 -1 0 -1 0 0 0 -1 1 -1 0 -2 -1 -1 1 -1 0 0 0 0 -1 1 0 0 0 0 0 1
-2 1 -1 -1 0 -2 -2 1 -1 0 -1 2 1 0 1 2 1 1 -1 1 -1 0 0 1 1 -1 -1 -1 -1 -1 -1 1 -1 0 -1 -1
5 -1 -3 0 -1 1 4 2 1 -1 -2 -1 0 0 -3 0 2 0 2 0 0 0 0 0 2 -1 -1 -1 0 1 1 0 1 1 1 1
0 -1 3 3 1 3 1 -3 -2 -1 1 -3 0 -1 -1 -1 -1 1 1 -2 0 -1 1 -1 0 0 1 1 0 0 0 -1 0 0 0 1
-2 3 0 -1 1 -4 -5 1 0 1 0 3 0 2 2 2 1 1 -2 4 0 2 -1 3 0 -1 0 -1 0 -2 -2 1 -1 -1 0 -2
3 1 -2 0 1 -1 1 3 -1 1 0 1 1 2 2 -1 1 -1 -1 0 -1 0 1 -1 0 0 -1 0 -1 0 0 0 0 0 -1 0
-2 0 2 1 0 1 0 -2 -1 -1 0 -1 0 -1 -1 0 -1 1 0 -1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 3 -2 -1 1 -3 -2 3 0 1 -1 3 1 2 2 2 2 0 -2 3 -1 1 0 2 1 -1 0 -1 0 -1 -2 1 -1 0 0 -1
-7 -1 3 0 -1 -1 -4 -3 -1 0 0 1 0 -1 0 1 -1 1 0 0 0 0 -2 1 -1 0 0 0 0 -1 0 0 0 -1 0 -1
-4 0 4 1 1 -1 -2 -3 -2 -1 0 0 -1 0 -1 1 0 1 0 0 -1 0 -1 1 0 -1 1 0 0 0 -1 0 -1 -1 0 0
1 0 -1 0 0 0 0 1 0 0 -1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-3 -2 2 1 0 0 0 -2 -2 -2 0 -1 0 -1 -2 -1 0 1 1 0 -1 -1 0 0 1 -1 -1 -1 -1 0 0 0 0 1 0 0
1 0 0 1 -1 0 2 -1 -3 -3 -1 -2 0 0 -1 -1 1 0 0 -2 -1 -2 1 0 1 0 1 -1 -1 1 1 -1 0 1 1 1
3 3 -3 0 1 -1 -1 3 -1 1 0 1 1 1 2 2 2 2 -1 3 0 2 1 2 2 -2 -1 -1 -2 -2 -2 1 -1 0 -1 -1
0 -3 -2 0 0 1 1 1 2 1 1 0 -1 -1 -2 -1 0 0 1 1 1 1 0 0 1 -1 -2 0 0 -1 1 0 1 1 0 0
-2 1 0 -1 0 -1 -2 0 1 1 0 2 -1 0 0 2 0 1 0 2 0 2 -1 2 1 -1 0 0 0 -1 -1 1 -1 -1 0 -1
-2 -1 1 -1 0 1 0 -1 -3 0 -1 1 1 -1 1 1 0 1 1 -1 -1 -1 0 -1 0 0 0 0 -1 0 -1 0 -1 -1 -1 0
1 -2 -1 1 1 0 1 1 -1 0 1 0 0 0 0 -1 1 0 0 0 -1 0 1 0 1 -1 -1 0 -1 0 0 0 0 1 -1 0
-4 -2 1 1 -3 2 -1 -2 2 0 -1 -1 1 -2 -2 0 -2 0 2 -2 1 -1 -1 -1 0 1 -1 0 1 0 2 0 2 1 0 0
0 0 2 1 0 2 0 -1 1 0 0 -1 0 -1 -1 1 -1 1 1 -1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
36
-1 0 -2 -2 -2 0 -1 1 0 1 -1 1 1 -1 1 1 -1 1 1 0 0 0 0 0 1 0 -1 0 0 -1 0 0 0 0 -1 0
-1 3 -2 -1 0 -3 -3 2 0 1 -1 2 1 2 2 1 1 -1 -2 2 0 1 0 1 0 0 0 -1 0 -1 -1 1 -1 0 0 -1
-1 -3 -1 -1 -2 1 2 -1 1 0 0 0 -1 -2 -2 0 -1 1 2 -1 0 0 -1 0 1 0 -1 0 0 1 1 -1 1 0 0 0
-2 -2 3 1 -1 3 2 -3 0 -1 1 -3 -1 -2 -2 -2 -2 0 2 -3 1 -2 0 -2 -1 1 0 1 0 1 2 -1 1 0 0 1
-4 -1 3 1 0 -1 -2 -3 -1 -1 -1 0 0 0 -1 0 0 0 0 0 0 -1 -1 0 -1 0 1 0 1 0 0 0 0 0 1 0
1 3 1 1 3 -2 -2 1 -2 -1 1 1 0 2 2 1 2 0 -3 2 -1 1 1 2 0 -1 1 -1 -1 -1 -2 1 -2 0 0 -1
4 0 -2 0 1 0 3 2 1 0 1 -1 -1 1 -1 -1 1 0 0 1 0 1 0 0 1 -1 -1 0 -1 1 0 0 0 0 0 0
-4 -4 6 3 -2 4 3 -7 0 -3 0 -4 -2 -3 -5 -2 -2 0 3 -5 1 -3 -1 -2 -2 2 2 1 1 3 3 -2 2 0 2 1
1 -2 0 0 2 0 1 0 0 0 1 1 -1 0 0 0 1 0 0 1 0 1 0 0 0 -1 0 0 0 0 -1 0 0 0 0 0
6 1 -5 0 0 -1 2 4 2 1 0 0 1 2 1 -1 1 -1 -1 1 0 1 1 0 1 0 -1 0 0 0 0 0 1 1 0 0
4 4 -1 1 1 0 0 3 1 1 0 0 1 2 2 0 1 -2 -2 0 0 1 1 0 -1 1 1 0 0 0 0 1 0 0 0 0
-4 1 2 -1 0 0 -3 -1 0 1 0 2 0 -1 1 2 -1 1 0 1 0 1 -1 1 0 0 0 0 0 -1 -1 1 -1 -1 -1 -1
2 3 -2 -1 1 -3 -1 3 1 1 -1 3 0 2 1 2 2 0 -2 3 -1 2 -1 2 1 -1 0 -1 0 0 -1 1 -1 -1 0 -1
2 -1 3 3 4 2 1 -1 0 0 3 -1 -1 0 0 -1 0 0 -1 0 0 1 1 0 -1 0 1 1 0 0 -1 0 0 0 0 0
-2 -3 1 -1 0 0 0 -1 0 0 1 0 -1 -1 -1 0 0 0 1 0 0 0 -1 0 0 -1 -1 0 0 0 0 0 0 0 0 0
3 -2 1 3 1 3 4 -1 1 -1 2 -4 -1 0 -2 -4 -1 -1 1 -2 1 -1 1 -2 -1 1 0 1 0 1 2 -1 2 1 1 1
4 3 -3 -1 1 -2 0 4 0 1 -1 2 1 2 2 1 2 -2 -2 1 -1 1 1 1 0 0 0 -1 0 0 -1 1 -1 0 0 0
1 0 2 2 1 1 1 -1 1 0 0 0 0 0 -1 0 0 -1 0 -1 0 0 0 0 -1 1 1 0 1 1 0 0 1 0 1 0
-3 0 2 0 0 0 -2 -2 0 1 0 0 0 0 1 0 -1 -1 0 -1 1 0 0 -1 -2 1 1 1 1 0 0 0 0 -1 0 0
3 2 -1 1 1 0 1 1 0 0 1 -1 0 1 1 -1 0 0 -1 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 0 0
-4 -3 4 0 -3 3 2 -4 1 -2 -1 -2 -2 -4 -5 0 -2 1 3 -3 0 -2 -2 0 0 1 0 0 1 2 3 -1 1 0 1 1
-4 0 -1 -2 -1 -2 -3 0 0 2 0 2 0 0 1 1 -1 1 0 2 0 1 -1 1 1 -1 -1 0 0 -1 -1 0 -1 -1 -1 -1
2 -1 0 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0
4 1 0 0 3 0 1 2 1 1 1 1 -1 1 0 1 2 0 -1 2 0 2 0 1 0 -1 0 0 0 0 -1 1 -1 -1 0 0
-3 -3 2 1 -3 2 1 -3 -1 -2 -1 -2 0 -3 -3 0 -1 1 2 -3 -1 -2 -1 0 1 0 0 0 0 1 2 -1 1 1 0 1
5 1 1 2 0 4 5 0 0 0 0 -3 0 -1 -1 -2 -1 -1 1 -4 0 -2 2 -2 -1 2 1 1 0 2 2 -1 1 0 0 2
-1 -1 1 1 0 0 -1 -2 -1 -1 0 -1 0 0 0 0 0 1 0 0 0 0 0 0 0 -1 1 1 0 0 -1 0 0 0 0 0
-1 0 0 1 -1 1 0 -1 2 1 -1 0 0 -1 -2 0 -1 0 1 0 1 0 -1 0 0 1 0 0 1 0 1 0 1 0 1 0
1 3 0 0 0 -1 -1 2 0 0 -1 0 1 1 0 1 1 -1 -1 0 -1 0 0 1 0 0 0 -1 0 0 0 1 -1 0 0 0
-1 2 1 1 1 -2 -3 1 2 1 0 2 0 1 0 1 1 -1 -2 2 0 1 -1 2 -1 0 0 -1 1 -1 0 1 0 0 1 -1
-2 -1 1 1 -1 1 -2 -2 1 1 0 -1 1 -1 0 0 -2 1 1 0 1 0 -1 0 0 0 0 1 1 -1 0 0 1 0 0 0
1 0 1 1 -1 1 0 0 0 -1 0 -2 1 -1 -1 0 0 0 0 -1 0 -1 0 0 0 0 0 0 0 0 1 0 1 1 0 1
-1 1 -1 0 1 -3 -3 1 -2 0 0 2 1 2 2 1 2 0 -2 2 -1 1 0 1 0 -1 0 -1 -1 -1 -2 1 -1 0 0 -1
2 2 -3 -1 1 -2 -1 3 3 3 0 2 0 2 1 0 0 -1 -1 3 1 2 0 1 0 0 -1 0 1 -1 -1 1 0 0 0 -1
-2 -3 1 1 -2 1 1 -2 1 -1 0 -1 0 -1 -2 -1 -1 -1 1 -2 0 -1 -1 -1 0 1 0 0 1 1 2 -1 2 1 1 0
-2 -2 5 1 3 2 1 -3 0 0 3 0 -2 -1 0 -1 -1 -1 0 -1 0 0 0 -1 -2 1 1 1 0 1 0 0 0 -1 0 0
-
PROPERTIES
INTEGRAL=1
UNIMODULAR=1
-
NOTES
The automorphism group (Sp4(4).2 subdir C_4 otimes D8).2
is a maximal finite subgroup of GL(36,Q).
Found by gabi@momo.math.rwth-aachen.de (Gabriele Nebe) Mon Feb 16 1998
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe