The Lattice U3(3)U3(3):2.2
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 13:14:38 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME (required)
DIMENSION (required)
GRAM (floating point or integer Gram matrix)
DIVISORS (elementary divisors)
MINIMAL_NORM
KISSING_NUMBER
GROUP_ORDER
GROUP_GENERATORS
PROPERTIES
NOTES
LAST_LINE (required)
-
NAME (required)
U3(3)U3(3):2.2
-
DIMENSION (required)
36
-
GRAM (floating point or integer Gram matrix)
36 0
6
2 6
3 1 6
2 2 3 6
2 2 3 2 6
1 1 2 3 1 6
1 3 2 1 1 1 6
2 2 1 2 2 1 3 6
1 3 2 1 1 0 2 -1 6
1 3 2 1 1 1 2 -1 2 6
0 1 1 1 1 1 1 2 1 0 6
3 1 2 3 -1 1 2 1 2 2 1 6
1 0 1 2 -1 3 1 1 0 1 2 3 6
2 1 3 2 1 2 1 0 1 2 0 2 2 6
2 1 3 1 1 3 1 0 1 2 2 1 2 2 6
1 3 0 1 1 2 1 1 2 1 3 1 1 1 1 6
1 2 1 1 0 1 2 1 1 2 2 2 1 1 1 2 6
1 2 1 0 1 1 3 1 2 1 2 1 2 1 2 3 1 6
2 1 2 1 1 2 1 1 1 1 1 2 2 3 1 2 2 1 6
3 1 1 1 0 2 0 1 0 1 1 2 3 3 3 2 2 1 2 6
2 1 2 3 1 2 0 1 1 0 1 2 2 3 1 1 0 1 1 2 6
1 2 1 0 1 1 3 2 1 1 2 1 0 2 1 3 3 2 1 1 1 6
2 2 1 2 0 2 1 1 1 1 1 2 2 1 2 1 1 0 1 3 3 0 6
2 1 2 2 1 3 1 2 0 0 0 1 2 2 2 1 1 1 3 2 3 1 2 6
1 2 0 1 0 2 2 3 0 0 2 1 1 1 1 2 1 1 0 1 2 3 1 1 6
3 1 2 2 1 2 1 1 1 0 1 2 1 1 2 2 1 1 2 2 2 1 3 3 0 6
2 0 2 2 2 1 0 1 0 0 0 1 1 2 0 1 1 0 2 1 1 1 -1 2 0 1 6
1 1 1 1 1 2 0 0 0 2 0 0 2 3 1 0 1 0 1 2 2 1 1 1 1 -1 2 6
1 1 2 2 1 2 2 1 1 1 1 2 1 3 2 1 0 1 2 2 2 1 3 1 1 1 0 1 6
1 1 0 0 2 1 1 1 1 0 2 0 0 1 0 2 1 1 1 0 1 3 0 0 2 0 2 2 1 6
1 3 0 1 1 -1 1 1 2 1 1 1 0 1 -1 1 2 0 0 1 1 1 1 -1 1 0 1 1 0 1 6
2 1 1 1 0 1 1 0 2 1 0 3 2 2 0 1 1 2 3 1 3 1 2 2 1 2 0 1 2 1 0 6
1 2 0 1 0 0 0 1 1 1 0 1 1 2 0 1 1 0 0 2 2 1 1 1 2 -1 2 2 0 2 3 0 6
1 0 3 2 1 1 1 1 1 0 1 1 1 1 1 0 2 0 1 2 1 0 1 1 0 1 2 1 1 -1 1 0 0 6
0 1 1 0 1 1 0 0 1 2 2 0 0 1 1 1 2 0 1 1 1 1 1 0 1 -1 0 3 2 1 1 1 0 1 6
0 1 0 1 1 1 2 1 1 0 0 0 1 1 0 1 0 2 -1 1 2 1 1 1 2 1 0 1 1 1 1 1 1 1 0 6
-
DIVISORS (elementary divisors)
1^18 3^18
-
MINIMAL_NORM
6
-
KISSING_NUMBER
-
GROUP_ORDER
2^13 * 3^6 * 7^2
-
GROUP_GENERATORS
4
36
-3 2 3 0 -1 1 -4 0 0 0 1 3 -3 -1 -2 -3 -1 3 1 3 -2 1 2 1 1 -1 1 1 -1 1 0 -1 -2 -1 -1 1
-3 2 2 -1 -1 2 -3 1 0 0 2 3 -4 1 -2 -3 -1 3 0 3 -2 0 3 1 0 -2 2 0 -2 1 0 0 -2 -1 -1 1
2 -1 -2 1 0 0 0 0 1 1 0 -2 1 -1 0 -1 1 0 1 -1 1 1 -1 -1 0 1 0 0 1 -1 -1 -1 1 0 0 0
-2 1 2 -1 0 1 -2 0 0 0 1 2 -2 -1 -2 -2 0 2 0 2 -1 0 1 1 1 0 1 1 0 0 0 -1 -1 -1 -1 0
-3 2 3 1 -1 0 -3 -1 0 0 0 2 -2 -1 -3 -4 -1 4 1 4 -2 1 2 1 2 0 1 0 -1 2 0 -2 -2 -1 0 0
-1 1 2 -1 0 0 -4 0 1 1 0 1 0 -2 -3 -3 1 3 1 1 0 1 0 1 2 1 0 1 2 0 0 -3 -1 -1 -1 0
1 0 -2 0 1 0 0 0 1 0 0 -1 1 0 0 -1 1 0 1 -1 1 0 -1 -1 0 1 0 0 1 -1 -1 -1 1 0 0 0
-3 2 3 0 0 0 -3 -1 0 0 0 2 -1 -2 -3 -3 0 3 1 3 -1 0 0 1 2 1 0 1 1 1 0 -2 -1 -1 -1 0
2 0 -3 0 0 3 1 0 0 0 4 0 -3 2 0 -2 -1 0 0 0 -1 1 2 -1 -2 -2 2 -1 -2 -2 -1 2 1 0 0 1
2 -1 -2 0 0 0 1 1 1 0 0 -2 1 1 1 1 1 -1 0 -2 1 0 0 -1 -1 0 0 0 0 -1 -1 0 1 0 0 0
2 0 -2 0 0 2 0 -1 1 1 3 -1 -1 0 -2 -3 0 1 0 0 0 1 0 0 0 0 1 0 1 -2 -1 0 1 0 -1 0
3 -2 -3 0 1 1 2 0 1 0 2 -2 0 0 1 1 1 -2 0 -2 1 0 -1 -1 -1 0 0 1 1 -3 -1 1 2 0 -1 0
1 1 0 -2 1 0 -2 0 1 0 0 0 2 -1 -1 -1 2 0 0 -2 1 0 -2 0 1 2 -1 1 3 -1 -1 -2 1 0 -1 0
0 0 1 0 -1 1 -2 1 1 1 1 0 -1 -1 -1 -2 0 1 1 1 0 1 1 0 0 -1 1 0 0 0 0 -1 -1 -1 -1 1
0 1 0 0 0 0 -3 0 1 1 0 0 1 -1 -2 -3 0 2 1 0 0 2 0 0 1 1 0 0 1 0 -1 -2 0 0 0 0
0 0 0 0 -1 3 -2 0 1 1 4 1 -4 1 -3 -4 -1 3 0 2 -2 1 3 1 0 -2 2 0 -1 -1 0 0 -1 -1 -1 1
1 -1 -1 1 -1 2 0 0 1 1 3 -1 -3 0 -1 -2 -1 1 1 1 -1 1 2 0 0 -2 2 0 -1 -2 0 1 0 -1 -1 1
0 1 -1 -1 1 0 -2 0 1 0 0 1 1 1 -1 -2 1 1 0 -1 0 0 0 0 1 1 0 0 1 0 -1 -2 0 0 0 0
1 -1 0 1 -1 1 -1 0 1 1 2 -1 -2 -1 -1 -2 0 1 1 1 0 1 1 0 0 -1 1 0 0 -1 0 0 0 -1 -1 1
-1 1 2 0 -1 2 -4 0 1 1 2 1 -2 -1 -3 -4 -1 3 1 2 -2 2 2 1 1 -1 1 0 0 0 0 -1 -1 -1 -1 1
-6 4 6 -2 -1 2 -7 1 0 0 1 6 -4 -1 -4 -5 -1 5 0 5 -3 1 3 2 2 -1 2 1 -1 2 1 -2 -4 -2 -2 1
0 0 0 1 -1 2 -1 0 1 1 3 0 -3 0 -2 -3 -1 2 1 2 -1 1 2 0 0 -2 2 0 -1 -1 0 0 -1 -1 -1 1
-6 4 6 -2 -1 2 -7 1 0 0 1 5 -4 -1 -4 -5 -1 5 0 5 -3 1 3 2 2 -1 2 1 -1 2 1 -1 -4 -2 -2 1
-7 4 7 -1 -1 0 -8 1 0 0 -1 6 -3 -2 -4 -5 -1 6 1 5 -3 1 3 2 3 0 1 1 -1 3 1 -3 -4 -2 -1 1
-6 4 6 -1 -2 2 -7 1 0 1 2 5 -5 -1 -5 -6 -2 6 1 6 -3 1 3 2 2 -1 2 1 -1 2 1 -2 -4 -2 -2 1
-4 2 4 0 -1 2 -4 0 0 0 2 4 -5 -1 -3 -4 -2 4 0 5 -3 1 3 2 1 -2 2 1 -2 1 1 0 -3 -2 -1 1
0 0 1 1 -1 1 0 -1 0 0 2 0 -2 -1 -1 -2 -1 1 1 2 -1 1 1 0 0 -1 1 0 -1 -1 0 0 0 -1 0 1
-1 2 2 -1 -1 1 -2 0 0 0 1 1 -1 -1 -1 -2 0 1 1 1 0 1 1 0 0 -1 1 0 0 0 0 -1 -1 -1 -1 1
-1 0 1 0 0 1 -2 0 1 1 1 0 -1 -1 -2 -3 0 2 1 2 0 1 1 0 1 0 1 0 0 0 0 -1 -1 -1 -1 0
0 1 1 0 -1 2 -1 -1 0 0 3 1 -3 0 -2 -3 -1 2 1 2 -1 1 2 0 0 -2 2 0 -1 -1 0 0 -1 -1 -1 1
0 0 0 0 -1 2 1 0 0 0 3 0 -3 0 0 -1 -1 0 0 2 -1 0 1 0 -1 -2 2 0 -1 -1 0 2 0 -1 -1 1
-4 2 4 -1 -1 2 -4 1 0 0 2 4 -5 0 -2 -3 -1 3 0 4 -2 0 3 1 1 -2 2 1 -2 1 1 0 -3 -2 -2 1
-1 1 2 -1 -1 1 -2 1 0 0 1 1 -1 0 -1 -1 0 1 0 1 -1 0 1 0 0 -1 1 0 0 0 0 0 -1 -1 -1 1
1 -1 -1 2 -1 3 1 -1 0 1 4 -1 -4 0 -1 -3 -2 1 1 2 -2 2 2 0 -1 -2 2 -1 -2 -2 0 2 1 -1 0 1
-1 1 1 0 -1 1 -2 0 1 1 1 0 -1 -1 -2 -3 0 2 1 2 0 1 1 0 1 0 1 0 0 0 0 -1 -1 -1 -1 0
-7 5 6 -1 -1 2 -6 0 -1 -1 1 7 -5 0 -4 -6 -3 6 1 6 -4 1 4 2 2 -1 2 0 -3 3 1 -2 -4 -2 0 1
36
0 0 0 0 1 -2 -1 0 0 -1 -3 0 3 0 1 1 1 0 0 -2 0 0 -1 0 1 2 -2 0 1 1 0 -1 1 1 1 -1
1 -1 -2 1 0 -1 1 0 0 0 -1 -1 1 1 1 1 0 0 0 -2 0 0 0 0 0 1 -1 0 0 0 0 0 1 1 1 -1
3 -2 -3 0 2 -3 1 0 1 0 -4 -3 6 0 2 3 3 -2 0 -5 3 -1 -3 -1 1 3 -3 0 3 0 -1 -2 2 2 1 -2
1 -1 -1 0 1 -2 0 0 0 0 -2 -1 3 0 1 2 2 -1 0 -3 1 -1 -2 0 1 2 -2 1 2 0 0 -1 1 1 0 -1
1 -2 -2 1 1 -1 1 0 0 0 -1 -1 1 1 1 1 0 0 0 -2 0 0 0 0 0 1 -1 0 0 0 0 0 1 1 1 -1
5 -3 -4 1 1 -1 3 -1 1 1 0 -5 4 0 1 2 2 -3 0 -4 2 0 -3 -1 0 2 -2 0 3 -2 -1 0 3 1 0 -1
3 -2 -4 0 2 -3 2 0 1 0 -4 -3 6 0 2 3 3 -2 0 -5 3 -1 -3 -1 1 3 -3 0 3 0 -1 -2 2 2 1 -2
1 -1 -2 0 1 -1 1 0 0 0 -1 -1 2 0 1 1 1 -1 0 -2 1 0 -1 0 0 1 -1 0 1 0 0 0 1 1 0 -1
4 -2 -4 0 1 -2 2 0 1 0 -2 -3 4 1 2 3 2 -2 0 -5 2 -1 -2 -1 0 2 -2 0 2 -1 -1 -1 2 2 1 -1
2 -1 -3 1 1 -2 1 0 0 0 -3 -2 4 1 2 2 1 -1 0 -4 1 0 -1 -1 0 2 -2 -1 1 0 -1 -1 2 2 2 -1
3 -1 -4 -1 2 -2 3 0 0 -1 -2 -2 5 1 3 4 2 -4 -1 -5 3 -1 -3 -1 -1 2 -2 0 2 -1 -1 0 2 2 1 -1
2 0 -2 -1 2 -3 0 0 0 -1 -4 -1 6 0 2 3 3 -2 0 -5 2 -1 -3 -1 1 3 -3 0 3 0 -1 -2 2 2 1 -1
3 -1 -3 0 1 -2 2 0 0 0 -2 -3 5 1 2 3 2 -3 -1 -4 2 -1 -3 -1 0 2 -2 -1 2 0 -1 0 2 2 1 -1
2 0 -2 0 1 -1 -1 0 1 0 -2 -2 4 1 0 0 2 0 0 -3 1 0 -1 -1 1 2 -1 -1 2 0 -1 -2 1 1 1 -1
3 -1 -3 -1 2 -3 1 0 1 0 -4 -3 7 0 2 3 3 -3 -1 -5 3 -1 -4 -1 1 4 -3 0 4 0 -1 -2 2 2 1 -2
3 -1 -3 0 1 -2 1 0 1 0 -2 -3 5 0 1 2 2 -2 0 -4 2 0 -3 -1 0 3 -2 0 3 -1 -1 -1 2 1 1 -1
3 -2 -3 1 1 -2 2 0 1 0 -2 -3 4 0 1 2 2 -2 0 -3 2 0 -2 -1 0 2 -2 0 2 -1 -1 -1 2 1 1 -1
3 -1 -3 -1 2 -3 1 0 1 0 -4 -3 7 0 1 3 3 -2 -1 -5 3 -1 -4 -1 1 4 -3 0 4 0 -1 -2 2 2 1 -2
3 -2 -3 1 1 -1 2 0 1 0 -1 -3 3 1 1 2 1 -2 0 -3 1 0 -1 -1 0 1 -1 -1 1 -1 -1 0 2 1 1 -1
3 -1 -3 0 1 -1 1 0 1 0 -1 -3 4 1 1 1 2 -2 -1 -3 1 0 -2 -1 0 2 -1 -1 2 -1 -1 0 2 1 1 -1
0 1 1 -1 0 0 -2 0 0 0 0 0 1 0 -1 -1 1 1 0 -1 0 0 0 0 1 1 0 0 1 0 0 -1 0 0 0 0
2 0 -2 0 1 -2 -1 0 1 0 -3 -2 5 -1 0 0 2 0 1 -3 2 1 -2 -1 1 3 -2 0 3 0 -1 -3 1 1 1 -1
0 0 0 -1 0 0 0 1 0 0 0 0 0 1 1 1 1 -1 -1 -1 0 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 1 0 0 -1 -2 0 1 1 -1 -1 2 -1 -2 -1 1 1 0 0 0 0 -1 1 2 2 -1 0 2 1 0 -2 0 0 0 -1
0 1 0 0 0 0 -1 -1 0 0 0 0 1 -1 -1 -2 0 1 1 0 0 1 0 0 1 1 0 0 1 0 0 -1 0 0 0 0
-1 0 1 -1 1 -2 -2 1 1 0 -3 0 3 -1 0 1 2 0 0 -1 1 -1 -2 0 2 3 -2 1 2 1 0 -2 0 0 0 -1
2 -1 -2 1 1 -3 0 0 1 0 -3 -3 5 -1 1 1 2 -1 1 -3 2 0 -3 -1 1 3 -2 0 3 0 -1 -2 2 1 1 -1
3 -1 -3 2 0 0 2 -1 0 0 1 -3 1 1 1 0 0 -1 0 -2 0 1 0 -1 -1 0 0 -1 0 -1 -1 1 2 1 1 0
4 -2 -4 -1 2 -1 2 0 1 0 -1 -3 4 1 2 3 3 -3 -1 -5 2 -1 -2 -1 0 1 -1 0 3 -2 -1 0 2 1 0 -1
3 -1 -3 0 1 -1 2 0 0 -1 -1 -2 3 1 2 2 1 -2 0 -4 1 0 -1 -1 -1 1 -1 0 1 -1 -1 0 2 1 1 0
4 -3 -5 2 0 0 4 0 0 0 1 -3 0 2 3 2 0 -2 0 -3 1 0 0 -1 -2 -1 0 -1 -1 -2 0 2 2 1 1 0
0 0 1 0 0 0 -1 0 0 0 0 0 0 0 -1 0 0 1 0 0 -1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0
3 0 -3 0 0 0 1 0 0 0 0 -2 2 1 1 0 1 -1 0 -3 1 0 -1 -1 -1 1 0 -1 1 -1 -1 0 2 1 1 0
4 -3 -4 1 1 -1 2 0 2 1 0 -4 3 0 1 1 2 -2 0 -3 2 0 -2 -1 0 1 -1 0 2 -2 -1 0 2 1 0 -1
5 -3 -5 2 1 0 5 -2 0 0 2 -4 1 1 2 2 0 -3 0 -3 1 1 0 -1 -2 -1 0 -1 0 -3 -1 2 3 1 1 0
1 -1 -1 0 0 0 -1 0 1 1 0 -1 1 0 -1 -1 1 1 0 -1 0 0 0 0 1 1 0 0 1 0 0 -1 0 0 0 0
36
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 0
0 1 0 0 0 1 -1 -1 0 0 1 1 -1 0 -1 -2 -1 1 0 1 -1 1 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 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 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 -1 0 0 0 0 0 1 -1 0 -1 0 0 0 0 0 1 -1 0 0 1 0 0 1 0 0 0 0 0 0 0
0 0 0 -1 0 0 -1 1 1 0 -1 0 1 0 0 0 1 0 0 -1 1 0 -1 0 0 1 0 0 1 0 0 -1 0 0 0 0
4 -2 -4 0 2 -1 2 -1 1 0 -1 -3 4 0 1 1 2 -2 0 -4 2 0 -3 -1 0 3 -2 0 3 -2 -1 -1 3 1 1 -1
-2 2 2 0 0 -1 -4 0 0 0 -2 2 1 -1 -2 -3 0 3 1 1 -1 1 0 1 2 2 -1 0 1 2 0 -3 -1 0 1 0
5 -2 -5 0 1 2 5 -1 0 0 3 -3 0 2 2 2 0 -4 -1 -3 1 0 -1 -1 -3 -1 0 -1 0 -3 -1 3 3 1 0 0
1 -1 -2 1 0 2 2 -1 0 0 3 0 -3 1 0 -1 -2 0 0 1 -1 1 1 0 -1 -1 1 0 -2 -2 0 2 1 0 0 0
3 -2 -3 2 0 0 3 -1 0 0 0 -3 1 0 2 1 0 -2 1 -2 1 1 -1 -1 -1 0 -1 -1 0 -1 0 1 2 1 1 0
5 -3 -5 1 1 1 5 -1 0 0 2 -3 0 2 2 2 0 -3 0 -3 1 0 0 -1 -2 -1 0 -1 -1 -3 -1 2 3 1 1 0
4 -3 -4 1 0 1 4 0 0 0 1 -3 0 2 2 2 0 -2 0 -3 1 0 0 -1 -2 -1 0 -1 -1 -2 0 2 2 1 1 0
2 -1 -2 0 0 0 1 0 0 0 1 -1 0 1 1 1 0 -1 0 -2 0 0 0 0 -1 0 0 0 0 -1 0 1 1 1 0 0
-2 2 2 -1 0 0 -2 0 0 -1 -1 2 0 0 -1 -1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 -1 -1 0 0 0
3 -2 -3 1 0 1 1 0 1 1 1 -2 0 1 1 0 0 -1 0 -2 0 1 0 0 -1 -1 0 -1 0 -1 0 1 1 1 0 0
1 -1 -2 1 1 -1 2 -1 0 0 -1 -1 1 0 1 1 0 -1 0 -1 1 0 -1 0 0 1 -1 0 0 0 0 0 1 1 1 -1
7 -4 -7 1 2 0 5 -1 1 0 0 -5 4 1 3 3 2 -4 0 -6 3 0 -3 -2 -2 1 -2 -1 2 -3 -1 1 4 2 1 -1
3 -2 -3 1 0 0 3 0 0 0 1 -2 0 2 2 2 0 -2 -1 -2 0 0 0 0 -2 -1 0 -1 -1 -1 0 2 1 1 1 0
1 0 -1 0 0 0 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 1 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 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 -2 0 1 1 0 0 0 -1 -1 -2 0 1 1 0 0 1 0 0 1 1 0 0 1 0 0 -1 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 0 0 0 0 0 0 0 0 0 0 0 0 0
-5 3 5 -1 -1 0 -5 1 0 0 -1 4 -2 0 -3 -3 -1 4 0 4 -2 0 2 2 2 0 1 0 -1 3 1 -2 -4 -1 0 0
2 -1 -2 0 1 -2 0 0 1 0 -3 -2 4 -1 1 1 2 -1 1 -3 2 0 -3 -1 1 3 -2 0 3 0 -1 -2 2 1 1 -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 0 0 0
-5 3 5 -2 -1 0 -5 2 0 0 -1 4 -2 0 -2 -2 0 3 -1 3 -2 -1 2 2 2 0 1 1 -1 3 1 -1 -4 -1 -1 0
-1 0 1 0 -1 1 0 0 0 0 2 1 -3 0 -1 -1 -1 1 0 2 -1 0 1 1 0 -1 1 1 -1 0 1 1 -1 -1 -1 0
4 -2 -4 0 1 -1 2 0 1 0 0 -3 3 1 2 2 2 -3 0 -4 2 0 -2 -1 -1 1 -1 0 2 -2 -1 0 2 1 0 0
2 -1 -2 0 0 0 1 1 1 0 0 -2 1 0 2 1 1 -2 0 -2 1 0 -1 -1 -1 0 0 0 1 -1 0 1 1 0 0 0
4 -1 -4 0 1 -1 3 -1 0 0 -1 -3 4 0 2 2 1 -3 0 -4 2 0 -3 -1 -1 2 -2 0 2 -1 -1 0 3 2 1 -1
7 -5 -7 2 1 1 8 -1 0 0 3 -5 0 2 4 4 0 -5 0 -4 2 0 -1 -2 -4 -2 0 -1 -1 -4 -1 4 4 1 1 0
-3 3 2 -1 -1 1 -4 1 0 0 0 3 -2 1 -2 -3 -1 3 0 2 -2 0 2 1 1 0 1 0 -1 2 0 -1 -2 0 0 0
2 -2 -2 0 1 -2 3 0 0 0 -2 -2 3 0 2 4 2 -3 -1 -3 2 -2 -3 0 0 2 -2 1 2 0 0 0 1 1 0 -1
0 0 -1 1 0 0 1 -1 0 0 1 0 -1 0 0 -1 -1 0 1 1 0 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0
6 -4 -6 1 2 -3 5 0 1 0 -3 -6 7 0 4 5 3 -5 0 -7 4 -1 -5 -2 -1 3 -3 0 4 -2 -1 0 4 2 1 -2
36
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 0
-4 4 3 -1 0 -1 -3 0 -1 -1 -2 4 0 0 -1 -2 -1 2 0 2 -1 0 1 1 1 1 0 0 -1 3 0 -2 -2 0 1 0
6 -3 -5 0 1 0 4 0 1 0 0 -4 3 0 3 3 2 -4 0 -5 3 0 -2 -2 -2 0 -1 0 2 -3 -1 1 3 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 0 0 0 0 0 0 0 0 0 0 0 0
1 1 -1 -1 1 -1 0 0 0 -1 -2 0 3 0 1 1 1 -1 0 -3 1 0 -1 -1 0 2 -1 0 1 0 -1 -1 1 1 1 0
1 -1 -2 0 0 0 1 1 0 0 0 0 0 2 2 2 0 -1 -1 -2 0 -1 1 0 -1 -1 0 0 -1 0 0 1 0 1 0 0
1 0 -1 0 0 0 1 0 0 0 0 0 0 0 1 1 0 -1 0 -1 1 0 0 0 -1 -1 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 0 0 0 0 0 0 0 0 0 0 0 0
-5 3 5 -1 0 -1 -4 0 -1 -1 -2 5 -1 -1 -2 -2 -1 3 0 3 -2 0 2 2 2 0 0 1 -1 3 1 -2 -3 -1 0 0
2 0 -2 0 0 0 1 0 0 0 0 -1 1 1 1 0 0 -1 0 -2 1 0 0 -1 -1 0 0 -1 0 0 -1 0 1 1 1 0
0 0 0 0 0 0 2 0 -1 -1 0 0 0 1 2 2 0 -2 -1 -1 0 -1 0 0 -1 -1 0 0 -1 0 1 2 0 0 0 0
0 -1 1 1 -1 1 0 0 0 1 2 0 -3 0 -1 -1 -1 1 0 2 -1 0 2 1 0 -2 1 0 -1 0 1 1 -1 -1 -1 0
1 -2 -1 2 -1 0 3 0 -1 0 1 -1 -2 1 2 2 -1 -1 0 0 0 -1 1 0 -1 -2 0 0 -2 0 1 2 0 0 0 0
2 -2 -2 0 0 1 3 1 0 0 1 -1 -1 1 2 2 0 -2 -1 -1 1 -1 0 -1 -2 -1 0 0 -1 -1 0 2 1 0 0 0
3 -2 -3 0 0 0 3 1 0 0 0 -2 1 1 3 3 1 -3 -1 -3 2 -1 -1 -1 -2 -1 0 0 0 -1 0 2 1 1 0 0
-5 4 4 -1 -1 2 -3 0 -2 -1 2 6 -5 2 -2 -3 -3 3 -1 4 -4 0 4 2 0 -2 2 0 -4 2 1 1 -3 -1 0 1
2 -1 -2 1 0 -1 2 0 0 0 -1 -2 2 1 2 2 0 -2 -1 -2 1 0 -1 0 -1 0 -1 -1 0 0 0 1 1 1 1 -1
-3 2 2 0 -1 2 0 0 -2 -1 2 4 -5 1 0 -1 -3 1 0 3 -2 0 3 1 -1 -3 2 0 -4 1 1 2 -2 -1 0 1
2 -2 -2 1 0 0 3 0 0 0 1 -1 -1 1 2 2 0 -2 -1 -1 0 -1 0 0 -1 -1 0 0 -1 -1 0 2 1 0 0 0
-2 1 2 0 -1 0 -1 1 -1 0 0 2 -2 1 0 0 -1 1 -1 2 -1 -1 1 1 0 -1 0 0 -2 2 1 1 -2 0 0 0
-5 3 5 -2 -1 0 -5 2 0 0 -2 4 -1 -1 -2 -2 0 3 0 3 -1 -1 1 1 2 1 0 1 0 3 1 -2 -3 -1 -1 0
0 1 0 -1 0 1 -1 1 0 0 0 1 0 1 0 0 0 0 -1 -1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0
-6 4 6 -2 -1 -1 -6 1 0 0 -2 5 -1 -1 -3 -3 0 4 0 4 -1 -1 1 2 3 1 0 1 0 4 1 -3 -4 -1 -1 0
1 -1 -1 1 -1 0 0 1 1 1 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
-4 3 4 -2 -1 0 -4 2 0 0 -1 3 -1 0 -1 -1 0 2 -1 2 -1 -1 1 1 1 0 1 1 0 2 1 -1 -3 -1 -1 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 0 0
3 -1 -2 1 0 1 2 -1 0 0 2 -2 0 0 0 0 0 -1 0 -1 0 1 0 -1 -1 0 0 0 0 -2 -1 1 2 0 0 0
1 0 -1 -1 1 -2 1 1 0 -1 -3 -1 4 1 2 3 2 -2 -1 -3 2 -2 -2 -1 0 2 -2 0 1 1 -1 -1 1 1 1 -1
-5 3 5 -2 -1 2 -4 1 0 0 2 5 -5 0 -3 -3 -1 3 -1 5 -2 -1 3 2 1 -2 2 1 -2 2 1 0 -4 -2 -2 1
-1 1 1 -1 1 -1 -1 0 0 -1 -2 1 2 0 0 1 1 0 -1 -1 0 -1 -1 0 1 2 -1 1 1 1 0 -1 0 0 0 -1
0 1 0 0 1 -2 1 -1 -1 -1 -2 0 3 -1 1 1 0 -1 0 -1 1 0 -2 0 0 2 -2 0 1 1 0 -1 1 1 1 -1
-6 3 6 -1 -1 0 -5 1 0 0 -1 5 -3 -1 -3 -3 -1 4 0 5 -2 -1 2 2 3 0 1 1 -1 3 1 -2 -4 -2 -1 0
-1 1 1 0 0 -1 -1 0 0 0 -1 0 1 -1 -1 -1 0 1 0 1 0 0 -1 0 1 2 -1 1 1 1 0 -1 0 0 0 -1
1 0 0 0 0 -1 0 0 0 0 -1 -1 2 -1 1 1 1 -1 0 -1 1 0 -1 0 0 0 -1 0 1 0 0 0 0 0 0 0
-3 3 3 -2 0 0 -3 1 0 -1 -1 3 0 1 -1 -1 0 1 -1 1 -1 -1 1 1 1 0 0 0 -1 2 0 -1 -2 0 0 0
-5 3 5 -1 -1 -1 -3 1 -1 -1 -2 4 -1 -1 -1 0 -1 2 0 3 -1 -1 1 1 1 0 0 1 -1 3 1 -1 -3 -1 0 0
-
PROPERTIES
INTEGRAL = 1
MODULAR = 3
-
NOTES
Lattice of a maximal finite matrix group
-
LAST_LINE (required)
Haftungsausschluss/Disclaimer
Gabriele Nebe