The Lattice SL2(5)(Sp4(3)xC3.2).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 13:13:52 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(5)(Sp4(3)xC3.2).2
-
DIMENSION
32
-
GRAM (floating point or integer Gram matrix)
32 0
12
3 12
6 2 12
3 2 6 12
3 0 3 2 12
6 6 3 6 -1 12
0 4 3 6 2 6 12
6 3 3 6 2 6 6 12
3 -1 6 6 4 0 3 6 12
3 4 4 6 0 4 2 3 2 12
3 4 4 6 2 4 2 3 2 6 12
6 3 0 3 4 3 3 6 0 3 3 12
3 0 3 2 6 -1 2 2 4 1 2 4 12
3 2 4 6 2 4 2 3 2 6 6 3 2 12
3 1 3 1 6 1 4 4 2 0 0 2 6 2 12
3 4 4 6 1 4 2 3 2 6 6 3 2 6 0 12
3 4 4 6 1 4 2 3 2 6 6 3 0 6 0 0 12
3 0 3 2 6 -1 2 2 4 2 2 4 6 2 6 0 2 12
2 2 6 4 0 2 3 1 2 6 4 -1 3 2 0 4 2 0 12
3 2 3 2 6 -1 2 2 4 0 0 4 6 1 6 0 0 6 0 12
4 2 2 2 0 4 3 1 -1 2 0 2 3 0 3 0 1 3 4 3 12
3 6 2 2 0 6 4 3 -1 6 2 3 1 4 0 2 4 -1 3 0 4 12
3 6 2 2 2 6 4 3 -1 4 0 3 1 0 2 2 2 0 2 1 4 6 12
4 3 1 3 4 3 3 6 2 3 3 6 4 0 2 3 0 4 1 4 1 3 3 12
3 6 2 2 1 6 4 3 -1 4 2 3 1 0 2 4 0 1 2 1 4 6 6 6 12
4 4 2 2 0 4 3 1 -1 3 2 2 3 1 0 2 1 0 6 0 6 6 4 1 4 12
3 2 3 1 6 1 4 4 2 -1 1 2 6 0 6 -1 0 6 3 6 3 2 2 6 3 3 12
0 4 3 4 4 2 6 3 2 2 4 3 4 0 2 2 0 4 3 4 3 4 4 6 6 3 6 12
0 4 3 4 0 2 6 3 2 4 0 3 2 0 2 0 2 4 3 4 3 2 2 3 2 0 2 6 12
4 3 1 3 4 3 3 6 2 0 0 6 0 0 2 3 0 2 0 4 2 0 3 6 3 0 2 3 3 12
4 0 1 3 6 3 3 6 2 0 3 6 2 3 4 3 0 4 0 2 0 0 0 6 3 0 4 3 0 6 12
6 3 4 3 0 3 0 4 2 6 3 2 3 3 0 3 3 0 6 0 2 3 3 4 3 6 3 0 0 0 0 12
-
DIVISORS (elementary divisors)
1^16 15^16
-
MINIMAL_NORM
12
-
KISSING_NUMBER
4800
-
GROUP_ORDER
2^11 * 3^6 * 5^2
-
GROUP_GENERATORS
5
32
0 0 0 0 0 0 0 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 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 0 0 0 -1 0 0 0 0 0 1
0 0 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 0 0 0 0
1 0 0 0 1 -1 1 2 -2 0 0 -2 1 0 -2 0 0 1 0 1 0 0 0 0 0 0 -1 -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
0 -1 0 -1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 -1 0 -1 0 0 0 0 0 1 0 0 0 0 0 1 1 -1 -1 0 0 -1 0 0 0 1 1 0 1 0 0 0
1 0 0 0 0 -1 1 1 -1 1 0 -1 1 0 -1 0 0 0 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0
0 -1 -1 -1 0 0 0 -1 1 -1 1 0 -1 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1
-1 -1 0 -1 0 2 -1 -1 1 0 0 1 -1 -1 1 1 1 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 1
-1 -1 0 -1 0 1 -1 -1 1 -1 0 1 -1 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1
0 -1 -1 -1 0 1 0 -1 1 -1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1
0 -1 -1 0 0 0 -1 -1 1 -2 2 0 -1 0 1 1 0 0 0 0 0 1 1 0 0 0 0 -1 2 0 0 1
0 0 0 0 1 0 0 1 -1 0 0 -1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0
1 -1 -1 0 0 -1 0 0 0 -1 1 -1 0 0 0 1 1 0 0 0 0 0 1 0 1 0 0 -1 1 0 0 0
-1 0 0 0 0 1 -1 -1 1 0 0 1 -1 0 1 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 1
-2 -1 0 -1 0 2 -1 -1 1 -2 0 1 -1 -1 1 2 1 1 0 0 0 1 0 0 -1 0 0 0 1 0 0 2
0 -1 -1 -1 0 1 0 -1 1 -1 0 1 -1 0 1 1 1 0 1 0 0 0 0 0 0 -1 0 1 0 0 -1 1
0 1 1 0 1 0 1 3 -3 1 -1 -2 2 0 -2 -1 0 1 0 1 0 -1 -1 0 0 0 -2 0 -1 0 0 0
1 0 -1 1 0 -1 1 0 -1 -1 0 -1 0 0 0 0 0 1 1 0 0 1 0 0 0 -1 -1 0 0 0 0 1
0 -1 -1 -1 0 0 0 -1 1 -1 1 0 -1 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1
1 1 0 0 0 -1 1 1 -1 2 -1 -1 1 1 -1 -1 0 0 0 0 0 -1 0 0 0 0 0 0 -1 0 0 -1
-3 -1 1 -3 0 3 -1 -1 2 1 -1 2 -1 -1 1 2 2 -1 -1 0 1 -1 -1 0 -1 1 1 1 0 0 0 1
0 -1 -1 -1 0 0 0 -1 1 -1 0 0 -1 -1 1 2 2 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1
2 -1 -2 1 -1 -2 1 -1 0 -2 2 -1 0 0 0 0 0 1 1 0 -1 2 1 -1 1 -1 0 -1 1 1 0 1
-1 -1 0 -2 0 2 0 0 0 0 -1 0 0 -1 0 2 2 0 0 1 0 0 -1 0 -1 0 0 1 0 0 0 1
-1 -1 0 -2 0 2 0 -1 1 0 -1 1 -1 -1 1 2 2 0 0 0 0 0 -1 0 -1 0 0 1 0 0 0 1
-1 -1 0 -1 0 1 0 -1 1 -1 0 1 -1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1
1 0 0 1 1 -2 1 3 -3 0 0 -2 1 0 -2 0 0 1 0 1 0 0 0 -1 1 0 -1 -1 0 0 0 0
0 -1 0 0 0 0 0 -1 0 0 1 0 0 -1 0 1 0 0 -1 0 0 1 0 -1 0 0 1 -1 1 1 0 1
0 -1 -1 -1 -1 0 0 -2 2 -1 1 1 -1 0 1 1 1 -1 0 0 0 0 1 0 0 0 1 0 1 0 0 1
32
-6 0 2 -3 0 6 -3 -2 4 1 -2 5 -2 -1 3 1 1 -1 0 -1 1 -1 -2 1 -2 1 1 2 -1 0 -1 1
0 0 0 0 0 0 0 1 -1 0 0 -1 1 0 -1 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 1 0 0
-5 1 2 -3 0 6 -3 -3 5 2 -2 6 -2 0 3 0 0 -2 0 -2 1 -2 -2 1 -2 1 2 2 -1 0 -1 0
-3 0 1 -2 0 4 -2 -2 3 0 -1 3 -1 0 2 1 1 -1 0 -1 0 -1 -1 1 -1 1 1 1 0 0 -1 0
0 0 0 -1 0 1 1 0 0 1 -1 0 0 -1 0 1 1 0 0 0 0 0 -1 0 -1 0 0 1 -1 0 0 0
-4 0 1 -2 0 4 -3 -1 3 0 -1 3 -1 0 2 1 1 -1 0 -1 1 -1 -1 1 -1 1 1 1 0 0 -1 0
1 0 -1 0 0 0 0 0 0 -1 0 -1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
-2 0 0 -1 0 3 -1 -1 1 0 -1 1 0 -1 1 1 1 0 0 0 0 0 -1 0 -1 0 0 1 0 0 0 1
-2 0 0 -1 0 3 -1 -3 3 0 -1 3 -1 -1 2 1 1 -1 0 -1 0 0 -1 0 -1 0 1 1 0 0 0 1
0 0 0 1 0 -1 0 1 -1 -1 2 -1 1 0 -1 -1 -1 1 0 0 -1 1 1 -1 1 0 0 -2 1 1 0 0
-2 1 1 0 -1 2 -1 -2 2 1 0 2 0 0 1 -1 -1 0 0 -1 0 0 0 0 -1 0 1 0 -1 1 0 0
-2 0 1 -1 0 2 0 1 -1 0 -1 0 0 -1 0 1 1 1 0 1 0 0 -1 0 -1 0 -1 1 -1 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 0 0 0 0 0 0 0 0 0 0
-2 1 1 0 1 2 -1 1 0 0 0 1 0 0 0 -1 -1 1 1 0 0 0 -1 0 0 0 -1 0 -1 0 -1 0
1 1 0 0 0 0 1 1 -1 2 -1 -1 1 0 -1 -1 0 0 0 0 0 -1 -1 0 0 0 0 1 -1 0 0 -1
-1 0 1 0 0 1 0 0 0 1 1 0 1 0 -1 -1 -1 0 -1 0 0 0 0 -1 0 0 1 -1 0 1 0 0
-3 1 1 -1 0 3 -2 -1 2 0 -1 3 -1 0 2 0 0 0 1 -1 0 -1 -1 1 -1 1 0 1 -1 0 -1 0
-1 1 1 0 0 1 0 0 0 1 -1 1 0 -1 0 0 0 0 0 0 0 0 -1 0 -1 0 0 1 -1 0 0 0
1 -2 -2 0 -1 -1 0 -2 2 -3 3 0 -1 0 1 1 0 0 0 0 -1 2 2 -1 1 0 1 -2 3 1 0 1
-1 -1 0 -2 0 2 0 -1 1 0 -1 1 -1 -1 1 2 2 0 0 0 0 0 -1 0 -1 0 0 2 0 0 0 1
-1 -1 0 -1 0 1 -1 0 1 -1 0 1 -1 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 -1 0
-1 0 0 0 1 1 -1 2 -1 -1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 -1 0 0 0 -1 0
-1 -1 0 -1 0 1 -1 1 0 -1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0
-2 -1 0 -1 0 2 -1 -1 1 -1 0 1 -1 -1 1 2 1 0 0 0 0 1 0 0 -1 0 1 0 1 0 0 1
0 0 0 0 0 0 0 1 -1 1 0 -1 1 0 -1 0 0 0 -1 0 0 0 0 -1 0 0 1 0 0 1 0 0
2 -1 -1 1 0 -2 1 2 -2 -1 1 -3 1 0 -1 0 0 1 0 1 -1 1 1 -1 1 0 -1 -1 1 1 0 0
0 -1 -1 -1 0 1 0 -1 1 -1 0 0 -1 -1 1 2 1 0 0 0 0 1 0 0 -1 0 0 1 1 0 0 1
0 0 0 -1 0 1 0 0 0 0 -1 0 0 0 0 1 1 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 0
0 0 0 -1 0 0 0 0 0 -1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
-1 -1 0 -2 0 2 0 0 0 0 -1 0 0 -1 0 2 2 0 0 1 0 0 -1 0 -1 0 0 1 0 0 0 1
-1 0 0 -1 0 2 0 0 0 1 -1 0 0 -1 0 1 1 0 0 1 0 0 -1 0 -1 0 0 1 -1 0 0 0
0 -1 -1 1 0 -1 0 0 0 -2 2 -1 0 0 0 0 -1 1 0 0 -1 2 1 -1 1 0 0 -2 2 1 0 1
32
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 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 0 0 0 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
-1 0 1 -1 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
1 0 0 0 1 -1 1 2 -2 0 0 -2 1 0 -1 0 0 1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0
-1 0 1 0 0 1 -1 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 1 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 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 -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 1 0 -1 0 0 0 -1 2 0 0 0 0 -1 -1 0 0 0 0 1 1 0 1 0 0 -2 1 0 0 0
1 -1 -1 0 0 -1 0 0 0 -2 1 -1 0 0 0 1 1 0 0 0 0 1 1 0 1 0 0 -1 2 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 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 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 0 0 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 -1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -1 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
1 0 0 1 -1 -2 1 -1 0 0 2 -1 1 0 -1 -1 -1 0 -1 0 0 1 1 -1 1 0 1 -2 1 1 1 0
0 0 0 0 0 0 0 -1 1 0 0 1 -1 0 1 0 0 0 0 -1 0 0 0 0 0 0 1 0 0 0 0 0
-1 0 1 0 -1 1 -1 -2 2 1 1 2 0 0 1 -1 -1 -1 -1 -1 0 0 0 -1 0 0 2 0 0 1 0 0
0 1 1 1 0 0 0 1 -1 2 0 0 1 0 -1 -2 -1 0 0 0 0 -1 0 0 0 0 0 0 -1 0 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
-1 -1 0 -1 0 1 -1 0 1 -1 0 1 -1 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 1 -1 0 0
-1 -1 0 0 0 1 -1 -1 1 -1 1 1 -1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1
2 -1 -1 1 -1 -2 1 0 -1 -1 2 -2 1 -1 -1 0 0 1 0 1 -1 2 1 -2 1 -1 0 -1 1 1 1 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
1 0 0 0 0 -1 1 1 -1 1 0 -1 1 1 -1 -1 0 0 0 0 0 -1 0 0 1 0 0 0 0 0 0 -1
0 1 1 1 0 -1 1 1 -1 1 0 0 1 1 -1 -2 -1 0 0 0 0 -1 0 0 1 0 0 -1 -1 0 0 -1
1 0 0 0 0 -1 1 1 -1 1 0 -1 1 0 -1 0 0 0 -1 0 0 0 0 -1 0 0 0 0 0 0 1 0
3 -1 -1 1 0 -3 2 2 -3 0 1 -4 2 0 -2 0 0 1 -1 1 -1 1 1 -1 1 0 -1 -1 1 1 1 0
-1 -2 -1 -1 -1 1 -1 -3 3 -3 2 2 -2 -1 2 2 1 0 0 0 0 2 1 0 0 0 1 -1 2 0 0 2
32
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 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 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 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 -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
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 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 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 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 -2 -1 -1 0 1 -1 -2 2 -3 1 1 -2 -1 2 3 2 0 0 0 0 2 0 0 0 0 0 0 2 0 0 2
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 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 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 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 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
1 0 0 0 1 -1 1 2 -2 0 0 -2 1 0 -1 0 0 1 0 1 0 0 0 0 0 0 -2 0 0 0 0 0
2 -2 -2 1 0 -2 1 0 -1 -4 2 -2 -1 -1 0 2 1 2 1 1 -1 3 1 -1 1 -1 -1 -1 2 0 0 2
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
3 0 -1 1 1 -2 2 2 -3 0 0 -3 1 0 -2 0 0 1 0 1 0 0 0 -1 1 -1 -1 0 0 0 0 0
0 0 0 -1 0 1 0 0 0 0 -1 0 0 0 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 1 0 0 0
-1 -1 0 -1 0 1 -1 0 1 -1 0 1 -1 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 -1 0
1 -1 -1 0 0 -1 0 0 0 -2 1 -1 0 0 0 1 1 0 0 0 0 1 1 0 1 0 0 -1 2 0 0 0
5 0 -2 3 0 -5 3 2 -4 -1 2 -5 2 0 -3 -1 -1 2 0 1 -1 2 1 -2 2 -1 -1 -2 1 1 1 0
1 0 0 0 0 -1 1 2 -2 0 0 -2 1 0 -1 0 0 1 0 1 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
-2 -1 0 -1 0 2 -1 -2 2 -2 0 2 -2 -1 2 2 1 0 0 0 0 1 0 0 -1 0 0 1 1 0 0 2
-1 0 0 0 0 1 -1 0 1 -1 0 2 -1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 -1 0
2 -1 -1 1 0 -2 1 2 -2 -1 1 -2 1 0 -1 0 0 1 0 1 -1 1 1 -1 1 0 -1 -1 1 0 0 0
1 -1 -1 1 0 -2 0 0 0 -3 2 -1 -1 0 0 1 0 1 0 0 0 2 1 0 1 0 0 -2 2 0 0 1
32
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 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 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 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
1 0 0 0 1 -1 1 2 -2 0 0 -2 1 0 -1 0 0 1 0 1 0 0 0 0 0 0 -2 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 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 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 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 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 0 0 0 0 0 0 0 0 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 -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
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 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 0 0 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 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 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 -1 2 -1 -4 3 1 -3 0 1 -4 2 0 -2 -1 0 1 0 1 -1 1 1 -1 1 -1 -1 -1 0 1 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
3 0 -1 2 -1 -3 2 -1 -1 0 2 -2 1 0 -1 -1 -1 0 -1 0 0 1 1 -1 1 -1 1 -2 1 1 1 0
0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 -1 1 0 0 0
0 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -1 1 0 0 0
-1 -1 0 -1 0 1 -1 0 1 -1 0 1 -1 0 1 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 -1 0
1 -1 -1 0 0 -1 0 0 0 -2 1 -1 0 0 0 1 1 0 0 0 0 1 1 0 1 0 0 -1 2 0 0 0
2 0 -1 1 -1 -2 1 -1 0 -1 1 -1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 -1 1 0 1 0
1 0 0 0 0 -1 1 2 -2 0 0 -2 1 0 -1 0 0 1 0 1 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
-1 1 1 0 0 1 0 0 0 1 -1 1 0 0 0 -1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
3 -1 -1 1 0 -3 2 2 -3 0 1 -4 2 0 -2 0 0 1 -1 1 -1 1 1 -1 1 0 -1 -1 1 1 1 0
1 -1 -1 0 -1 -1 0 -1 1 -2 1 0 -1 0 1 1 1 0 0 0 0 1 1 0 0 0 0 0 1 0 0 1
-
PROPERTIES
INTEGRAL = 1
MODULAR = 15
-
REFERENCES
G. Nebe, Finite quaternionic matrix groups,
Representation Theory 2, 106-223 (April 1998)
-
NOTES
strongly modular lattice
-
URL (links to other sites for this lattice)
All the quaternionic matrix groups
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe