The Lattice SL2(11)Q8D8.Alt5.2
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 13:14:50 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(11)Q8D8.Alt5.2
-
DIMENSION
40
-
GRAM (floating point or integer Gram matrix)
40 0
6
2 6
3 2 6
3 3 3 6
2 2 3 1 6
2 2 2 2 3 6
3 1 1 2 1 1 6
1 1 1 1 1 2 1 6
1 2 3 0 3 1 1 2 6
3 1 1 2 1 0 2 3 2 6
3 3 2 3 1 2 3 2 1 1 6
2 1 1 2 3 2 2 2 1 1 2 6
1 2 1 1 3 3 2 2 2 2 2 1 6
2 2 3 2 2 3 2 1 3 1 2 1 1 6
3 1 2 1 3 1 2 2 1 3 2 2 2 0 6
1 2 2 1 3 0 2 1 3 3 0 2 3 1 2 6
2 1 2 2 2 3 1 3 1 2 2 1 3 2 1 1 6
2 2 1 1 2 1 2 3 3 3 3 1 2 1 3 1 1 6
2 3 2 2 1 1 1 0 0 1 2 0 1 2 2 1 -1 1 6
2 1 1 1 2 3 2 3 2 2 1 1 1 3 2 0 3 2 0 6
0 1 1 0 -1 -1 1 -1 0 -1 1 -1 -1 1 0 0 -1 -1 2 0 6
-1 1 0 0 -1 -1 -1 0 0 -1 -1 -1 -1 0 -1 -1 -1 -1 1 0 2 6
0 2 1 1 0 -1 0 0 1 0 1 1 0 0 0 1 -1 0 2 -1 3 3 6
1 0 1 1 -1 -1 0 -1 -1 0 1 -1 -1 0 1 -1 0 0 2 0 3 1 2 6
0 0 1 -1 1 0 -1 -1 1 -1 -1 -2 0 0 0 -1 0 0 0 1 1 2 0 1 6
-1 0 1 0 0 -1 -2 -1 0 -1 -1 -1 0 0 -1 0 1 -2 0 -1 1 3 2 2 2 6
0 1 0 0 -1 -1 -1 0 0 0 0 -2 0 0 -1 0 1 -1 0 0 1 2 0 1 1 3 6
2 1 3 1 1 0 1 0 2 1 0 0 0 1 1 2 0 1 1 0 1 0 1 1 1 0 0 6
1 2 2 1 1 0 1 0 1 0 2 0 1 1 1 1 -1 1 3 -1 3 1 3 1 1 0 0 2 6
1 0 1 1 -2 -1 0 -1 -1 -1 0 -1 -2 0 -1 -1 -1 -1 1 -1 2 2 1 3 0 1 2 3 1 6
0 1 2 1 1 0 0 -2 1 -1 0 0 0 1 0 1 0 -1 1 0 3 1 3 3 2 3 0 2 1 1 6
1 1 0 0 0 -1 0 1 0 0 1 0 0 -1 0 0 1 1 0 0 0 1 1 1 1 1 3 1 1 2 -1 6
1 1 2 1 -1 0 1 0 1 0 1 0 0 1 -1 1 0 -1 1 -1 3 1 3 1 -1 1 1 3 2 3 2 0 6
1 1 1 0 0 -1 -1 0 1 1 0 -1 0 -1 0 1 0 1 1 -1 0 0 2 2 1 1 2 3 1 2 1 3 2 6
1 0 2 0 0 -1 1 -1 1 0 1 -1 0 1 0 0 0 0 1 -1 3 1 2 2 2 2 0 2 3 1 2 0 3 1 6
2 0 1 1 0 -1 1 1 0 1 1 0 -1 0 1 -1 0 1 1 1 1 2 1 2 2 0 1 1 2 2 -1 3 0 1 2 6
0 0 2 1 -1 0 -1 1 1 0 0 -1 -1 1 -1 -1 0 0 1 0 1 3 2 2 1 2 1 2 1 3 1 0 3 2 2 2 6
0 0 -1 -1 0 0 0 -1 -1 -1 -1 -1 0 0 0 -1 0 -1 1 1 1 3 0 2 2 2 2 -1 -1 1 1 1 -1 0 0 1 0 6
1 1 1 0 0 -1 0 -1 0 -1 1 0 0 -1 0 0 -1 -1 1 -2 2 2 3 1 1 2 2 1 3 2 1 2 3 2 3 2 1 1 6
0 1 1 0 -1 0 -1 0 0 0 0 -2 0 1 -1 0 1 0 1 -1 1 1 0 1 0 2 2 2 1 2 0 1 2 2 2 -1 2 0 0 6
-
DIVISORS (elementary divisors)
1^32 11^8
-
MINIMAL_NORM
6
-
KISSING_NUMBER
13200
-
GROUP_ORDER
2^10 * 3^2 * 5^2 * 11
-
GROUP_GENERATORS
3
40
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 4 -4 1 -1 -1 -1 -1 1 -1 2 1 2 1 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 1 1 -2 0 -1 0 -1 0 0 -1 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 0 0 1 -1 -1 -1 -1 0 -1 0 0 2 0 0 1 0 1 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 3 -4 1 -1 1 -2 -1 1 -1 1 0 2 2 -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 -1 0 0 -1 1 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 -2 2 -1 0 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 0 0 0 0 0 0 0 0 1 -1 0 -1 0 0 0 0 0 1 0 0 -1 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 -1 0 0 0 -1 0 0 0 1 0 0 0 -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 0 0 -1 0 -1 0 0 0 -1 0 1 1 0 0 0 0 1 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 -1 0 0 0 0 1 1 -1 0 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 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 -1 0 0 0 -1 -1 0 0 1 0 1 0 -1 1 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 -1 0 0 0 0 0 1 0 -1 -1 0 0 1 0 1 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 -3 1 -1 0 -1 -1 1 -1 1 1 1 1 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 -1 -1 0 0 1 0 1 0 -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 0 1 -1 1 -1 0 0 0 0 -1 1 0 -1 -1 0 0 1 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 2 -3 0 -1 0 -1 -1 1 0 2 1 0 1 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 -3 0 -1 0 -1 -1 1 -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 -1 1 -1 0 0 0 0 0 1 0 -1 -1 0 0 1 0 0 0 1
0 0 3 -1 -1 -1 -2 -1 -3 1 1 1 2 0 -2 1 -2 1 -1 3 0 0 0 0 -1 -1 0 1 0 -1 0 1 -1 -1 1 -1 1 1 1 0
0 -1 -3 2 0 1 0 0 3 -1 0 -1 -2 0 2 0 2 -1 1 -2 0 2 -2 0 0 0 -1 0 1 -1 0 1 2 1 0 0 -1 0 -1 -1
0 0 2 -1 -1 -1 -2 -1 -3 1 1 1 2 1 -1 1 -2 1 -1 2 0 2 -3 0 -1 -1 -1 0 0 -2 2 2 1 0 0 0 1 0 1 0
1 -1 0 1 -1 0 -1 0 0 -1 0 0 1 0 0 1 -1 0 0 1 1 0 0 -1 -1 -1 0 0 -1 -1 1 1 -2 0 1 0 1 0 1 1
1 -1 -3 2 0 0 0 1 3 -2 0 -1 -1 0 1 0 1 -1 1 -1 0 3 -4 1 -1 1 -2 0 1 -2 1 0 2 2 -1 1 -2 -1 0 0
1 -1 -2 2 0 0 -1 1 1 -2 0 -1 0 1 1 1 0 0 0 -1 1 1 -1 0 0 0 -1 0 -1 -1 0 0 1 1 0 1 -1 0 0 0
0 -1 -2 2 1 0 0 1 2 -1 0 -1 -1 0 1 0 1 -1 1 -1 0 0 1 0 1 -1 0 0 -1 1 -1 0 0 0 1 -1 -1 0 0 0
0 -1 -1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 -1 0 0 -1 1 0 0 0 -2 1 0 0 2 2
0 1 4 -2 -1 -2 -2 -1 -4 2 1 2 3 1 -2 0 -3 1 -2 3 0 4 -6 1 -2 0 -2 -1 2 -2 2 2 2 2 0 -1 0 0 0 -1
0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 3 -1 1 -1 1 1 -1 0 -1 0 -2 -1 0 -1 1 1 1 1
1 -1 1 0 -1 -1 -2 0 -2 -1 1 0 2 1 -1 2 -2 1 -1 2 0 1 -1 0 -1 -1 -1 0 -1 -2 2 0 0 0 -1 2 0 0 2 2
1 -1 -3 2 1 0 0 1 2 -1 0 -1 -1 0 1 0 1 -1 1 -1 1 2 -2 0 0 0 -1 0 0 0 0 1 0 1 1 -2 0 -1 0 -1
-1 0 3 -1 0 -1 -1 -1 -3 2 1 1 2 0 -2 0 -2 1 -1 2 1 -4 4 -1 1 -1 1 2 -2 0 -1 0 -2 -3 -1 0 2 2 2 2
0 -1 -1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 -2 0 0 0 -1 0 -1 -1 1 1 0 0 -1 0 0 -1 2 1
0 0 1 0 0 0 -1 0 -1 1 1 0 1 0 -1 0 -2 0 -1 1 1 0 -1 0 -1 1 -1 1 0 -1 0 1 0 0 0 0 0 1 0 0
0 0 -1 1 0 0 0 0 1 0 0 0 0 0 1 -1 0 -1 0 0 1 1 -2 -1 -1 1 -1 0 1 0 0 1 0 2 1 -1 0 0 -1 -1
-1 0 1 0 -1 0 0 -1 0 1 0 1 1 0 0 -1 0 0 0 0 2 -2 1 -2 0 0 0 1 -1 0 0 0 -2 0 -1 1 1 1 1 1
1 -2 -6 4 1 2 1 1 6 -3 0 -3 -4 -1 3 1 3 -2 2 -3 0 0 1 0 1 1 -1 0 0 0 -2 0 1 0 0 0 -1 0 -1 0
0 0 1 0 1 -1 -1 0 -2 1 1 0 1 1 -1 0 -2 0 -1 1 0 2 -2 2 0 0 -1 1 0 -2 -1 2 2 0 0 -2 0 0 0 -1
0 -1 -1 1 0 1 0 0 2 0 0 0 -1 -1 0 0 1 0 1 -1 1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0
40
-1 0 0 0 0 0 0 -1 0 1 1 0 0 0 0 0 0 0 0 0 0 -2 2 0 1 0 0 1 -1 0 -1 0 0 -2 -1 0 1 1 1 1
-1 0 2 -1 0 -1 0 -1 -2 1 0 1 1 0 -1 0 0 1 0 1 -1 0 1 1 1 -1 1 0 0 0 -1 0 1 -1 0 -1 0 0 0 0
-1 -1 -2 1 1 1 1 0 2 0 1 -1 -2 -1 1 0 1 -1 1 -1 -1 -3 4 0 2 0 1 1 -1 1 -2 -1 0 -2 0 0 0 1 0 1
0 -1 -1 1 1 0 0 0 0 0 1 -1 -1 0 0 1 0 0 0 0 -1 0 1 1 1 0 0 0 0 0 -1 0 1 -1 0 -1 0 0 0 0
-1 0 1 -1 0 0 0 0 -1 1 1 0 0 0 0 0 0 0 0 0 -1 -2 3 -1 1 -1 1 0 -1 1 0 -1 0 -1 0 1 0 1 0 1
-1 -1 0 0 0 1 0 -1 1 1 1 0 -1 -1 0 0 1 0 1 0 -1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 -1 0 0 0
0 0 2 -1 -1 -1 -2 -1 -3 1 1 1 2 1 -1 1 -2 1 -1 2 0 0 0 0 0 -1 0 0 -1 -1 1 1 0 -1 0 0 1 0 1 1
-1 0 2 -1 -1 0 -1 -1 -2 1 1 1 1 0 -1 1 -1 1 -1 2 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 0 0 1 0 0 0 0 0 0 -3 3 -1 1 0 1 0 -1 1 -1 -1 0 -1 0 1 0 1 0 1
0 0 0 0 0 -1 -1 0 -1 0 1 0 1 1 0 1 -1 0 -1 1 0 0 -1 0 0 0 -1 -1 0 0 1 0 1 0 -1 1 0 0 1 1
-1 0 3 -1 0 -1 -1 -1 -3 2 1 1 2 0 -2 0 -2 1 -1 2 0 -2 3 0 1 -1 1 1 -1 0 -1 0 -1 -2 0 -1 1 1 1 1
-1 1 4 -2 -1 -1 -1 -1 -4 2 1 1 2 1 -1 0 -2 1 -2 2 0 -1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0
0 -1 0 0 0 0 -1 0 0 0 1 0 0 0 0 1 0 0 0 0 -1 1 0 0 0 -1 0 -1 0 0 1 0 1 0 0 1 -1 0 0 1
-1 0 2 -1 0 -1 -1 -1 -2 1 1 1 1 0 -1 0 -1 1 0 2 -1 1 -1 1 0 0 0 0 0 -1 0 0 2 0 0 0 -1 0 0 0
-1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 -1 0 0 0 -2 2 -1 1 -1 0 0 -1 1 0 0 -1 -1 0 0 1 1 1 1
0 0 1 -1 0 -1 -1 0 -2 0 1 0 1 1 0 1 -1 0 -1 1 -1 0 0 0 0 -1 0 -1 0 0 1 0 1 0 0 1 0 0 0 1
-1 0 3 -2 0 0 -1 -1 -3 2 2 1 1 0 -2 1 -2 1 -1 2 -1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 -1 0 0 0
-1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 -3 3 -1 1 -1 1 0 -1 1 0 0 -1 -2 0 0 1 1 1 1
0 -1 -1 1 0 -1 0 0 1 -1 0 0 0 0 0 0 1 0 1 0 -1 0 0 1 1 -1 0 0 0 -1 0 0 1 -1 -1 0 0 0 1 1
-1 0 2 -1 -1 0 -1 -1 -2 1 1 1 1 0 -1 1 -1 1 0 2 0 0 0 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 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 3 -3 2 0 1 -1 0 1 -1 -1 1 2 1 0 -1 -1 -1 -1 -2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 -2 0 1 0 0 -1 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 -2 2 0 1 0 0 0 0 1 -1 0 -1 -1 0 -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 -2 3 0 1 0 1 1 -1 1 -2 -1 -1 -1 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 -1 1 0 1 -1 0 1 0 -1 0 1 1 0 0 -1 0 -1 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 -3 2 -1 0 -1 0 1 -1 0 1 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 -3 3 0 1 0 1 1 -1 1 -2 0 -1 -2 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 -1 0 1 1 1 -1 1 0 0 0 -1 0 0 -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 1 0 0 0 1 0 0 -1 1 -1 -1 1 -2 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 -2 2 0 1 1 0 0 0 1 -2 -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 1 1 0 -1 1 1 0 0 -1 1 -1 -1 1 -2 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 -1 1 1 1 1 0 1 0 0 -2 0 0 -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 -3 3 0 1 0 1 1 0 1 -2 0 -1 -2 0 -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 -3 4 0 2 0 1 1 -1 1 -2 -1 -1 -2 0 0 0 1 0 1
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 -1 1 1 -1 0 -1 0 -1 -2 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 -1 1 1 1 1 0 1 0 0 -2 0 0 -1 0 -1 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 1 0 0 -1 0 0 -1 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 0 1 1 1 0 0 1 0 0 -2 0 0 -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 -1 1 -1 1 0 0 0 0 1 0 0 1 1 0 1 -1 -1 0 -1 -1
40
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 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 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 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 1 1 -1 0 0 1 0 0 1 0 0 0 0 0 -1 0 -1 0 0 0 -1 1 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0
0 1 1 0 0 -1 0 1 -1 0 -1 0 1 1 0 -1 -1 0 -1 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
-1 1 2 -1 0 -1 0 0 -1 1 0 1 1 0 -1 -1 -1 0 0 1 -1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 -1 0 0 0
-1 1 2 -1 -1 -1 0 -1 -1 1 0 1 1 0 0 -1 0 0 0 1 0 -2 1 -1 0 0 0 0 0 1 0 0 -1 0 0 0 1 1 0 0
0 1 2 -1 1 -1 0 0 -2 1 0 0 1 0 -1 -1 -1 0 -1 1 0 -2 3 0 1 0 1 1 0 1 -2 0 -1 -1 1 -2 1 1 -1 -1
0 1 2 -1 0 -2 -1 0 -2 1 0 1 2 1 -1 -1 -1 0 -1 1 0 2 -3 1 -1 0 -1 0 1 -1 1 1 1 1 0 -1 0 0 0 -1
1 0 -2 1 0 0 0 1 2 -1 0 -1 -1 0 1 0 1 -1 0 -1 0 2 -3 0 -1 1 -1 -1 2 0 1 0 1 2 0 0 -1 0 -1 -1
0 0 1 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 1 -1 0 0 1 1 -1 -1 0 -1 -1
0 0 0 0 1 0 0 1 0 0 1 -1 0 0 0 0 -1 -1 0 0 -1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 -1 0 -1 0
0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 -1 0 0 0 0 0 1 0 0 -1 0 0 0 0 1 0 0
-1 1 2 -1 0 -1 0 -1 -1 1 0 1 1 0 -1 -1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 -1 0 0 0 0 -1 0 0 0 -1
1 0 0 0 0 -1 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 -1 1 -1 0 0 0 0 -1 1 0 1 0 1 1 0 0 -1 0 -1 0
-1 0 0 0 0 1 1 0 2 1 0 0 -1 -1 0 -1 1 -1 1 -1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 -1 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 -1 -1 0 0 1 0 1 0 -1 1 -1 0 0 0 0 -1 1 1 0 0 1 1 1 -1 -1 0 -1 -1
-1 1 1 -1 1 0 1 0 0 2 0 0 0 0 0 -2 0 -1 0 -1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 -1 0 0 -1 -1
0 0 -1 1 1 0 1 1 1 0 0 -1 -1 0 1 -1 0 -1 0 -1 0 -2 2 -1 1 1 0 0 0 1 -1 0 0 0 0 0 0 1 -1 0
-1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 -1 1 -1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0
1 0 -3 2 0 0 1 1 3 -2 -2 -1 -1 0 2 -1 2 -1 1 -2 1 -2 1 -1 0 0 0 0 0 0 0 0 -1 0 0 0 1 1 0 0
0 0 -2 1 1 1 1 1 3 0 0 -1 -2 -1 1 -1 1 -2 1 -2 -1 1 -1 1 0 0 0 0 1 0 0 1 1 0 1 -1 -1 0 -1 -1
0 1 3 -2 -1 -1 -1 0 -3 1 0 1 2 1 -1 0 -1 1 -1 1 0 1 -1 -1 -1 -1 0 -1 0 1 2 0 -1 1 1 0 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
Haftungsausschluss/Disclaimer
Gabriele Nebe