The Lattice U3(5).3C3.2
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 13:14:48 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
U3(5).3C3.2
-
DIMENSION
40
-
GRAM (floating point or integer Gram matrix)
40 0
8
2 8
-2 -4 8
4 0 -4 8
1 0 2 -1 8
0 0 -1 2 2 8
0 -2 2 -1 2 1 8
4 1 -1 2 -1 -2 2 8
2 0 -2 4 1 -1 1 4 8
2 1 1 -1 1 -2 -1 -2 -2 8
-2 -3 2 -1 0 -2 4 0 0 1 8
0 4 -1 -1 1 -2 0 0 1 4 1 8
-2 1 0 -1 -2 -1 -3 -2 -3 -2 0 -1 8
0 3 -2 -2 -2 0 1 -1 -1 0 -1 1 0 8
1 -2 1 1 -1 0 0 0 -1 0 2 -2 1 -1 8
2 0 -1 3 1 4 0 0 1 -2 -2 -2 -1 -1 2 8
0 0 1 1 -1 -1 -1 1 1 0 1 2 0 -2 2 1 8
0 0 0 0 -1 2 1 -1 -1 -1 -1 0 -1 2 1 2 3 8
-1 -1 1 -2 -1 0 2 0 -2 1 1 0 -1 1 2 0 2 4 8
1 1 -1 0 -1 0 -3 0 0 2 -2 1 0 1 1 0 2 2 2 8
-1 -2 2 0 1 0 1 1 2 0 2 0 0 -2 1 0 2 1 3 1 8
1 2 -2 0 0 -2 0 2 2 -1 -2 0 0 1 0 0 1 0 1 1 3 8
0 -1 0 2 -2 -2 -1 1 2 -1 1 0 2 -1 2 0 4 3 1 2 4 3 8
0 0 0 0 -1 -1 -1 -1 -2 1 1 -1 2 0 1 0 2 2 1 2 2 2 4 8
1 -2 0 1 0 -2 0 0 0 1 0 0 0 -2 4 0 3 1 3 2 1 3 3 1 8
-1 -1 1 0 2 1 -1 -1 1 0 -2 1 -1 -1 0 1 1 2 2 3 4 2 2 2 2 8
0 0 -2 1 1 3 -1 0 0 -2 -1 -1 1 -1 0 2 2 2 1 4 2 2 2 2 1 2 8
1 2 -2 0 0 -1 0 1 2 1 1 2 -1 2 1 1 3 1 2 2 2 3 1 1 1 0 2 8
1 1 -1 2 0 2 1 1 1 -2 -1 0 0 1 0 2 2 3 0 2 2 3 4 2 1 2 4 2 8
2 1 -1 0 -1 -2 1 1 0 1 0 0 1 2 2 0 1 2 4 1 1 3 2 2 3 0 0 4 1 8
1 1 -1 2 0 0 0 1 0 -1 0 -1 0 0 1 2 3 1 1 0 1 3 2 2 2 0 2 4 4 2 8
2 1 0 -1 1 1 1 1 -1 0 -1 0 1 1 0 1 1 1 0 2 2 4 2 4 1 2 4 2 4 2 2 8
1 1 0 1 0 1 0 1 1 0 -1 -1 -2 1 2 2 2 2 1 2 1 2 1 2 1 1 0 4 2 2 4 1 8
0 1 1 -1 0 -1 -2 0 -2 0 -2 -1 2 -1 2 0 1 1 0 2 1 2 2 2 2 1 2 0 2 0 2 2 2 8
-1 -1 0 -1 0 -2 0 -1 -1 2 2 0 -1 0 2 -1 1 0 1 1 1 2 2 4 3 1 0 2 1 1 3 2 3 1 8
0 0 -1 2 2 1 -1 0 2 -1 0 1 -1 -2 1 2 4 1 -1 2 1 1 2 1 2 2 4 2 3 -2 3 1 2 2 1 8
-1 0 0 0 0 2 -1 0 -1 -1 0 0 0 -1 2 2 3 2 2 2 1 0 1 0 1 1 4 1 2 1 1 1 1 2 -1 3 8
0 -2 -1 1 1 0 1 -1 1 -1 2 0 0 0 3 1 1 1 1 1 0 0 1 0 3 1 2 1 1 1 0 0 -1 -2 2 2 0 8
2 0 0 0 0 -2 -1 2 2 0 -1 0 -1 0 1 0 4 2 2 2 2 2 2 1 2 1 1 4 1 2 2 1 2 1 1 2 -1 2 8
2 0 0 0 0 -2 1 2 1 0 0 0 1 0 2 0 2 2 2 2 2 4 4 3 4 1 1 2 2 4 1 3 2 1 1 0 0 1 2 8
-
DIVISORS (elementary divisors)
1^20 5^20
-
MINIMAL_NORM
8
-
KISSING_NUMBER
10500
-
GROUP_ORDER
2^6 * 3^4 * 5^3 * 7
-
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
-1 -1 0 -1 0 3 -2 3 2 3 2 -1 2 0 -1 0 0 2 0 0 -2 2 -1 0 0 1 -2 0 0 0 1 0 -1 1 0 0 0 1 0 0
-4 2 1 2 1 0 -3 3 0 3 3 -3 0 2 0 1 1 1 0 -2 -1 0 -1 -2 1 1 2 -1 1 2 -2 1 0 0 0 1 -2 -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 1
0 0 -1 -1 0 0 1 0 1 2 0 -2 1 0 0 0 1 0 0 0 -1 0 1 -1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 0 0 0 0 0 0 1 0 1 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 1 1 2 0 -1 -1 -1 -2 -2 1 0 -2 1 0 0 1 -1 0 0 1 -1 0 -2 -1 0 1 -1 0 2 -1 1 0 0 1 1 -1 -1 0 1
0 1 0 1 0 -1 0 -1 -1 -1 0 0 -1 0 0 0 0 0 0 0 1 -1 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1
0 0 0 1 0 -1 0 -1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -1 -1 0 0 0 0 -1 0 1 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 1 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 2 1 -3 0 -2 -3 -3 -1 1 -3 1 1 0 1 -2 0 0 2 -2 1 -1 0 -1 2 -1 0 1 -1 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 0 0 0 0 0 0 -1 0 0 0 1 0 -1 0 0 0 0 0 0 0
0 0 0 -1 0 1 0 1 1 1 0 0 1 0 0 0 0 1 -1 0 0 1 -1 1 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1
2 -1 1 0 -1 1 1 -1 0 -2 -1 2 0 -1 0 -1 -1 0 0 1 0 1 0 1 -1 0 -1 1 -1 0 1 -1 -1 0 1 0 1 0 0 0
-2 0 1 1 1 1 -2 2 1 2 1 -1 1 1 0 0 0 1 0 -1 -1 1 -1 0 1 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0
0 -1 0 -1 0 1 0 1 0 1 0 0 1 0 0 0 0 1 -1 0 0 1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0
-4 0 0 -1 1 2 -4 5 4 7 3 -3 3 2 0 1 1 3 0 -3 -2 1 -3 0 2 1 1 -2 2 0 0 0 0 0 -1 0 -1 0 0 0
0 -1 0 -1 0 1 0 1 1 1 0 0 1 0 0 0 0 1 -1 0 0 1 -1 1 0 0 -1 0 0 0 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 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 1 0 0 0
2 -1 1 0 -1 1 2 -1 0 -1 -1 2 1 -1 0 0 -2 0 0 1 -1 2 1 1 -1 0 -1 1 -1 -1 1 -2 -1 0 1 0 2 0 1 0
-1 0 0 0 0 1 0 1 1 2 0 -1 1 0 0 0 0 1 0 0 -1 1 0 0 0 0 -1 1 0 -1 0 0 -1 0 0 0 1 0 0 0
0 -2 0 -3 -1 5 -2 3 5 5 2 -1 4 0 -1 0 0 2 1 -1 -3 3 -2 1 0 1 -2 0 1 -1 1 -1 -1 1 0 0 1 1 0 0
0 -1 0 -1 0 2 0 1 2 2 0 0 2 0 0 0 0 1 0 0 -1 2 -1 1 0 0 -1 0 0 -1 1 -1 -1 0 0 0 1 0 0 0
2 -1 0 -2 -1 2 1 0 1 0 -1 1 1 0 0 0 0 0 -1 0 0 1 0 1 0 0 0 0 -1 0 1 -2 -1 0 1 0 1 0 0 0
1 -1 0 -1 0 1 0 0 2 1 0 0 2 0 0 0 0 0 1 0 -1 1 -1 1 0 0 -1 0 1 -1 0 -1 0 0 0 0 1 0 0 0
2 -1 0 -1 -1 1 3 -1 0 -1 -2 1 1 -1 0 0 -1 0 -1 2 0 1 1 1 -1 0 -2 2 -1 -1 1 -2 -2 0 1 0 2 0 0 0
2 -1 0 -1 -1 1 3 -1 0 0 -2 1 1 -1 0 0 -1 0 -1 1 0 1 1 1 -1 0 -1 1 -1 -1 1 -2 -1 0 1 0 2 0 1 0
0 -1 0 -1 0 1 -2 1 2 2 1 0 1 0 0 0 0 1 1 -1 -1 1 -1 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0
2 -1 1 0 -1 2 1 -1 -1 -2 0 2 0 -1 0 0 -1 0 -1 2 0 2 0 0 -2 0 -1 0 -1 1 1 -2 -2 0 2 1 1 -1 1 1
1 -1 -1 -2 0 0 -1 0 2 1 0 0 1 0 0 0 1 0 1 -1 0 0 -1 0 0 0 0 -1 1 0 0 0 1 0 0 0 0 0 -1 0
0 -1 -1 -2 0 2 -1 2 2 3 1 -1 2 0 0 0 1 1 0 -1 -1 1 -1 0 0 1 0 -1 1 0 0 -1 0 0 0 0 0 0 0 0
1 -1 0 -2 -1 2 1 1 2 2 -1 0 2 0 0 0 0 1 -1 0 0 1 -1 1 0 0 0 0 0 0 1 -2 -1 0 1 0 1 0 0 0
0 -1 0 -1 0 1 -2 1 2 1 1 0 1 0 0 0 0 1 1 -1 -1 1 -1 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0
-1 -1 1 0 0 4 -1 3 2 3 2 -1 3 0 -1 0 -1 2 0 0 -3 3 -1 0 0 1 -2 1 0 0 0 -1 -2 1 1 1 1 0 1 0
5 -1 -1 -1 -1 -2 5 -5 -2 -5 -5 3 -1 -2 1 -1 0 -3 0 2 2 -1 2 1 -2 -1 0 1 -1 -1 1 -2 0 -1 1 -1 2 0 0 0
0 -1 0 -1 0 2 0 1 2 2 0 0 2 0 0 0 -1 1 0 0 -1 1 0 1 0 0 -1 0 0 -1 1 -1 -1 0 0 0 1 0 1 0
-1 -1 -2 -2 1 -1 1 1 2 3 -2 -1 2 0 1 0 0 1 0 -1 0 -1 0 1 1 0 0 0 1 -2 1 0 1 -1 -1 -1 1 0 0 -1
4 0 2 2 -1 -1 3 -5 -4 -7 -2 4 -3 -1 0 0 -1 -3 -1 3 2 0 2 0 -2 -1 0 1 -2 1 0 -2 -1 0 2 0 1 -1 1 1
-3 1 3 2 0 4 -4 4 2 4 5 -2 2 1 -2 1 -1 3 0 -1 -3 3 -2 -1 1 1 -1 0 0 1 -1 0 -2 1 1 1 0 0 1 1
2 -1 0 -2 -1 1 0 -1 2 0 0 1 1 0 0 0 0 0 0 0 0 1 -1 1 0 0 0 -1 0 0 1 -1 0 0 0 0 1 0 0 0
40
-8 1 2 1 2 5 -9 10 5 11 8 -6 4 4 -1 1 1 5 1 -5 -5 3 -4 -2 3 2 1 -2 3 1 -2 2 0 1 -1 1 -3 0 0 0
0 0 1 2 0 0 0 -1 -2 -2 1 1 -1 0 0 0 0 0 -1 1 0 1 0 -1 -1 0 0 0 -1 1 0 0 -1 0 1 0 0 -1 1 1
-5 1 -1 -1 2 1 -4 6 4 8 3 -5 3 2 -1 1 1 3 1 -3 -2 0 -2 0 3 1 0 -1 2 -1 -1 2 1 0 -2 0 -1 1 -1 -1
0 -1 1 0 0 2 -3 1 1 0 2 1 0 1 0 0 0 0 1 -1 -1 1 -1 0 0 0 0 -1 1 1 0 0 0 1 0 0 -1 0 0 0
-3 1 1 0 1 2 -3 4 2 5 3 -3 2 2 -1 1 1 2 0 -2 -2 1 -1 -1 2 1 1 -1 1 0 -1 0 0 0 0 0 -1 0 0 0
2 0 1 -1 -1 2 -1 -1 0 -2 1 1 -1 0 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 -1 1 1 0 0 0 0 1
-1 1 -1 0 1 -1 0 1 0 2 0 -3 0 1 0 0 2 0 0 -1 0 -1 0 -1 0 1 1 0 1 0 -1 0 0 0 0 0 -1 0 -1 0
-3 1 0 1 1 0 -2 3 1 4 2 -3 1 2 0 0 1 1 0 -2 -1 0 -1 -1 1 1 1 -1 1 0 -1 1 1 0 -1 0 -1 0 0 0
0 0 1 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 0 0
-5 1 2 1 1 4 -6 6 3 6 6 -3 2 2 -1 1 0 4 0 -2 -3 3 -3 -1 2 1 0 -1 1 1 -1 1 -1 1 0 1 -2 0 0 0
4 -1 -3 -2 0 -4 5 -5 -1 -4 -5 2 -1 -2 2 -1 1 -2 0 2 3 -2 1 1 -2 -1 0 0 0 -1 1 -1 1 -1 0 -1 1 0 -1 -1
0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 -1 1 0 1 0 0 0 0 -1 0 -1 0 1 0 -1 0 0 0 0 0 0 0
5 -2 -3 -2 -1 -4 6 -6 -2 -5 -6 4 -1 -3 2 -1 0 -3 0 2 3 -2 2 1 -3 -1 0 0 -1 -1 2 -1 1 -1 0 -1 2 0 0 0
-1 0 0 0 0 0 0 1 0 1 0 -1 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 1 0 0 0 0 -1 0 0 0 0 0 0 0
-3 0 -1 -2 1 1 -3 4 3 5 2 -3 2 1 0 0 1 2 0 -2 -1 0 -2 0 2 1 0 -1 2 0 0 1 1 0 -2 0 -1 1 -1 -1
-1 -1 1 -1 0 4 -3 3 3 3 3 -1 2 1 -1 0 0 1 1 -1 -3 2 -1 0 1 1 -1 0 1 0 0 0 -1 1 0 0 0 0 0 0
-2 -1 -2 -2 1 1 -2 3 3 4 1 -2 2 1 0 0 1 2 0 -1 0 0 -2 1 2 0 -1 -1 1 -1 1 1 1 0 -2 -1 0 1 -1 -1
-2 -1 -1 -1 1 2 -3 3 2 3 2 -2 1 1 -1 0 1 1 1 -1 -1 0 -1 0 1 0 -1 0 1 0 0 1 0 1 -1 0 -1 1 -1 0
-3 1 0 1 1 1 -2 3 0 3 2 -3 0 1 -1 0 1 1 0 -1 -1 0 0 -1 1 1 0 1 0 0 -1 1 0 1 -1 0 -1 1 -1 0
-3 0 0 -1 0 3 -3 4 4 6 3 -3 3 1 -1 0 0 3 0 -2 -2 1 -2 0 2 1 -1 0 1 -1 0 1 0 1 -1 0 0 1 0 0
0 -1 0 -1 0 2 -1 2 2 3 1 -1 2 1 -1 0 1 1 0 -1 -1 1 -1 0 0 1 0 0 0 0 0 -1 0 1 0 0 0 1 -1 0
-1 -1 0 0 0 1 0 2 1 3 0 -1 2 1 0 0 1 1 -1 -1 -1 1 -1 0 0 1 1 0 0 0 0 -1 0 0 0 0 0 0 0 0
3 -3 -3 -3 0 -1 3 -2 1 -1 -4 2 1 -1 1 -1 1 -1 0 1 2 -1 0 2 -1 -1 -1 0 0 -1 2 -1 1 0 -1 -1 1 1 -1 -1
1 -2 -1 -1 0 1 0 0 1 0 0 1 1 0 0 0 1 0 0 0 0 1 -1 0 -1 0 0 -1 0 1 0 -1 0 1 1 0 0 0 0 0
-3 0 -1 -1 1 1 -2 4 2 5 1 -3 2 1 0 0 1 2 0 -2 -1 0 -1 0 2 1 0 0 1 -1 0 1 1 0 -2 0 -1 1 -1 -1
-3 0 2 0 0 6 -5 6 3 6 6 -3 3 2 -3 1 0 3 0 -2 -4 3 -1 -1 2 2 -1 0 0 1 -1 0 -1 2 0 1 -1 1 0 0
2 -1 -1 -2 -1 1 2 -1 2 1 -2 0 2 -1 0 -1 0 0 0 0 0 0 0 1 0 0 -1 1 0 -2 1 -1 0 0 0 -1 2 1 0 0
-2 0 1 1 0 1 -1 2 1 2 1 -1 1 1 0 0 0 2 -1 0 0 1 -2 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0
1 -2 -2 -3 0 1 1 1 3 3 -2 -1 3 0 0 -1 1 1 0 -1 0 0 -1 2 1 0 -1 1 1 -2 1 -1 0 0 -1 -1 1 1 -1 -1
-2 0 -1 1 1 -2 -1 1 -1 1 0 -1 -1 1 1 0 2 0 0 -1 1 -1 -1 -1 0 0 2 -1 1 1 -1 1 1 0 -1 0 -2 0 -1 0
-2 -1 0 0 1 1 -2 3 2 3 1 -1 2 1 0 0 0 2 0 -1 -1 1 -2 1 2 0 0 0 1 -1 0 0 0 0 -1 -1 0 0 0 -1
-1 -1 -1 -2 0 2 -1 3 3 5 1 -2 3 1 0 0 1 2 -1 -2 -1 1 -2 0 1 1 1 -1 1 0 0 -1 0 0 0 0 0 0 0 0
-5 0 1 0 1 3 -6 6 4 6 5 -3 2 3 -1 1 1 3 0 -3 -2 1 -4 0 3 1 1 -2 2 1 -1 1 0 1 -1 0 -2 0 0 0
-4 0 0 0 1 2 -3 5 3 6 2 -3 3 1 -1 0 0 3 0 -2 -2 1 -2 0 2 1 -1 0 1 -1 0 1 0 0 -1 0 0 1 0 0
0 -1 0 -1 0 1 0 1 1 1 0 0 1 0 0 0 0 1 -1 0 0 1 -1 1 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1
-2 0 0 -2 0 3 -2 4 5 6 2 -3 4 1 -1 0 0 3 0 -2 -2 1 -2 1 3 1 -1 0 1 -2 1 0 0 0 -1 -1 1 1 0 -1
2 -1 -3 -3 0 -2 2 -2 1 -1 -3 1 0 -1 1 -1 1 -1 0 0 2 -2 0 2 1 -1 0 0 1 -2 1 0 2 -1 -2 -2 1 1 -1 -1
-1 0 -1 -2 0 1 0 2 2 4 0 -3 2 0 0 0 1 1 0 -1 -1 0 0 0 1 1 -1 1 1 -1 0 0 0 0 -1 0 0 1 -1 -1
-7 1 2 1 1 5 -6 9 4 10 6 -6 4 3 -2 1 0 5 0 -3 -4 3 -3 -1 3 2 -1 0 1 0 -1 1 -1 1 -1 1 -1 1 0 0
-1 -1 -2 -1 1 -1 0 1 1 2 -1 -1 1 1 1 0 2 0 0 -1 1 -1 -1 0 0 0 1 -1 1 0 0 0 1 0 -1 0 -1 0 -1 0
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
7 -2 -2 -1 -1 -4 6 -8 -4 -9 -6 6 -3 -2 2 -1 0 -5 0 3 4 -2 3 1 -3 -2 1 0 -1 0 1 -2 1 -1 1 -1 1 -1 0 0
-7 2 2 1 1 4 -6 8 4 9 6 -6 3 2 -2 1 -1 5 0 -3 -4 2 -2 -1 3 2 -1 0 1 0 -1 2 -1 1 -1 1 -1 1 0 0
2 -1 -1 -1 0 0 0 -1 0 -1 0 1 0 0 0 0 1 -1 1 0 0 0 0 0 -1 0 0 -1 0 0 0 0 1 0 0 0 0 0 0 0
-1 -1 -1 -3 0 2 -1 3 4 5 1 -2 3 0 0 0 0 2 0 -1 -2 1 -1 1 1 1 -1 0 1 -1 1 0 0 0 -1 0 0 1 -1 -1
0 -1 -1 -1 0 1 0 1 0 1 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 1 0 0 0 0
-2 0 1 1 0 1 -1 2 1 2 1 -1 1 0 0 0 -1 2 0 0 -1 1 -1 0 0 0 -1 1 0 0 0 1 -1 0 0 1 0 0 0 0
0 0 1 1 0 0 -1 0 0 -1 0 1 -1 0 0 0 -1 0 1 0 0 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 -1 0 -1 0 1 -1 0 1 0 1 1 0 0 0 0 0 0 1 0 -1 1 0 0 -1 0 0 -1 0 0 1 0 0 0 0 0 0 0 0 0
1 0 0 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 0 0 0 0 0 0 0 0 0
-1 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 -1 0 0 0 0 0 -1 0 -1 0 1 0 0 0 0 0 -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 -1 0 0 -1 1 -1 0 0 -1 0 0 0 0 0 1 -1 0 0 1 -1 0 0 0 0 1 -1 0 0 0 0 1 0 0 -1 0 0 0 0
4 -1 -2 0 0 -4 5 -6 -4 -7 -5 4 -3 -2 2 -1 0 -3 -1 3 4 -2 2 1 -2 -2 0 1 -1 0 1 -1 0 -1 0 -1 1 -1 0 0
-1 1 0 2 1 -2 1 0 -1 0 -1 -1 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 1 0 -1 -1 1 0 0 0 0 0 0 0 0
2 0 1 1 -1 2 2 -1 -2 -2 0 1 0 -1 -1 0 -1 -1 0 2 -1 1 2 -1 -2 1 -2 2 -2 0 0 -1 -2 1 2 1 1 0 1 1
0 1 2 3 0 1 -1 -1 -2 -3 2 1 -2 0 -1 0 -1 -1 1 1 -1 1 1 -1 -1 0 -1 0 -1 1 -1 1 -1 1 1 1 0 0 1 1
-1 1 2 3 0 2 0 1 -2 0 2 -1 0 0 -1 0 -1 0 0 1 -2 2 1 -1 -1 1 -2 2 -1 0 -1 0 -2 1 1 1 1 0 1 1
2 0 0 2 0 -3 3 -4 -3 -5 -3 2 -2 -2 1 -1 -1 -2 1 2 1 -1 2 0 -2 -1 -1 2 -1 -1 0 1 0 0 0 0 1 0 0 0
4 0 -1 1 0 -4 5 -6 -4 -7 -5 3 -3 -2 1 -1 -1 -3 0 3 3 -2 3 1 -1 -2 -1 2 -2 -2 1 0 0 -1 0 -1 2 0 0 0
0 0 2 2 0 1 -2 0 -1 -2 2 1 -1 0 -1 0 -1 0 1 1 -1 1 0 -1 -1 0 -1 0 -1 1 0 1 -1 1 1 1 0 0 0 1
6 -1 1 1 -1 -2 4 -7 -4 -10 -4 6 -4 -2 1 -1 -1 -4 0 4 3 -1 2 1 -3 -2 0 1 -2 1 1 -2 -1 0 2 0 1 -1 0 1
0 0 2 2 0 2 -1 0 0 -1 2 1 0 0 -1 0 -1 0 1 1 -2 2 0 0 -1 0 -1 0 -1 0 0 0 -1 1 1 0 1 0 1 1
1 0 1 2 0 0 0 -2 -2 -4 0 2 -2 0 0 0 0 -1 0 2 1 0 0 0 -1 -1 -1 0 -1 1 0 0 -1 1 1 0 0 0 0 1
-1 1 1 2 1 -1 0 0 0 0 0 -1 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 1 0 -1 -1 1 0 0 0 0 0 0 0 0
-1 0 0 0 1 0 -1 1 0 1 0 -1 0 0 0 0 0 0 1 0 -1 0 1 0 0 0 -1 1 0 -1 0 1 0 0 -1 0 0 1 -1 0
4 -1 0 0 -1 0 4 -4 -2 -5 -3 3 -1 -2 0 -1 -1 -2 0 3 1 0 2 1 -1 -1 -2 2 -2 -1 1 -1 -1 0 1 0 2 0 0 0
7 -1 -1 1 -1 -4 6 -9 -6 -12 -5 6 -5 -3 1 -1 0 -5 0 5 4 -2 3 0 -4 -2 -1 1 -2 1 1 -1 -1 0 2 0 1 -1 0 1
4 -1 0 0 -1 0 4 -4 -2 -5 -3 3 -1 -2 0 -1 -1 -2 0 3 1 0 2 1 -2 -1 -2 2 -2 -1 1 -1 -1 0 1 0 2 0 0 1
3 -1 -1 0 0 -2 3 -4 -1 -4 -3 2 -1 -2 1 -1 0 -2 1 2 1 -1 1 1 -2 -1 -1 1 0 -1 1 0 0 0 0 -1 1 0 0 0
7 -1 -1 1 -1 -4 6 -9 -6 -12 -5 6 -5 -3 1 -1 0 -5 0 5 4 -2 3 0 -4 -2 -1 1 -2 1 0 -1 0 0 2 0 1 -1 0 1
0 0 2 2 0 2 -1 0 -1 -2 1 1 -1 0 -1 0 -1 0 0 2 0 1 0 0 0 -1 -2 1 -1 1 0 0 -2 1 1 1 0 0 0 1
4 0 -1 1 0 -4 3 -6 -5 -9 -3 4 -5 -1 1 0 0 -4 0 3 4 -3 2 0 -2 -2 0 0 -1 1 0 0 0 0 1 0 0 -1 0 1
0 2 2 2 0 0 1 0 -1 -1 0 -1 0 0 -1 0 -1 0 0 1 0 0 1 0 1 0 -1 2 -1 -1 -1 0 -1 0 1 0 1 0 0 0
3 0 0 2 0 -4 3 -6 -4 -8 -3 4 -4 -1 1 0 0 -3 0 3 3 -2 1 0 -2 -2 0 0 -1 1 0 0 0 0 1 0 0 -1 0 1
1 0 0 0 0 0 1 -1 -1 -2 0 1 -1 0 0 0 0 -1 0 1 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0
1 -1 -1 -2 0 1 2 0 2 1 -2 0 2 -1 0 -1 -1 0 1 0 -1 0 1 2 1 0 -2 2 0 -3 1 0 0 0 -1 -1 2 1 0 -1
1 0 0 1 0 -1 2 -2 -2 -2 -1 1 -1 -1 0 0 0 -1 0 1 0 0 1 0 -1 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0
0 2 2 3 0 0 -1 -1 -3 -3 2 0 -3 0 -1 0 0 -1 0 1 0 0 1 -2 -1 0 0 0 -1 2 -1 1 -1 1 1 1 -1 0 0 1
0 0 1 1 0 1 -1 0 1 0 1 0 0 0 0 0 0 0 1 0 -1 1 -1 0 -1 0 0 0 0 0 0 0 -1 1 1 0 0 0 0 1
-
PROPERTIES
INTEGRAL = 1
MODULAR = 5
-
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