The Lattice (U5(2) x 2^(1+4)_-.Alt_5).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 13:14:52 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME (required)
DIMENSION (required)
GRAM
DIVISORS (elementary divisors)
MINIMAL_NORM
KISSING_NUMBER
HERMITE_NUMBER
GROUP_ORDER
GROUP_NAME
GROUP_GENERATORS
PROPERTIES
REFERENCES
URL (links to other sites for this lattice)
LAST_LINE
-
NAME (required)
(U5(2) x 2^(1+4)_-.Alt_5).2
-
DIMENSION (required)
40
-
GRAM
40 0
4
1 4
1 2 4
1 2 1 4
1 2 0 1 4
1 1 1 2 1 4
1 1 2 2 0 1 4
1 1 2 1 0 1 2 4
1 1 2 1 0 0 2 2 4
1 1 1 1 1 2 1 2 2 4
2 1 2 1 0 1 1 1 2 1 4
2 2 2 1 2 2 1 1 1 2 1 4
1 2 1 1 1 1 1 1 2 2 2 1 4
1 0 1 1 1 1 2 2 1 1 2 1 1 4
1 2 1 2 1 2 1 1 1 1 2 1 2 1 4
1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 4
1 1 2 1 0 2 1 2 2 2 2 1 2 1 2 2 4
1 1 1 2 1 2 1 1 1 2 2 2 1 2 1 2 1 4
1 1 1 1 1 1 2 2 2 2 1 2 1 2 2 1 1 1 4
1 1 1 1 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 4
1 0 0 0 0 0 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 4
-1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 4
-1 -1 -1 0 -1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -1 0 -1 -1 1 2 4
-1 0 -1 0 0 0 -1 -1 -1 0 -1 0 -1 -1 0 -1 -1 0 0 0 1 2 2 4
0 0 0 0 -1 -1 0 0 0 -1 1 -1 0 0 1 0 0 0 0 -1 1 1 0 0 4
0 -1 -1 -1 -1 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 1 1 1 0 2 4
-1 0 0 0 -1 0 0 0 -1 0 0 -1 0 0 0 0 0 0 -1 0 1 2 2 1 1 1 4
0 0 -1 0 0 0 0 0 -1 0 -1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 2 1 4
0 -1 -1 0 -1 -1 0 0 -1 -1 -1 -1 -1 0 -1 0 -1 0 -1 -1 1 0 1 0 1 2 1 2 4
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 0 1 1 2 1 2 1 4
0 0 0 0 0 0 0 1 -1 0 -1 0 -1 0 0 1 0 0 0 0 2 1 0 0 1 1 1 1 2 1 4
-1 0 0 0 0 0 0 0 -1 0 -1 0 -1 0 0 0 -1 0 0 0 1 2 1 2 0 0 2 0 1 1 2 4
0 -1 0 0 -1 0 0 0 -1 -1 0 -1 -1 0 0 0 0 0 -1 -1 2 1 1 0 2 1 1 0 2 1 2 1 4
0 0 0 1 0 1 0 1 0 1 0 0 0 0 1 1 1 1 0 0 1 2 1 1 1 1 1 1 1 2 2 1 2 4
0 -1 0 0 -1 0 0 0 0 0 0 0 -1 0 0 0 0 1 0 -1 1 1 1 1 1 2 0 1 2 2 1 1 2 2 4
0 0 0 0 -1 0 0 0 0 0 1 -1 0 0 1 0 1 0 0 0 2 1 1 1 2 2 2 1 0 2 0 0 1 1 1 4
0 0 0 0 0 0 1 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 1 2 1 2 1 2 1 1 0 1 1 1 4
0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 1 0 0 0 0 -1 0 1 1 1 2 2 1 1 1 2 1 1 1 2 2 1 2 4
0 0 -1 0 0 0 -1 -1 -2 -1 -1 0 -1 -1 0 0 -1 0 -1 -1 1 0 1 1 1 1 1 2 2 1 2 1 1 1 1 0 1 2 4
-1 -1 -1 -1 0 -1 -1 -1 -1 0 -1 0 -1 0 -1 -1 -1 0 0 0 1 2 1 2 0 1 1 1 1 1 1 2 0 0 1 0 0 0 1 4
-
DIVISORS (elementary divisors)
1
-
MINIMAL_NORM
4
-
KISSING_NUMBER
39600
-
HERMITE_NUMBER
4
-
GROUP_ORDER
2^18 * 3^6 * 5^2 * 11
-
GROUP_NAME
(U5(2) otimes 2^(1+4)_-.Alt_5).2
-
GROUP_GENERATORS
12
40 40
0 -2 1 0 1 0 1 1 -1 -1 1 -1 1 -3 0 0 -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 -2 2 0 1 0 0 0 -1 -1 0 -1 2 -2 0 0 -1 1 1 1 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 0 0 1 -1 0 2 2 0 0 -1 0 0 -2 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 1 0 0 0 1 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 0 0 1 0 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
-1 1 -2 0 -1 1 0 0 1 0 1 2 -1 2 0 0 0 -2 -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 -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 2 0 0 1 -1 0 0 -1 -2 -2 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
1 -1 2 0 1 0 0 0 -1 0 -1 -2 1 -1 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
0 0 0 0 0 1 0 0 0 0 0 0 0 1 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
1 -2 2 0 1 0 0 1 -1 -1 -1 -2 2 -2 0 -1 -1 2 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 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
2 -3 4 -1 2 0 0 0 -1 -2 -3 -4 3 -3 1 -1 -1 4 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 2 -1 0 1 -1 0 1 -1 -3 -3 1 0 1 -1 -1 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 -2 3 -1 1 0 0 0 -1 -1 -2 -3 2 -2 1 -1 -1 3 1 2 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 -1 1 -1 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 -1 1 0 1 0 0 1 -1 -1 0 -1 1 -1 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
0 0 0 0 0 1 0 0 1 0 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
2 0 3 -1 0 1 -1 -1 0 0 -3 -4 1 0 1 -1 -1 2 1 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 1 -1 0 0 -1 -1 -2 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
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 -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 0 0 0 0 0 -1 0 0 0 1 1 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 -1 1 0 -2 -1 -1 -2 1 1 -1 0 1 0 0 -1 3 0 1 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 -2 -2 -1 -2 1 1 -2 -1 1 1 0 -1 4 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 1 0 0 1 0 0 0 1 -1 0 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 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 0 0 0 0 -1 1 -1 -1 -1 -1 -1 1 1 -1 0 0 1 0 -1 2 0 1 0 1
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 -2 1 1 -1 0 1 1 -1 -1 3 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 2 0 -1 -1 -2 -2 0 2 0 1 0 0 -1 -1 3 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 -1 0 1 -1 0 0 1 -2 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 -1 0 0 0 0 -1 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 -1 1 -1 -1 -2 -1 -1 0 1 -1 0 0 1 0 -1 3 0 1 1 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 -1 -1 0 -1 1 0 2 -2 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 0 0 -1 1 0 0 -1 -1 0 0 0 0 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 0 0 0 0 1 0 0 -1 -1 0 -1 1 0 1 -1 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 0 0 0 -1 0 1 1 1 2 0 -1 0 1 -1 0 0 1 -2 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 -1 0 1 0 0 0 1 -1 1 -1 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 -1 3 -1 -2 -3 -3 -3 1 2 -2 0 0 2 -1 -2 5 1 3 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 5 -2 -3 -4 -4 -5 1 4 -3 -1 1 2 -1 -3 8 1 4 1 2
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 -1 0 1 -1 -1 1 0 1 -1 2 0 0 1 0
40 40
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 4 -2 -3 -4 -3 -5 1 4 -3 -2 1 2 0 -3 7 1 4 1 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 -1 -1 -1 -2 -1 1 1 -1 0 0 0 -1 0 2 0 2 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 -2 -2 -1 0 1 -1 0 -1 1 -1 0 2 1 2 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 0 -2 -1 -3 -3 1 2 -1 0 1 0 0 -1 4 0 2 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 -1 -1 -1 -1 -2 1 1 -1 -1 1 0 0 -1 2 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 3 -1 -3 -3 -3 -5 2 2 -3 -1 2 2 0 -2 7 0 3 1 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 3 0 -2 -2 -3 -3 1 2 -1 0 0 1 -1 -1 4 1 2 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 0 -2 -1 -1 0 1 -1 1 -1 1 -1 0 2 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 3 -1 -1 -2 -2 -2 0 2 -1 0 -1 1 -1 -1 3 1 2 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 -1 -2 -1 -2 1 1 -2 0 0 1 0 -1 3 0 2 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 4 -2 -3 -3 -3 -4 1 3 -3 -2 1 2 0 -2 6 1 3 1 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 4 -2 -2 -4 -3 -4 1 3 -3 -1 0 2 -1 -2 6 1 4 1 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 -2 -1 -2 -2 2 1 -2 -1 1 1 0 -1 3 0 2 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 3 -1 -2 -2 -2 -3 1 2 -2 -1 1 1 0 -1 4 1 1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 -2 -1 -2 -3 2 1 -2 -1 2 1 0 -1 4 0 2 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 -2 0 -1 -2 2 0 -1 0 2 0 0 0 2 -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 -1 -1 -1 -1 -1 1 0 -1 0 0 1 0 0 2 0 1 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 3 -1 -2 -2 -2 -3 1 2 -2 -1 1 1 0 -1 4 0 2 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 3 -1 -1 -2 -2 -3 1 2 -2 0 0 1 -1 -1 4 1 2 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 4 -2 -2 -4 -3 -4 1 3 -3 0 0 2 -1 -2 7 1 3 1 2
3 0 3 -1 0 0 -1 -1 0 0 -4 -4 1 0 1 -1 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 -3 5 -1 2 -1 0 0 -2 -1 -3 -5 3 -4 1 -1 -1 5 2 3 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 0 0 -1 0 -1 -3 1 -2 0 -1 0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 3 -1 0 0 -1 -1 0 0 -3 -4 1 -1 1 -1 -1 3 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 -2 4 -1 1 -1 0 0 -1 -1 -3 -4 2 -2 2 -1 -1 4 1 2 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 0 0 0 0 0 -2 -2 1 0 1 -1 0 2 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 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 3 -2 0 -2 1 -1 0 1 1 -1 1 -1 3 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 1 -1 0 -1 0 0 0 1 1 -1 1 -1 2 1 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
1 1 1 -1 -1 0 -1 -1 1 1 -3 -1 0 2 2 -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
1 0 1 -1 0 0 0 0 0 0 -2 -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 2 -1 0 0 0 -1 0 1 -2 -2 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
3 -2 5 -1 1 0 -1 -1 0 -1 -5 -5 2 -1 2 -1 -1 4 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 -2 4 -1 1 0 -1 0 0 -1 -4 -4 2 -2 2 -1 -1 4 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 -1 3 -1 0 0 -1 -1 1 0 -4 -3 1 0 2 -1 -1 3 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 3 -1 0 0 -1 -1 0 0 -3 -4 1 0 1 -1 0 3 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 2 -1 -1 -1 1 0 0 1 1 -1 0 -1 2 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 2 -1 0 0 0 0 0 0 -2 -2 1 -1 2 -1 -1 2 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 0 0 0 1 0 1 -1 1 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 -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 0 0 0 0 0 0 0 0
40 40
-1 1 -2 0 -1 0 0 0 1 0 0 2 -1 2 0 0 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 -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 0 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 0 0 0 0 0
0 -2 1 0 1 -1 0 1 -1 -1 0 0 1 -2 0 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 -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
1 -2 2 0 1 -1 0 0 -1 -1 -1 -2 1 -2 0 0 0 2 2 1 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 -2 -2 1 -1 0 -1 0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 -1 2 -1 1 0 0 -1 0 -1 -2 -2 1 -1 0 0 0 2 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 0 1 0 0 0 -1 -1 0 -1 1 -1 -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
1 -2 2 0 1 0 0 0 -1 -2 -1 -2 2 -2 -1 0 0 2 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 -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 -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 1 0 0 0 -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
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 -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 -2 1 0 1 -1 1 0 -1 -1 0 0 1 -2 0 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 -1 1 0 1 0 0 0 -1 -1 0 -1 1 -1 -1 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 -3 3 0 1 -1 0 0 -1 -1 -2 -2 2 -2 1 0 -1 2 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 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 -1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -3 1 1 3 2 3 0 -2 2 0 0 -2 1 2 -5 -1 -2 -1 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 0 0 1 1 1 1 -1 0 -1 1 0 1 0 -2 -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 0 1 2 1 2 0 -1 1 0 0 -1 1 1 -3 -1 -1 -1 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 0 0 1 1 2 0 -1 0 0 0 -1 1 1 -2 -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 -1 0 1 1 1 2 0 -1 1 0 0 -1 0 1 -3 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 -1 1 0 2 0 1 1 -1 1 0 1 -1 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 1 -2 1 0 2 1 1 1 -2 1 0 1 -1 1 1 -3 -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 -2 1 1 2 1 2 0 -2 1 1 0 -1 0 2 -3 -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 -2 1 1 2 1 2 0 -2 2 1 0 -1 0 1 -3 -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 -2 1 0 2 1 1 1 -2 0 0 1 -1 1 1 -2 -1 -1 -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 2 2 2 0 -2 2 0 0 -1 0 1 -4 -1 -1 -1 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -2 1 0 1 1 1 0 -1 1 0 0 -1 1 0 -2 -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 -3 1 1 3 2 2 0 -2 2 0 1 -2 1 1 -4 -1 -2 -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 1 1 0 1 -1 0 0 1 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 -2 1 0 2 1 1 0 -1 1 0 1 -1 1 0 -2 -1 -1 -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 0 3 1 2 1 -2 1 0 1 -2 1 2 -4 -1 -2 -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 1 0 -1 1 1 0 -1 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 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 -1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -3 1 1 2 2 3 0 -2 1 0 0 -1 1 1 -4 -1 -1 -1 -1
40 40
2 -1 3 -1 0 0 0 -1 0 0 -3 -3 1 -1 2 -1 -1 3 0 2 0 -3 1 1 2 2 2 0 -2 1 1 0 -1 1 1 -3 -1 -2 -1 0
3 0 4 -1 0 1 -2 -1 1 -1 -5 -5 2 0 1 -2 -1 4 1 2 -1 1 0 -2 -1 -1 -2 0 1 -1 0 1 0 0 -1 3 0 1 1 1
3 0 4 -1 0 1 -2 -1 0 -1 -5 -5 2 0 1 -2 0 4 2 1 0 0 0 0 0 0 0 -1 1 0 0 0 -1 0 0 0 0 0 0 0
2 0 2 -1 0 1 -1 0 1 -1 -3 -2 1 0 1 -1 -1 2 0 1 -2 2 0 -3 -2 -2 -4 1 2 -2 -1 2 1 0 -2 6 0 2 1 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 -2 1 -1 2 1 0 1 -2 0 0 2 -1 1 1 -1 -1 -1 0 0
1 1 0 -1 0 1 0 0 1 0 -2 -1 0 1 1 -1 0 1 -1 0 -1 0 0 -1 0 -1 -1 1 0 -1 0 1 0 0 0 2 -1 1 0 1
1 0 1 0 0 1 -1 0 0 -1 -1 -1 1 0 0 -1 0 1 1 0 -1 1 0 -1 -1 -1 -2 0 2 -1 0 1 0 0 -1 3 0 1 0 1
1 0 2 0 0 1 -1 0 0 -1 -2 -2 1 0 0 -1 0 2 1 0 0 0 0 0 -1 0 -1 -1 1 0 0 0 0 0 -1 1 0 1 0 1
2 0 3 -1 0 0 -1 -1 0 -1 -3 -3 1 0 1 -1 0 3 1 1 0 0 0 -1 -1 0 -1 0 1 -1 -1 1 0 1 -1 1 0 1 0 1
1 -1 2 -1 1 0 0 0 0 -1 -2 -2 1 -1 1 -1 0 3 0 1 0 -1 0 -1 0 0 -1 1 0 -1 -1 2 0 1 -1 1 -1 1 0 1
3 0 4 -2 0 1 -1 -2 1 -1 -5 -5 1 0 2 -1 -1 4 1 2 1 -2 1 0 2 1 2 0 -1 1 0 0 -2 1 1 -3 -1 -1 -1 0
2 -1 3 -1 1 0 0 0 -1 -1 -3 -4 2 -2 1 -2 0 4 1 2 0 -2 0 0 1 1 1 0 -1 0 0 1 -1 1 1 -1 -1 -1 0 0
1 2 0 -1 -1 1 -1 -1 2 0 -2 -1 -1 2 1 -1 0 1 -1 0 0 0 0 -2 0 0 -1 1 0 -1 -1 2 0 1 -1 1 -1 1 0 1
0 0 0 0 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 1 -2 1 0 2 1 1 0 -1 1 0 1 -2 1 1 -2 -1 -1 -1 0
2 1 2 -1 0 1 -1 -1 1 0 -3 -3 0 1 1 -1 -1 2 0 1 -1 1 0 -2 -1 -1 -2 1 1 -1 0 1 0 0 -1 3 -1 2 0 1
2 0 2 -1 0 1 -1 0 1 -1 -3 -3 1 0 1 -1 -1 3 0 1 -1 0 1 -2 0 -1 -2 1 0 0 0 2 0 0 -1 2 -1 1 0 1
2 1 2 -1 0 1 -1 -1 1 0 -3 -3 0 1 1 -1 0 2 0 0 -1 2 -1 -2 -2 -2 -3 1 2 -2 -1 1 1 0 -2 4 0 3 0 2
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40 40
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40 40
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0 0 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 -1 0 0 0 0
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0 0 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 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 1 0 0 0 0 -1 0 0 0 0 0 0 0 0
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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1 0 -2 -1 -1 0 1 -1 0 -1 2 -1 -1 2 1 1 1 1
-
PROPERTIES
Unimodular=1
-
REFERENCES
G. Nebe, Finite quaternionic matrix groups.
Represent. Theory 2 (1998) 106-223
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URL (links to other sites for this lattice)
All the quaternionic matrix groups
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe