The Lattice 5^1+2.SL2(5).2SL2(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 13:14:49 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
5^1+2.SL2(5).2SL2(5).2
-
DIMENSION
40
-
GRAM (floating point or integer Gram matrix)
40 0
4
0 4
1 1 4
0 0 1 4
0 0 1 1 4
0 0 0 -1 -1 4
-1 1 0 0 1 0 4
-1 0 0 0 1 0 1 4
0 0 0 0 -1 0 0 -1 4
0 0 0 0 0 0 0 -2 0 4
0 0 0 1 1 0 1 0 1 0 4
0 -1 0 0 0 0 0 -1 1 1 0 4
0 0 0 -1 0 0 1 0 1 0 0 1 4
0 0 1 0 0 0 1 -1 0 1 0 0 0 4
-1 0 1 0 0 0 0 0 0 1 -1 1 1 0 4
1 0 0 -2 0 0 0 -1 -1 1 -1 0 1 0 0 4
0 0 0 0 -1 -1 0 0 0 0 -1 0 0 1 0 0 4
0 0 0 1 0 0 0 0 -1 0 0 0 -1 0 0 0 0 4
0 0 -1 -1 0 0 0 0 -1 0 0 0 0 0 0 1 1 -1 4
0 0 0 0 1 0 0 0 0 0 1 0 -1 0 0 0 -2 0 0 4
0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 -1 0 0 4
0 0 -1 0 0 0 -1 1 0 -1 0 -1 0 -1 0 -1 0 -1 1 0 -1 4
1 0 1 -1 0 0 -1 0 0 0 0 0 0 0 0 1 1 -1 0 0 1 0 4
0 0 -1 1 0 0 0 0 0 0 0 0 -1 -1 0 -1 0 0 0 0 0 1 -1 4
0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 0 1 -1 -1 1 -1 4
1 -1 -1 0 0 0 -1 -1 0 1 0 1 0 0 0 0 0 -1 1 1 0 1 0 1 0 4
1 -1 1 0 0 0 0 0 -1 0 -1 0 0 1 1 1 0 0 0 1 1 -1 0 0 1 1 4
0 0 -1 1 0 -1 0 0 0 0 0 0 0 0 -1 -1 0 0 -1 0 -1 1 -1 0 0 0 -1 4
1 -1 0 -1 0 0 -1 0 -1 0 -2 0 0 0 1 1 0 1 0 0 0 0 0 -1 0 0 1 -1 4
-1 1 0 0 0 0 1 0 0 0 0 0 1 1 -1 0 1 1 0 -1 -1 -1 -1 -1 1 -1 -1 1 -1 4
-1 1 0 0 1 1 1 0 0 0 1 0 -1 0 0 0 -1 0 0 1 1 0 0 1 -1 -1 -1 0 -1 0 4
0 0 0 0 0 0 0 0 -1 0 0 0 -1 0 -1 1 2 1 1 -1 1 -1 1 1 0 0 0 -1 -1 1 1 4
0 0 1 0 1 -1 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 -1 -1 0 -1 1 0 0 0 4
0 0 -1 -1 -2 1 -1 0 0 0 0 -1 0 -1 0 0 0 -1 1 0 0 1 1 0 1 1 0 0 -1 -1 -1 0 -1 4
0 0 1 1 2 0 1 0 -1 0 0 0 0 1 0 0 0 1 -1 0 0 -1 -1 1 0 0 1 0 0 1 1 1 1 -2 4
0 0 -1 0 -2 1 0 -1 1 1 -1 1 0 0 0 0 0 1 -1 -1 0 -1 -1 0 0 0 0 1 0 1 0 0 -2 0 -1 4
0 0 0 0 1 -1 0 1 0 -1 1 -1 -1 0 -1 -1 0 -1 1 1 0 1 1 0 0 0 0 -1 0 -1 0 0 2 0 -1 -2 4
0 0 1 0 1 0 0 1 -1 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 -1 0 0 0 1 0 -1 2 -2 0 4
0 0 -1 -1 -2 1 0 -1 0 1 -1 0 1 0 1 1 0 0 0 -1 1 0 0 0 0 0 0 1 0 0 0 0 -1 2 -1 2 -2 -2 4
0 0 0 1 -1 0 0 0 1 0 0 0 1 -1 1 -1 -1 0 -1 -1 0 0 -1 0 0 0 0 0 0 -1 -2 -2 -1 1 -1 1 -1 -1 1 4
-
DIVISORS (elementary divisors)
1^36 5^4
-
MINIMAL_NORM
4
-
KISSING_NUMBER
3600
-
GROUP_ORDER
2^8 * 3^2 * 5^5
-
GROUP_GENERATORS
4
40
-3 0 5 1 -1 -3 -4 -1 -2 2 3 3 5 2 -2 2 2 1 0 4 2 0 0 10 -10 -13 -3 -6 7 4 -11 -8 -21 12 18 0 12 -12 -2 -10
0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 -1 -1 -2 0 0 -2 -2 -2 1 2 1 1 0 1 -3
0 0 0 0 0 0 0 0 0 0 0 0 0 0 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
1 0 -2 0 1 2 2 0 1 -1 -1 -1 -2 0 1 0 -1 -1 -1 -2 -1 0 0 -3 4 6 2 4 -1 0 6 5 9 -4 -10 -1 -5 5 -1 6
-2 0 3 1 -1 -2 -2 -1 -1 0 3 2 2 2 1 3 0 -1 0 3 0 0 1 6 -6 -8 -3 -2 6 3 -7 -3 -12 9 12 2 8 -6 -2 -5
1 0 -1 0 1 1 1 0 1 0 0 0 -2 0 1 0 -1 -1 -1 -1 -1 0 0 -1 1 2 2 2 1 2 3 3 3 -1 -5 -2 -2 2 0 3
1 1 -3 -1 0 3 3 1 3 0 -3 -3 -3 -2 0 -3 -3 1 1 -5 -1 -1 1 -6 7 10 4 5 -5 -3 7 5 13 -11 -14 -4 -9 7 2 5
-1 -1 3 0 0 -2 -2 -1 -2 0 2 2 2 1 0 2 2 0 0 3 1 0 0 5 -6 -7 -3 -3 4 3 -5 -5 -10 9 11 3 7 -5 -2 -4
0 0 -1 0 0 1 1 0 1 0 -1 -1 -1 -1 0 -1 -1 0 0 -1 -1 0 0 -2 2 3 2 2 -1 -1 2 3 4 -4 -5 -2 -3 2 1 2
0 -1 1 0 1 -1 -1 -1 -2 0 1 2 1 1 0 1 2 0 -1 2 1 1 0 3 -3 -4 -1 -2 2 3 -1 -3 -4 6 4 2 3 -2 -2 -1
0 0 -1 0 0 1 0 0 1 0 0 0 -1 0 1 0 -1 0 0 -1 -1 -1 1 0 -1 1 2 2 1 2 1 2 0 -1 -2 -3 0 0 0 2
1 0 -2 -1 1 2 1 0 1 0 -1 -1 -2 -1 0 -1 0 0 -1 -3 -1 -1 0 -2 3 5 4 3 -1 1 6 3 6 -5 -9 -5 -5 2 0 5
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 -1 0 0 1 0 -1 1 0 0 1 1 0 0 0 0
2 0 -3 -1 1 2 2 0 1 -1 -2 -1 -3 -1 1 -1 0 0 -1 -2 -1 0 0 -4 4 6 3 3 -3 0 6 4 9 -6 -10 -3 -6 4 0 6
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 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 -1 0 1 0 1 0 0 0 0 -1 1 1 0 -1 -2 -1 0 -2 2 -2 0 1 -1 1 2 0
1 0 -2 0 0 1 1 1 2 0 -2 -1 -2 -1 0 -1 -1 0 0 -2 -1 0 0 -4 4 5 2 2 -3 -1 5 3 7 -6 -7 -2 -4 4 2 4
0 1 -2 0 1 1 1 0 1 0 -1 -1 -1 -1 -1 -2 -1 1 1 -2 0 0 1 -2 2 3 3 1 -2 -1 2 1 5 -4 -6 -2 -5 2 1 1
0 0 0 0 0 0 0 -1 0 0 0 0 1 1 1 0 -1 0 0 1 1 1 0 1 -1 -2 -1 0 1 0 -2 1 -2 2 2 1 1 -1 -2 -1
0 -1 2 1 0 -2 -1 -1 -3 -1 2 2 1 2 1 3 2 -1 0 4 1 1 0 3 -4 -6 -5 -3 2 1 -5 -4 -6 8 10 7 6 -2 -2 -3
0 1 -2 -1 0 2 2 0 2 0 -2 -2 -1 -2 -1 -3 -2 2 1 -4 0 -1 1 -3 4 6 4 3 -3 -2 4 2 7 -7 -9 -4 -6 3 1 2
-1 0 1 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 1 1 0 1 0 0 1 0 -1 -1 -1 -1 -2 -3 -2 -1 0 2 1 0 -1 0 -3
0 0 1 0 0 0 -1 0 -1 -1 1 1 0 1 1 2 1 -1 -1 1 -1 0 -1 1 -1 -1 -1 0 1 1 0 0 -2 2 2 1 3 -1 0 1
0 1 -2 -1 0 2 1 1 3 1 -2 -2 -1 -1 -1 -3 -2 1 0 -4 0 0 -1 -3 5 5 4 2 -3 -3 3 4 6 -8 -9 -6 -7 1 1 1
-2 0 3 0 -1 -2 -2 -1 -1 1 2 1 3 1 -1 0 0 1 1 2 1 0 1 6 -6 -7 -1 -3 4 2 -7 -4 -12 6 10 0 6 -7 -1 -6
-1 1 1 0 -1 0 -1 0 1 1 1 0 1 1 0 0 -1 0 0 0 0 0 0 3 -2 -3 1 0 3 1 -3 1 -6 1 3 -3 2 -4 -1 -2
0 0 0 0 -1 0 0 0 0 1 0 0 1 0 0 -1 -1 0 0 0 1 0 0 1 -1 -2 0 0 1 0 -2 0 -3 1 2 -1 1 -2 -1 -2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 1 1 0 0 1
1 0 -2 0 0 1 1 1 1 0 -1 -1 -2 -1 0 -1 -1 -1 0 -2 -1 0 0 -4 4 5 2 2 -2 -1 5 3 8 -5 -7 -1 -5 4 1 4
0 -1 2 2 0 -2 -1 -1 -3 -2 3 3 1 3 3 5 1 -3 -1 5 0 1 0 4 -5 -7 -6 -2 5 3 -5 -2 -7 11 11 8 8 -2 -3 -2
0 0 0 1 0 0 0 1 0 -1 0 0 -1 0 0 1 0 -1 1 0 -1 0 0 -2 2 2 -1 0 -2 -2 1 0 4 -2 -1 3 -1 3 2 1
2 0 -3 -1 2 2 2 0 0 -1 -2 -1 -2 -1 0 -1 1 -1 -1 -1 -1 1 -1 -6 6 7 2 3 -4 -2 8 5 13 -6 -11 1 -7 7 0 8
-1 1 0 -1 0 0 0 0 1 1 -1 -1 1 -1 -2 -3 -1 2 1 -2 1 0 0 0 1 0 2 -1 -2 -3 -2 -1 -1 -3 -1 -3 -3 -2 1 -4
1 -1 1 1 0 -1 -1 0 -2 -1 2 2 0 2 2 4 2 -3 -2 3 -1 1 -1 2 -2 -3 -3 -1 3 3 0 0 -3 6 5 4 5 -1 -2 2
-2 0 3 1 -2 -2 -2 0 0 1 2 1 2 1 0 1 -1 0 1 2 0 -1 1 5 -6 -7 -2 -2 5 2 -7 -3 -12 6 11 0 7 -6 0 -6
0 1 -2 -1 1 2 2 0 2 0 -2 -2 -1 -1 -1 -3 -2 1 1 -3 0 0 0 -4 5 6 3 3 -3 -3 4 4 9 -7 -10 -2 -7 5 1 3
1 0 -1 0 0 1 0 1 0 -1 0 0 -2 0 1 2 1 -1 -1 -1 -1 0 -1 -2 3 4 0 1 -2 0 4 1 5 -3 -4 0 -1 3 1 4
0 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 1 0 0 -1 0 -1
0 0 0 -1 0 0 0 0 1 1 -1 -1 0 -1 -1 -2 0 2 0 -2 0 -1 0 0 0 1 2 0 -1 0 1 -1 -1 -2 -2 -4 -1 -1 1 -1
40
-2 -1 5 1 -1 -4 -3 -1 -3 1 3 3 4 2 -1 2 2 0 0 5 1 0 1 9 -10 -12 -4 -6 7 5 -9 -8 -18 13 17 3 11 -9 -2 -8
1 1 -4 -2 1 4 3 1 4 0 -4 -4 -3 -3 -1 -5 -3 2 1 -7 -1 -1 0 -8 9 12 7 6 -7 -5 9 7 16 -15 -19 -7 -13 7 2 6
0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 -4 -1 0 3 3 1 4 0 -4 -4 -3 -3 -1 -4 -3 2 2 -6 -1 -1 1 -8 9 12 5 5 -7 -5 9 5 16 -14 -16 -4 -11 9 3 6
1 0 -2 0 0 1 1 1 1 -1 -1 -1 -2 0 1 0 -1 -1 0 -1 -1 0 0 -4 4 5 0 2 -3 -2 4 3 8 -5 -6 1 -4 5 1 4
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 1 0 1 1 1 2 -1 0 -1 -2 0 -1 0 1
2 0 -3 -1 1 2 2 1 2 -1 -2 -2 -3 -1 1 -1 -1 0 0 -3 -1 0 -1 -6 7 8 2 4 -5 -3 7 5 13 -8 -12 -1 -8 7 1 6
1 0 -2 0 0 1 1 1 1 -1 -1 -2 -2 -1 1 0 -1 0 0 -2 -1 -1 0 -4 4 6 1 2 -4 -2 4 2 8 -6 -7 0 -4 5 2 3
0 1 -1 0 0 2 2 1 3 0 -2 -2 -2 -2 -1 -2 -2 1 1 -4 -1 -1 0 -4 5 7 3 3 -3 -3 4 3 8 -8 -9 -4 -6 4 3 2
1 -1 0 0 1 -1 0 -1 -2 0 0 2 0 1 0 1 2 -1 -1 3 1 2 0 1 -2 -4 -2 -2 1 2 -1 -1 -2 5 4 3 2 -1 -2 1
0 1 -2 -1 0 2 2 1 3 0 -2 -3 -2 -2 -1 -3 -2 1 1 -4 -1 -1 0 -5 6 8 3 3 -4 -4 5 4 10 -10 -11 -4 -8 5 3 3
0 0 0 1 0 0 0 0 1 1 0 1 0 1 0 1 0 0 -1 0 0 0 0 2 -2 -2 1 0 3 3 0 0 -4 3 1 -3 2 -2 -1 0
1 0 -1 0 1 1 1 0 1 0 0 0 -2 0 1 0 -1 -1 -1 -1 -1 0 0 -1 1 2 2 2 1 2 3 3 3 -1 -5 -2 -2 2 0 3
0 0 1 0 0 -1 -1 0 -1 0 1 1 1 1 0 1 1 -1 0 2 0 1 -1 1 -1 -3 -2 -1 1 -1 -2 0 -2 3 4 3 2 -1 -1 -1
3 -1 -3 0 2 2 2 0 -1 -2 -1 0 -3 0 2 2 2 -2 -2 0 -1 1 -1 -5 5 6 0 3 -3 0 8 4 12 -3 -9 3 -4 7 -1 9
-1 -2 5 1 1 -5 -4 -2 -6 0 5 6 4 4 1 5 5 -2 -2 9 2 2 0 11 -13 -17 -7 -8 9 8 -11 -9 -21 21 23 8 15 -11 -5 -7
0 0 1 0 0 -1 -1 0 -1 0 1 1 1 1 0 1 1 0 0 1 1 0 0 3 -2 -3 -1 -1 2 1 -2 -2 -4 4 4 1 2 -3 -2 -2
0 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 -1 0 1 0 -1 -1 -1 -1 0 -1 0 -1 1 1 1 0 1 0
0 -1 2 0 0 -2 -1 -1 -3 0 2 2 2 2 1 2 2 -1 -1 4 1 1 0 4 -5 -6 -3 -2 4 3 -3 -2 -7 9 8 4 5 -4 -4 -1
-1 0 1 0 0 0 0 0 0 -1 1 0 0 1 1 2 0 -1 0 1 -1 0 0 0 0 0 -2 1 1 -1 -1 1 0 1 2 3 2 1 0 1
0 0 0 0 1 0 0 -1 -1 -1 1 1 0 1 1 1 1 -1 -1 1 0 0 0 1 -1 -1 0 1 2 2 1 1 0 3 0 1 1 0 -2 2
0 0 0 0 -1 0 1 0 0 0 0 -1 0 -1 0 -1 -1 0 1 0 0 0 1 -1 0 1 0 0 -1 -1 -1 0 1 -2 0 1 -1 1 1 -1
-2 0 3 1 0 -2 -2 -1 -2 0 3 2 3 2 0 2 1 -1 0 4 1 0 1 7 -7 -9 -3 -3 6 3 -8 -4 -12 10 12 3 7 -7 -3 -6
1 0 -3 0 0 2 3 1 2 -1 -3 -3 -3 -2 0 -2 -2 1 2 -4 -1 -1 1 -7 7 10 2 4 -6 -4 7 3 14 -10 -12 0 -8 9 3 5
-1 0 1 0 0 0 -1 0 0 0 1 0 1 1 0 1 0 0 0 1 0 0 0 2 -1 -2 -1 0 2 0 -2 0 -3 2 3 1 2 -2 -1 -1
-1 -1 3 1 -1 -2 -1 -1 -2 0 2 2 2 2 1 3 1 -1 0 4 0 0 1 5 -6 -7 -4 -2 5 3 -5 -3 -10 9 11 4 8 -4 -2 -3
0 -2 3 1 0 -3 -2 -1 -4 -1 3 3 2 3 2 5 3 -2 -1 6 0 1 0 5 -6 -8 -6 -3 5 4 -4 -4 -9 12 13 8 10 -3 -3 -1
-1 1 0 0 -1 0 0 0 2 1 0 -1 0 -1 -1 -2 -2 1 1 -2 0 0 1 0 0 0 2 0 0 -1 -2 0 -2 -3 0 -3 -1 -1 2 -3
0 -1 3 1 0 -3 -3 -1 -4 0 3 4 3 3 1 4 3 -2 -2 6 1 1 -1 7 -8 -11 -5 -5 6 5 -7 -5 -14 13 15 5 11 -7 -3 -4
0 1 -1 -1 0 1 0 1 2 1 -1 -1 -1 -1 -1 -2 -1 1 0 -3 0 0 -1 -2 3 3 3 1 -2 -2 2 2 3 -5 -5 -4 -4 0 1 0
1 1 -4 -1 1 3 3 1 3 -1 -3 -3 -3 -2 0 -3 -2 0 0 -5 -1 0 -1 -8 9 11 4 5 -6 -5 8 7 16 -12 -16 -3 -11 8 2 6
-1 0 1 0 0 -1 -1 0 -1 0 1 1 1 1 0 1 1 0 0 1 1 0 0 3 -2 -3 -1 -1 2 1 -2 -2 -4 4 4 1 2 -3 -2 -2
0 0 1 0 0 -1 -1 0 -2 0 1 1 1 1 0 1 1 -1 0 2 1 1 -1 1 -1 -3 -3 -2 0 -1 -3 -2 -2 3 5 4 2 -1 -1 -2
-1 0 1 0 0 0 0 -1 -1 0 1 0 1 0 0 0 0 0 0 1 0 0 1 2 -2 -2 0 0 2 1 -2 0 -3 2 2 0 1 -2 -1 -1
1 0 -2 0 0 1 1 1 1 -1 -1 -1 -2 0 1 0 -1 -1 0 -2 -1 0 -1 -4 5 5 0 2 -3 -3 4 3 8 -5 -6 1 -4 5 1 3
0 0 0 0 0 0 0 0 1 1 -1 0 0 -1 -1 -1 0 1 0 -1 0 0 0 0 0 0 2 0 0 1 1 0 -1 -1 -1 -3 0 -1 1 0
-1 0 2 0 -1 -1 -1 0 -1 0 1 0 2 1 0 1 0 0 1 2 1 0 0 2 -2 -3 -3 -1 1 -1 -4 -2 -4 3 6 3 3 -2 -1 -3
1 0 -2 0 0 1 1 1 1 -1 -1 -1 -2 0 1 0 -1 0 0 -2 -1 -1 0 -3 3 5 1 2 -2 -1 4 2 6 -4 -6 -1 -3 4 1 3
0 0 0 0 1 0 0 -1 -1 0 1 1 0 0 0 0 1 -1 -1 1 0 1 0 1 -1 -2 1 0 2 2 0 1 -1 2 0 0 0 -1 -1 1
1 0 -2 0 0 2 2 0 2 0 -2 -2 -2 -2 0 -2 -2 1 1 -3 -1 -1 1 -4 4 6 3 3 -3 -1 5 3 8 -7 -9 -3 -5 5 2 4
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 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 -1 0 -1 0 0 0 0
1 1 -3 -1 1 4 2 1 3 0 -3 -3 -2 -2 -1 -3 -1 1 0 -5 -1 -1 -1 -6 8 10 5 5 -5 -4 8 6 13 -12 -16 -6 -10 6 2 6
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 -1 -1 0 0 -1 0 1 1 1 1 0 0 2 0 1 0 -2 -1 0 0 -1 1
0 1 -2 0 0 2 1 1 2 0 -2 -2 -1 -1 -1 -2 -2 1 1 -4 -1 -1 0 -4 5 6 3 3 -4 -4 4 3 8 -8 -9 -3 -6 4 2 2
2 0 -4 -1 1 3 3 1 3 -1 -3 -3 -4 -2 1 -2 -2 0 0 -4 -2 0 0 -8 8 11 4 5 -6 -3 9 7 16 -12 -16 -3 -10 9 3 8
0 0 0 0 0 0 0 0 -1 -1 1 0 0 1 1 1 0 -2 0 1 0 1 -1 -1 2 0 -2 1 0 -2 0 2 3 0 0 4 -1 2 -1 1
1 0 -2 -1 1 2 1 1 1 -1 -2 -2 -2 -1 0 -1 0 1 0 -3 -1 -1 -1 -5 6 8 2 3 -5 -3 7 3 11 -8 -11 -1 -6 6 2 5
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 -1 0 0 -1 -1 0 1 0 0 1 -1 0 -1 -1
-1 0 2 1 -1 -2 -1 0 -1 1 1 1 2 0 -1 0 0 0 1 2 1 1 0 2 -3 -5 -3 -4 1 -1 -6 -4 -7 4 9 3 4 -3 1 -6
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 -1 0 0 0 0 0 0 0 -1
-2 0 3 1 0 -2 -2 -1 -2 0 3 2 3 2 0 2 1 -1 0 4 1 1 0 6 -6 -9 -4 -4 5 1 -9 -4 -12 9 13 4 7 -7 -2 -7
0 0 0 0 0 0 0 1 0 -1 0 -1 0 0 0 0 0 -1 1 0 0 0 -1 -2 3 2 -2 0 -2 -4 0 1 4 -3 -1 3 -2 2 1 0
0 1 -1 0 0 1 0 0 1 1 0 0 0 0 0 -1 -1 -1 -1 -1 0 0 -1 0 1 0 2 1 1 0 0 3 0 -2 -3 -4 -2 -1 0 0
-1 -1 3 1 0 -2 -2 0 -2 0 2 2 2 2 0 3 2 -1 0 4 1 1 -1 4 -4 -7 -5 -4 3 1 -6 -4 -9 8 11 5 7 -4 -1 -4
0 1 -1 0 -1 1 1 1 2 0 -1 -2 -1 -1 0 -2 -3 0 2 -2 -1 -1 1 -3 3 4 1 2 -2 -3 1 3 5 -6 -4 -1 -4 3 2 1
-1 0 2 0 -1 -1 -1 -1 -1 1 1 1 2 1 0 0 0 0 0 2 1 0 0 4 -4 -5 -1 -1 4 2 -4 -1 -8 5 6 -1 4 -5 -2 -3
0 0 0 0 0 0 0 -1 -1 0 1 1 0 1 1 1 0 -1 -1 1 0 1 0 1 -2 -2 0 0 2 2 -1 1 -2 3 2 1 2 -1 -2 1
-2 0 3 1 -2 -2 -2 0 0 1 2 1 2 1 0 1 -1 0 1 2 0 -1 1 5 -6 -7 -2 -2 5 2 -7 -3 -12 6 11 0 7 -6 0 -6
0 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 -1 -2 -1 -1 0 2 1 1 0 1 -2
0 -1 2 1 0 -1 -1 0 -2 -1 1 1 1 1 1 3 2 -1 0 3 0 0 0 2 -2 -3 -4 -2 1 1 -2 -3 -3 5 6 5 4 -1 -1 -1
1 0 -2 0 0 1 1 1 2 0 -2 -1 -2 -1 0 -1 -1 1 0 -3 -1 -1 0 -3 3 5 3 2 -2 0 5 2 5 -5 -7 -4 -3 3 2 3
0 0 1 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 1 1 0 0 -2 0 0 -2 1 -1 1 0
-1 -1 3 1 -1 -3 -2 -1 -2 1 2 2 3 2 0 2 1 0 0 4 1 1 1 6 -7 -9 -3 -4 5 4 -6 -5 -13 10 13 3 9 -6 -2 -5
-1 0 2 0 0 -1 -1 -1 -1 0 2 1 1 1 1 1 0 -1 0 2 0 0 0 3 -4 -5 -2 -1 3 1 -5 -1 -7 5 7 2 5 -3 -1 -3
-1 -1 4 1 -1 -4 -3 -1 -3 1 3 3 4 2 0 2 2 0 0 5 2 1 0 8 -9 -13 -5 -7 5 3 -11 -8 -18 13 19 4 11 -10 -2 -10
0 0 1 0 0 0 -1 0 0 0 1 0 1 1 1 1 0 -1 0 1 0 0 -1 1 0 -2 -2 0 1 -1 -2 1 -2 2 3 2 2 -1 -1 -1
1 0 -2 0 1 1 1 0 0 -1 -1 0 -2 -1 0 0 1 0 0 -1 0 0 0 -3 3 4 1 1 -3 -1 4 0 7 -3 -5 1 -3 4 1 3
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 0 0 0 0 0 0 0 0
0 1 -2 -1 0 2 1 0 1 0 -1 -1 -1 -1 0 -2 -1 0 0 -2 0 0 0 -3 3 4 3 3 -2 -2 3 4 6 -6 -7 -3 -5 2 0 3
0 0 -1 0 0 1 1 0 1 0 -1 0 -1 0 0 0 -1 0 0 -1 -1 0 1 -1 1 2 2 2 0 1 3 2 3 -2 -4 -2 -2 2 0 3
-1 0 2 0 -1 -1 -1 -1 -1 1 1 1 2 1 0 0 0 0 0 2 0 0 1 4 -5 -5 0 -1 4 3 -3 -1 -8 5 6 -1 4 -5 -2 -2
0 1 -2 -1 0 2 1 1 2 1 -2 -2 -1 -2 -2 -3 -1 1 0 -4 -1 -1 0 -4 5 7 5 3 -3 -2 6 4 8 -9 -11 -6 -7 3 2 4
0 -1 2 0 0 -2 -1 0 -1 0 1 1 0 0 0 1 2 0 0 2 0 0 0 2 -3 -3 -2 -3 1 2 -2 -4 -5 4 6 2 4 -2 1 -2
0 1 -2 -1 0 2 1 0 2 1 -2 -2 0 -1 -1 -3 -2 1 1 -3 0 0 0 -3 4 4 4 3 -3 -3 3 4 6 -7 -8 -4 -6 2 0 2
0 -1 2 1 0 -2 -1 -1 -3 -1 3 3 1 2 2 4 2 -2 -1 5 1 2 0 4 -5 -7 -5 -3 4 3 -5 -3 -7 10 11 7 7 -3 -3 -2
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 1 1 1 1 1 2 1 0 0 -2 -2 0 0 0 1
0 1 -2 -1 0 2 1 0 3 1 -3 -3 0 -1 -1 -4 -3 2 1 -4 0 -1 0 -3 4 5 4 3 -3 -3 3 4 5 -8 -9 -6 -6 2 1 1
0 -1 2 1 0 -2 -1 0 -2 -1 2 2 0 1 1 3 2 -2 0 4 0 1 0 2 -3 -4 -4 -3 2 2 -3 -3 -4 6 8 6 5 -1 0 -1
0 -1 2 1 0 -2 -1 0 -2 -1 2 1 1 1 1 3 2 -1 0 3 1 1 -1 2 -2 -4 -5 -3 1 0 -4 -4 -4 6 8 7 5 -1 -1 -3
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
-2 1 2 0 -1 0 -1 0 1 1 1 0 2 0 -1 -1 -1 1 0 -1 0 -1 0 4 -3 -3 2 -1 3 1 -4 -1 -8 1 3 -5 2 -6 0 -5
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 -2 0 -1 2 2 1 3 0 -2 -3 -2 -2 0 -3 -4 1 2 -5 -1 -1 1 -5 6 8 3 4 -4 -4 4 4 10 -10 -10 -3 -7 6 3 2
1 2 -4 -1 0 4 3 1 4 0 -3 -3 -4 -2 1 -3 -4 0 0 -6 -2 -1 0 -7 8 11 6 7 -4 -3 8 9 14 -13 -17 -7 -10 7 2 7
0 -2 3 1 0 -3 -2 -1 -4 0 2 3 2 1 0 3 4 -1 -1 6 1 1 0 5 -7 -9 -5 -6 3 4 -6 -7 -11 11 14 6 9 -5 -1 -4
0 1 -2 0 0 2 2 1 3 0 -2 -2 -2 -1 0 -2 -3 0 0 -4 -2 -1 0 -4 5 7 4 4 -2 -2 5 6 8 -8 -11 -5 -6 4 2 4
1 0 -2 0 1 1 1 0 0 -1 -1 0 -2 0 1 0 0 -1 -1 -1 -1 0 0 -3 2 4 2 2 -1 1 5 3 6 -2 -6 -1 -3 3 0 5
1 0 -2 0 1 1 1 1 1 -1 -1 -1 -2 -1 0 0 0 0 0 -2 -1 0 0 -4 4 5 1 1 -4 -2 4 1 8 -5 -6 1 -4 5 2 3
-2 0 4 1 -1 -3 -3 -1 -3 1 3 3 4 2 -1 2 2 0 0 5 2 1 0 8 -8 -12 -5 -6 5 2 -11 -7 -16 11 17 4 10 -9 -2 -9
1 0 -2 0 0 1 2 0 1 0 -1 -1 -2 -1 1 -1 -2 0 0 -2 -1 0 1 -3 2 4 2 2 -2 0 3 3 6 -4 -6 -1 -3 4 1 3
2 0 -3 -1 2 2 1 1 1 -1 -2 -1 -3 -1 0 -1 1 0 -1 -2 -1 0 -1 -5 6 7 2 2 -5 -2 7 3 12 -7 -11 -1 -7 6 2 6
2 0 -3 0 1 2 2 1 1 -2 -2 -2 -3 -1 1 0 0 -1 -1 -2 -2 0 -1 -7 7 9 1 3 -5 -3 8 5 14 -8 -12 1 -7 8 2 7
-1 0 2 0 -1 -2 -1 0 -1 1 1 1 2 1 -1 0 0 0 0 2 1 1 0 3 -3 -5 -2 -3 2 0 -5 -2 -7 4 7 1 3 -4 -1 -4
0 0 0 0 1 0 0 0 -1 -1 0 0 0 0 0 0 1 0 0 1 0 0 0 -1 1 1 -1 0 -1 -1 1 0 3 0 -1 3 -1 2 0 1
0 0 1 0 0 0 -1 0 -1 0 1 1 1 1 0 2 2 -1 -1 2 0 0 -1 2 -1 -2 -1 0 2 1 0 0 -2 3 2 1 2 -2 -2 1
0 0 0 0 0 0 0 1 0 -1 0 -1 0 0 0 0 0 -1 1 0 0 0 -1 -2 3 2 -2 0 -2 -4 0 1 4 -3 -1 3 -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 1 1 0 0 0 0 1 0 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 -1 0 1 -1 0 0 0 1 1 0 0 -1 1 0 -1 0 -1 -1 0
0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 1 -2 -1 1 0 1 2 0 -1 -2 2 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 0 0 1 1 1 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 -1 0 0 0 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 1 1 0 0 1 0 -1 -1 0 0 0 0 -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 0 0 -1 0 0 -1 0 1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -1
0 0 -1 0 0 1 1 0 1 0 -1 -1 -1 -1 0 -1 -1 1 1 -1 0 0 1 -2 2 3 1 1 -2 -1 1 1 4 -4 -4 -1 -3 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 -1 0 0 -1 -1 0 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 0 0 -1 1 1 0 1 0 -1 1 1 2 0 -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 1 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 0 1 1 1 1 0 1 1 0 0 2 1 0 0 2 -2 -3 -2 -1 2 1 -2 -2 -4 4 5 2 3 -2 -1 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 0 1 -1 0 1 0 0 -1 0 0 0 1 0 -1 -1 -1 -1 -1 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 2 -2 -2 2 0 2 3 0 0 -3 2 0 -3 1 -2 -1 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 1 0 0 0 0 -1 0 1 1 -1 -1 0 -1 0 0 0
-1 1 1 0 -1 -1 0 0 1 1 0 0 1 0 -1 -1 -2 1 1 -1 1 0 0 1 -1 -2 0 -1 1 -1 -3 -1 -4 1 3 -1 1 -2 0 -4
-1 -1 2 1 0 -2 -1 -1 -2 0 1 1 2 0 -1 1 2 1 1 3 1 0 1 3 -5 -5 -3 -4 1 1 -5 -6 -7 6 9 4 5 -3 0 -5
1 1 -3 -1 0 3 3 1 3 0 -3 -3 -3 -2 0 -3 -3 0 0 -5 -1 0 -1 -7 9 10 4 5 -5 -5 7 7 14 -12 -15 -4 -10 7 2 5
-1 -1 3 1 0 -3 -3 -1 -3 0 3 3 3 2 0 3 3 -1 -1 5 1 1 0 7 -7 -10 -4 -5 5 4 -7 -6 -13 11 14 4 9 -7 -2 -5
-1 1 0 0 -1 0 0 0 2 1 0 0 0 0 0 -1 -3 1 1 -2 0 -1 1 1 -2 -1 2 1 2 1 -2 1 -4 0 1 -4 1 -2 0 -2
2 0 -3 -1 1 3 2 1 1 -1 -2 -2 -3 -1 1 -1 0 -1 -1 -3 -1 0 -2 -7 8 9 2 4 -5 -4 8 6 14 -9 -13 -1 -8 7 1 7
-1 -1 3 1 0 -3 -2 -1 -3 0 2 2 3 1 -1 2 3 0 0 5 1 1 0 5 -6 -8 -4 -5 3 2 -6 -6 -10 9 12 5 7 -5 -1 -5
0 0 -1 0 0 1 1 0 1 -1 -1 -2 -1 -1 0 -1 -1 1 1 -2 -1 -1 1 -3 3 5 1 2 -3 -2 3 1 6 -5 -5 0 -3 4 2 2
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PROPERTIES
INTEGRAL = 1
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REFERENCES
G. Nebe, Finite quaternionic matrix groups,
Representation Theory 2, 106-223 (April 1998)
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NOTES
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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