The Lattice SL2(7)SL2(9).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 13:14:05 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(7)SL2(9).2
-
DIMENSION
32
-
GRAM (floating point or integer Gram matrix)
32 0
6
3 6
1 1 6
2 1 2 6
2 3 1 1 6
2 2 3 2 3 6
3 3 2 2 3 2 6
2 1 2 3 1 3 1 6
2 2 1 3 2 2 1 2 6
1 2 2 3 2 2 2 3 2 6
2 2 1 3 1 1 2 2 3 3 6
1 1 2 2 1 2 2 2 2 2 2 6
3 2 2 2 1 2 3 2 1 3 3 1 6
2 2 2 2 2 3 1 3 1 2 2 1 3 6
2 2 2 3 1 2 3 2 2 2 3 2 3 1 6
2 2 2 2 2 2 2 1 1 2 2 3 2 1 2 6
2 1 3 3 1 2 2 1 1 2 2 2 3 2 3 2 6
1 3 1 2 2 3 1 2 2 2 3 1 2 3 3 2 2 6
2 1 1 3 3 3 2 2 2 2 2 2 2 2 3 2 2 3 6
2 2 1 3 1 0 2 2 3 3 2 2 2 2 2 1 1 1 1 6
3 3 1 3 2 3 3 1 2 2 2 1 3 1 3 3 2 2 3 1 6
3 2 2 2 1 2 2 2 2 1 2 0 3 2 2 1 1 2 1 2 2 6
2 2 2 2 2 3 1 2 3 3 2 0 2 2 0 1 1 2 1 1 2 3 6
1 2 1 1 3 2 2 2 3 3 2 1 1 1 1 0 0 2 3 2 1 1 3 6
1 2 1 2 3 2 2 2 3 3 1 1 2 1 2 0 1 1 2 2 2 1 2 3 6
3 2 0 2 2 2 3 3 2 2 2 1 2 1 1 1 0 1 2 2 3 2 2 3 2 6
1 2 2 3 1 3 3 3 2 3 2 3 3 2 3 2 2 2 2 2 3 1 2 2 3 2 6
1 1 2 1 1 2 2 1 1 2 3 3 2 1 3 3 3 3 2 0 1 1 1 1 0 0 2 6
3 2 1 1 3 2 3 1 2 1 1 0 2 2 2 0 2 2 2 2 1 1 2 3 2 2 1 1 6
1 1 2 1 3 3 1 2 1 2 1 2 2 2 0 3 2 2 2 0 1 1 2 1 1 1 1 2 1 6
1 3 2 2 3 2 2 2 2 1 1 0 1 2 3 0 1 3 2 2 1 2 1 2 3 1 1 0 3 1 6
2 2 0 0 3 2 1 0 2 1 2 1 1 1 0 2 0 2 1 0 1 2 2 1 1 1 -1 2 1 3 1 6
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DIVISORS (elementary divisors)
1^24 7^8
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MINIMAL_NORM
6
-
KISSING_NUMBER
26880
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GROUP_ORDER
2^8 * 3^3 * 5 * 7
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GROUP_GENERATORS
3
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
-6 5 1 1 1 1 2 6 -3 -8 1 -1 2 -2 3 0 1 0 2 5 -1 -3 5 -1 3 -1 -5 -1 0 -1 -7 2
-3 2 0 2 1 1 3 3 -2 -8 -1 0 3 0 4 0 0 2 -1 4 -1 -4 5 2 3 -1 -6 0 -3 0 -5 0
2 -2 -1 -1 -1 0 -1 -3 2 4 0 0 -1 1 -2 1 1 -1 -1 -3 0 2 -3 1 -2 1 3 0 0 0 4 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
-2 1 0 1 1 1 2 2 -1 -5 0 0 2 0 2 0 0 1 -1 3 0 -3 3 1 2 -1 -4 0 -2 0 -3 0
-1 1 0 1 1 1 1 2 -1 -4 0 0 2 -1 1 0 0 1 -1 2 0 -2 2 1 1 -1 -3 0 -1 0 -2 0
-2 1 -1 3 1 2 3 3 -3 -8 -1 1 4 0 4 0 0 2 -3 4 0 -5 5 4 3 -2 -7 0 -4 0 -4 0
1 -1 0 -1 -1 -1 -1 -2 1 3 0 0 -2 1 -1 1 1 -1 0 -2 0 2 -2 0 -1 1 3 -1 1 0 2 1
-3 2 0 1 1 1 1 3 -2 -5 0 0 2 -1 1 0 1 0 0 3 0 -2 3 1 1 -1 -3 0 -1 -1 -3 1
-3 2 0 1 0 1 2 3 -2 -5 0 0 1 -1 2 0 1 1 0 3 0 -2 3 1 2 -1 -4 -1 -1 0 -4 1
-3 2 0 2 0 2 4 4 -3 -9 0 0 3 -1 3 0 0 2 -1 5 0 -5 6 2 4 -2 -7 0 -3 0 -5 0
-3 2 0 2 1 2 3 4 -3 -8 0 0 3 -1 3 0 0 2 -1 5 0 -4 5 2 3 -2 -7 0 -3 0 -5 0
-1 1 0 0 0 1 0 0 -1 -1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 -1 0 0 0 -1 0
-3 2 0 3 1 2 3 4 -2 -8 -1 0 4 -1 3 0 0 2 -2 4 0 -4 4 3 3 -2 -7 0 -3 0 -5 0
-2 1 0 1 0 1 2 2 -1 -4 0 0 1 0 2 0 0 1 -1 2 0 -2 3 1 2 -1 -4 0 -1 0 -3 0
0 0 0 0 0 0 0 -1 1 1 0 0 0 0 -1 0 0 0 0 -1 0 1 -1 0 -1 0 1 0 0 0 1 0
-5 4 0 3 1 2 3 5 -3 -9 0 0 3 -1 4 0 0 1 -1 5 0 -4 5 2 4 -2 -8 0 -2 0 -7 0
1 -1 -1 1 0 1 2 0 0 -2 -1 0 1 1 1 0 0 1 -3 1 1 -2 1 3 1 -1 -3 1 -3 1 0 -1
1 -1 0 -2 -1 -1 -3 -2 1 5 1 0 -2 0 -4 1 1 -2 1 -3 1 4 -4 -1 -2 1 5 0 3 -1 4 1
-2 1 0 2 1 1 3 3 -1 -6 -1 0 3 0 3 0 0 2 -2 3 0 -4 4 2 2 -1 -6 0 -3 0 -4 0
-3 2 -1 2 0 2 3 3 -2 -7 -1 0 3 0 4 1 0 1 -1 4 -1 -4 5 2 3 -1 -7 0 -3 0 -4 0
-4 3 0 3 1 1 3 4 -3 -9 -1 0 3 0 5 0 0 1 -1 5 -1 -5 6 2 3 -1 -7 0 -3 0 -6 1
0 0 0 -1 0 -1 -1 0 0 1 0 0 -1 0 -1 0 1 -1 0 0 1 1 -1 0 -1 0 2 0 1 0 1 1
-4 3 0 4 2 2 4 5 -4 -11 -1 0 5 -1 5 0 0 2 -2 6 -1 -6 7 3 4 -2 -9 0 -4 0 -7 0
-1 0 -1 2 1 1 3 3 -2 -6 -1 1 3 0 3 0 0 2 -3 3 1 -4 4 3 2 -2 -6 0 -3 0 -3 0
-3 2 0 3 1 2 3 4 -3 -9 0 0 4 -1 3 0 0 2 -2 5 0 -5 5 3 3 -2 -7 0 -3 0 -5 0
-4 3 0 2 0 2 3 4 -2 -7 0 0 2 -1 2 0 0 1 0 4 0 -3 4 1 3 -2 -6 0 -1 0 -5 0
2 -1 1 -2 0 -2 -4 -3 2 7 1 0 -3 0 -4 0 0 -2 1 -4 1 5 -6 -2 -3 1 7 0 4 0 4 1
-2 1 0 1 1 1 2 2 -2 -5 0 0 1 0 3 0 0 1 -1 3 0 -3 4 1 2 -1 -4 0 -2 0 -3 0
-5 4 0 4 2 2 4 6 -4 -12 -1 0 5 -1 6 0 0 2 -2 6 -1 -6 7 3 5 -2 -10 0 -4 0 -8 0
-4 3 0 2 1 2 3 4 -3 -8 0 0 2 -1 4 0 0 1 0 5 -1 -4 6 0 4 -1 -7 0 -2 0 -6 0
32
-2 1 0 0 0 0 1 2 -2 -3 1 0 0 -1 1 0 1 0 1 2 0 -1 2 0 1 -1 -1 -1 0 0 -2 1
-4 2 0 3 1 2 4 5 -4 -10 0 0 3 -1 4 0 0 2 -1 6 0 -5 6 2 4 -2 -8 0 -3 0 -6 0
3 -3 0 -3 -1 -2 -2 -3 3 7 0 0 -3 1 -4 0 1 -1 1 -4 1 4 -5 -1 -3 1 6 0 2 0 5 0
1 -1 0 -2 0 -1 -3 -2 1 4 1 0 -2 0 -2 0 1 -2 1 -2 1 3 -3 -1 -2 1 4 0 2 0 3 0
-6 4 0 8 3 3 7 9 -7 -20 -2 1 8 -1 10 -1 -2 5 -5 10 0 -11 12 6 8 -4 -17 1 -7 1 -13 -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
-3 2 0 2 1 1 2 4 -3 -7 0 0 2 -1 3 0 0 1 0 4 0 -3 4 1 3 -2 -5 0 -1 0 -5 0
-3 2 0 3 2 1 3 4 -3 -9 -1 0 4 -1 5 -1 0 2 -1 5 -1 -5 6 2 3 -1 -7 0 -4 0 -6 0
3 -3 0 -4 -1 -2 -5 -5 4 11 2 0 -4 0 -7 1 1 -3 2 -6 1 7 -8 -3 -5 2 10 0 5 -1 8 0
-6 4 0 6 3 2 6 8 -6 -17 -2 1 7 -1 8 -1 -1 4 -3 9 0 -9 11 4 7 -3 -15 1 -6 0 -11 -1
-3 2 -1 2 1 2 3 4 -3 -8 0 0 3 -1 3 0 0 1 -1 5 0 -4 5 2 3 -2 -7 1 -3 0 -4 -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
-2 1 0 0 1 0 1 3 -2 -4 0 0 1 -1 1 0 1 0 1 3 0 -2 3 0 1 -1 -2 0 -1 -1 -2 1
-2 1 -1 5 2 2 4 4 -4 -11 -2 1 5 0 6 -1 -1 3 -4 6 0 -7 7 5 4 -2 -10 1 -6 1 -6 -1
1 -1 0 -4 -1 -1 -3 -2 2 7 2 -1 -4 0 -4 1 2 -3 3 -3 0 5 -5 -3 -3 1 7 -1 4 -1 4 1
2 -2 0 -3 -1 -1 -2 -2 1 5 1 0 -3 0 -3 0 1 -1 1 -2 1 3 -3 -2 -2 1 5 0 2 0 4 0
1 -1 0 -2 0 -1 -2 -1 1 4 1 0 -2 0 -3 0 1 -2 1 -2 1 3 -3 -1 -2 0 4 0 2 0 3 0
-1 0 -1 2 1 2 2 2 -2 -5 0 0 2 0 2 0 0 1 -2 3 0 -3 3 2 2 -1 -5 1 -3 0 -2 -1
0 0 0 1 1 0 -1 0 -1 -1 0 0 0 0 1 0 0 0 -1 0 0 0 0 1 0 0 0 0 0 0 -1 0
0 0 0 1 1 0 0 0 -1 -2 0 1 1 0 1 0 0 1 -1 1 0 -1 1 1 1 0 -2 0 -1 0 -1 -1
3 -3 1 -7 -2 -3 -7 -6 4 15 3 -1 -8 0 -8 1 2 -5 5 -7 1 10 -10 -6 -6 3 15 -1 8 -1 9 2
3 -3 -1 -2 -1 -1 -1 -3 2 5 0 0 -2 1 -2 1 1 -1 0 -3 0 2 -3 0 -2 1 4 0 0 0 5 0
0 -1 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0
-4 3 0 5 2 2 4 5 -4 -12 -1 0 5 -1 5 0 -1 3 -2 6 -1 -6 7 3 5 -2 -10 1 -4 0 -8 -1
-4 3 1 2 1 0 1 4 -2 -6 0 0 2 -1 2 0 0 0 1 3 0 -2 3 0 2 -1 -4 0 0 -1 -5 1
-3 2 0 2 1 1 2 3 -3 -7 0 0 2 -1 4 0 0 1 0 4 -1 -3 5 1 3 -1 -5 0 -2 0 -5 0
0 0 1 -2 0 -1 -3 -1 1 4 1 -1 -2 -1 -3 0 1 -2 3 -1 0 3 -3 -3 -2 1 5 0 3 -1 2 1
0 0 -1 1 0 1 1 1 -1 -2 0 0 1 0 0 0 0 0 -1 1 0 -1 1 1 1 -1 -2 1 -1 0 0 -1
-3 2 0 2 1 1 2 4 -3 -7 1 0 2 -1 2 0 0 1 0 4 0 -3 4 1 3 -2 -5 0 -1 0 -5 0
-1 0 0 3 2 1 3 4 -3 -8 -1 1 4 -1 3 -1 -1 3 -3 4 1 -5 5 3 3 -2 -7 1 -4 0 -4 -1
-2 1 0 2 1 1 2 3 -2 -6 0 0 2 0 3 0 0 1 -1 3 0 -3 3 2 2 -1 -5 0 -2 0 -4 0
-5 3 -1 5 1 3 6 7 -5 -14 -1 1 6 -1 6 0 -1 3 -3 7 0 -8 9 4 6 -3 -13 1 -5 0 -8 -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
6 -4 0 -6 -3 -2 -6 -8 5 16 2 -1 -7 1 -7 1 1 -4 3 -8 0 9 -10 -4 -6 3 14 -1 6 0 10 1
-1 1 0 2 0 1 2 1 -1 -4 -1 0 2 0 2 0 0 2 -1 2 -1 -3 3 1 2 0 -4 0 -2 0 -3 0
-2 2 -1 7 2 3 6 5 -5 -15 -3 2 8 0 8 -1 -2 5 -6 7 0 -10 10 7 6 -3 -15 1 -8 1 -8 -2
3 -2 0 -2 -1 -1 -2 -3 2 6 0 0 -2 0 -3 0 0 -1 1 -3 0 3 -3 -2 -2 1 5 0 2 0 4 0
3 -2 0 -1 -1 -1 -1 -3 2 5 0 0 -1 0 -3 0 0 0 0 -3 0 2 -3 -1 -2 1 4 0 1 0 4 0
1 0 0 1 0 1 1 0 -1 -2 -1 0 1 0 2 0 0 1 -1 1 -1 -2 2 1 1 0 -2 0 -2 0 -1 0
3 -2 0 0 0 0 -1 -3 1 3 0 1 0 0 -2 0 -1 1 -1 -2 0 1 -2 0 -1 1 2 0 0 0 3 -1
-4 3 -1 7 2 4 7 7 -6 -17 -2 1 8 -1 8 -1 -2 5 -5 9 0 -10 11 6 7 -4 -16 1 -7 1 -10 -2
9 -7 -1 -4 -2 -2 -6 -10 6 17 0 1 -5 2 -8 1 0 -2 -1 -10 1 8 -11 -1 -7 3 13 0 4 0 13 -1
1 0 -1 4 0 2 2 0 -1 -4 -2 1 3 1 3 0 -2 2 -4 1 0 -3 2 4 2 -1 -6 1 -3 1 -2 -2
-1 1 0 2 0 1 2 2 -2 -5 -1 0 2 -1 2 0 0 2 -1 3 0 -3 3 2 2 -1 -4 0 -2 0 -3 0
5 -3 0 -2 -1 -1 -3 -5 3 9 0 0 -3 1 -4 0 0 -1 0 -5 0 4 -6 -1 -4 2 7 0 2 0 6 0
4 -2 0 -2 -1 -1 -4 -5 3 9 1 0 -3 0 -5 0 0 -2 1 -5 0 5 -6 -2 -4 2 8 0 3 0 6 0
1 0 0 0 -1 1 0 -1 0 1 0 0 0 0 -1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 0
3 -2 0 -1 -1 -1 -1 -3 2 4 -1 0 -1 1 -1 0 0 0 0 -2 0 1 -2 0 -2 1 3 0 0 0 3 0
1 0 0 1 0 0 0 0 0 0 -1 0 1 0 0 0 0 1 -1 0 0 -1 0 1 0 0 -1 0 -1 0 0 0
6 -4 0 -4 -2 -2 -6 -8 5 15 1 0 -5 1 -7 0 0 -3 1 -8 1 8 -10 -3 -6 3 12 0 5 0 10 0
2 -1 0 1 0 0 0 -1 0 0 -1 1 1 0 0 -1 -1 1 -2 0 1 -1 0 1 0 0 -1 1 -1 1 1 -1
2 -1 -1 0 0 1 -1 -2 0 2 0 1 0 0 -1 0 0 0 -1 -1 0 1 -1 1 -1 0 1 0 0 0 2 -1
2 -1 0 -1 -1 0 0 -1 1 2 0 0 0 0 -1 0 0 0 0 -1 0 0 -1 0 -1 0 1 0 0 0 2 0
-1 1 0 3 1 1 2 2 -2 -5 -1 1 3 0 3 -1 -1 2 -2 2 0 -3 3 2 2 -1 -5 0 -2 0 -4 0
3 -3 -1 1 0 0 0 -2 1 2 -1 1 1 1 -1 0 -1 1 -3 -2 1 0 -1 2 -1 0 0 1 -1 0 3 -1
5 -4 -1 -1 -1 0 -2 -5 2 7 0 1 -2 1 -3 0 -1 0 -2 -4 1 3 -4 0 -2 1 4 1 1 1 6 -2
4 -3 0 -3 -1 -1 -3 -4 2 8 1 0 -3 0 -5 0 0 -1 1 -4 1 4 -5 -2 -3 1 7 0 3 0 6 0
2 -1 0 0 0 0 0 -1 0 1 0 1 0 0 0 0 -1 1 -1 -1 0 0 0 0 0 0 0 0 0 0 1 -1
3 -2 0 -1 -1 0 -1 -3 1 4 0 0 -1 0 -2 0 0 0 0 -2 0 1 -2 0 -2 1 3 0 0 0 4 0
4 -3 0 -1 -1 -1 -2 -4 3 7 -1 0 -2 1 -3 0 0 0 -1 -4 1 3 -5 0 -3 1 5 0 1 0 5 0
2 -1 -1 0 0 1 0 -1 0 1 0 0 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 0 1 -1 0 2 -1
4 -3 0 -2 -1 -2 -2 -4 3 7 -1 0 -2 1 -3 0 0 0 0 -4 0 3 -4 -1 -3 2 6 0 1 0 5 0
2 -1 0 -2 -1 0 -2 -3 1 5 1 0 -2 0 -3 0 0 -1 1 -2 0 3 -3 -2 -1 1 4 0 2 0 3 0
4 -3 0 -2 -1 -2 -3 -4 3 8 0 0 -3 1 -4 0 0 -1 0 -5 1 5 -6 -1 -3 1 7 0 3 0 5 0
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PROPERTIES
INTEGRAL = 1
-
REFERENCES
G. Nebe, Finite quaternionic matrix groups,
Representation Theory 2, 106-223 (April 1998)
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NOTES
-
URL (links to other sites for this lattice)
All the quaternionic matrix groups
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe