The Lattice SL2(9)D10SL2(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 13:13:57 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(9)D10SL2(5).2
-
DIMENSION
32
-
GRAM (floating point or integer Gram matrix)
32 0
8
2 8
2 2 8
2 2 2 8
2 2 2 2 8
1 4 1 0 1 8
1 2 3 0 1 0 8
2 2 2 2 2 0 2 8
1 4 1 1 1 4 2 -2 8
2 2 2 2 2 1 2 2 1 8
2 2 2 2 2 0 1 2 1 2 8
4 1 2 1 0 2 1 1 1 0 1 8
2 2 2 2 2 2 -1 2 1 2 2 2 8
3 2 1 -1 0 4 0 0 4 2 1 1 1 8
2 1 0 3 2 2 1 1 1 4 0 2 1 1 8
2 1 1 1 4 2 0 -1 2 0 2 2 2 0 2 8
1 0 1 1 2 2 4 2 2 1 1 2 0 2 2 2 8
1 2 0 -1 0 2 2 3 1 2 4 2 0 2 2 2 2 8
2 3 4 0 -1 1 2 2 1 0 0 4 2 2 0 0 1 1 8
4 1 4 1 1 1 2 1 2 -2 1 4 1 1 0 2 1 0 4 8
0 0 2 0 2 2 1 1 0 1 0 2 1 1 2 2 2 2 2 1 8
0 0 2 2 0 2 0 1 1 1 2 2 4 2 2 2 2 2 1 0 2 8
1 2 1 2 2 0 4 0 2 1 0 1 0 2 1 1 4 0 2 0 2 1 8
2 2 2 2 2 2 1 2 1 2 2 2 2 2 1 0 0 2 1 1 4 1 1 8
2 2 2 2 2 1 1 2 1 2 2 0 2 0 -1 3 2 1 1 1 2 0 1 2 8
2 1 2 1 0 1 2 2 2 2 1 0 1 2 2 1 1 2 0 2 0 1 1 -1 1 8
1 2 1 2 3 2 2 4 0 1 -1 2 1 0 2 2 2 2 1 1 2 2 2 1 0 1 8
3 2 2 0 1 2 4 2 2 1 1 3 -1 2 2 1 4 2 3 3 0 -1 2 1 1 1 0 8
0 2 2 2 1 2 3 1 2 4 -1 0 1 2 4 -1 3 0 2 0 1 2 3 0 0 2 1 2 8
1 4 1 2 3 4 0 0 4 1 -1 1 1 2 3 2 0 0 1 1 1 0 2 1 0 2 2 2 2 8
2 2 2 2 2 2 2 2 4 2 2 1 2 4 1 0 4 1 1 1 2 2 4 2 2 3 0 2 3 2 8
2 2 1 2 3 0 0 2 2 0 0 1 1 2 1 2 2 0 1 1 1 2 2 0 0 1 4 0 1 2 2 8
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DIVISORS (elementary divisors)
1^16 3^8 15^8
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MINIMAL_NORM
8
-
KISSING_NUMBER
3600
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GROUP_ORDER
2^8 * 3^3 * 5^3
-
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
0 9 0 3 -1 -14 2 -10 -5 -6 1 2 3 9 -2 0 6 -2 -2 -5 4 -1 -13 0 1 2 10 3 3 3 3 -6
0 0 0 0 0 -1 0 -1 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 6 0 1 -1 -9 0 -5 -2 -3 1 1 1 5 -1 0 4 -2 -2 -2 3 0 -7 0 0 1 6 2 2 2 1 -4
0 6 1 0 -2 -10 0 -7 -3 -4 2 1 2 5 0 0 5 -2 -2 -3 2 -1 -8 1 1 1 8 2 2 3 2 -4
0 9 0 3 0 -14 2 -10 -5 -6 0 2 3 9 -2 0 6 -1 -2 -5 4 -1 -13 0 1 2 9 3 3 3 3 -6
0 -18 -1 -1 3 26 0 17 8 10 -3 -2 -5 -14 2 0 -12 5 5 7 -7 1 21 -1 -2 -3 -19 -6 -6 -6 -5 12
1 2 0 -1 -1 -4 -1 -2 0 -2 2 0 0 1 0 0 2 -2 0 -2 1 0 -3 1 0 1 4 1 1 1 1 -2
-1 13 0 4 -1 -19 3 -13 -8 -7 0 3 4 13 -3 1 8 -2 -4 -5 5 -1 -17 0 1 2 12 4 4 4 4 -8
0 -1 0 0 0 0 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 -1 0
0 1 -1 1 0 -1 1 -2 -2 0 0 0 0 1 -1 0 1 0 0 0 0 0 -2 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 -1 0 0 0 0 1
0 5 0 1 -1 -8 0 -6 -3 -3 1 0 2 4 -1 0 4 -1 -1 -2 2 -1 -7 1 0 1 6 2 2 2 2 -3
-1 13 0 3 -1 -19 2 -12 -7 -7 0 3 4 12 -3 1 8 -2 -4 -5 5 -1 -16 0 1 2 12 4 4 4 4 -8
0 3 0 1 0 -5 0 -3 -1 -2 0 1 1 3 -1 0 2 -1 -1 -2 2 0 -4 0 0 1 3 2 1 1 0 -2
0 5 1 1 -1 -8 1 -6 -3 -4 1 1 2 5 0 0 3 -1 -2 -3 2 -1 -7 0 1 0 6 2 2 2 2 -3
0 -3 0 0 0 4 0 4 2 2 -1 0 -1 -2 0 1 -2 1 0 1 -1 0 4 0 -1 -1 -4 -1 -1 -1 -1 2
1 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 -1 0 0 0 1 0 1 1 0 0 0 0 -1 0 0 -1 0 0 0 0 0 1 0 0 0 -1 0 0 -1 0 1
0 0 0 0 0 0 1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 1
0 -1 0 0 0 1 0 0 0 0 0 0 0 -1 0 0 -1 1 0 0 0 0 1 0 0 0 -1 0 0 0 0 1
0 0 0 1 1 0 0 0 0 0 -1 0 0 0 -1 0 0 1 0 0 0 0 0 0 -1 0 -1 0 0 0 0 0
-1 -8 0 0 1 12 0 9 4 5 -2 0 -2 -6 1 0 -6 3 1 4 -3 0 11 -1 -1 -2 -10 -3 -3 -3 -3 6
-1 10 -1 3 -1 -15 3 -11 -7 -6 1 2 3 10 -2 1 6 -2 -2 -4 4 -1 -14 0 1 2 10 3 3 4 4 -6
0 -3 0 0 0 4 0 2 1 1 0 -1 -1 -2 1 0 -2 1 1 1 -1 0 3 0 0 -1 -2 -1 -1 -1 0 2
0 5 0 1 0 -7 0 -5 -3 -2 0 1 1 4 -1 0 3 -1 -1 -2 2 0 -6 0 0 1 5 2 1 1 2 -3
1 -1 1 -1 0 0 -1 1 2 -1 1 0 0 -1 1 -1 0 0 0 -1 0 0 1 0 0 0 0 0 0 0 -1 0
-1 -2 -1 1 1 3 2 2 0 1 -1 1 -1 0 0 1 -2 0 1 0 -1 0 1 0 0 0 -3 -1 -1 -1 0 2
0 -4 0 0 1 5 -1 4 3 2 -1 0 -1 -3 0 0 -2 1 1 1 -1 0 5 0 -1 0 -4 -1 -1 -2 -2 2
0 15 1 2 -2 -23 1 -15 -7 -9 2 3 4 13 -2 0 10 -4 -4 -7 6 -1 -19 1 2 3 16 5 5 5 4 -10
-1 7 0 2 -1 -10 1 -6 -4 -3 0 2 2 7 -2 1 4 -1 -3 -2 3 -1 -8 0 0 1 6 2 2 2 2 -4
0 18 1 2 -3 -27 1 -17 -8 -10 3 3 5 15 -3 1 12 -5 -5 -8 7 -1 -22 1 1 3 19 6 6 6 5 -12
32
-2 -1 -1 2 2 1 3 -1 -2 0 -1 1 0 2 0 0 -2 1 1 0 -1 0 -1 -1 1 0 -1 0 -1 0 1 1
-1 -1 -1 1 1 2 2 0 -1 1 -1 0 0 0 0 0 -1 1 1 1 -1 0 0 0 0 0 -2 -1 -1 0 0 2
-1 -16 -1 -1 3 23 0 15 7 9 -3 -2 -4 -12 2 -1 -11 5 4 7 -6 1 19 -1 -1 -3 -17 -5 -5 -5 -5 11
-1 -5 -1 1 2 8 2 4 1 3 -2 0 -1 -3 0 0 -4 2 2 2 -2 0 5 -1 0 -1 -6 -2 -2 -2 -1 4
-2 13 -1 4 -1 -19 4 -14 -9 -7 1 3 4 13 -3 1 8 -3 -3 -5 5 -1 -18 0 1 2 13 4 4 5 5 -8
0 -7 0 -1 1 10 -1 7 4 4 -1 -1 -2 -6 1 0 -4 2 2 3 -3 0 9 0 -1 -1 -8 -3 -2 -2 -3 5
-1 -2 -1 1 1 3 2 1 -1 1 -1 0 0 0 0 0 -1 1 1 1 -1 0 1 0 0 0 -3 -1 -1 0 0 2
-1 -2 -1 1 1 3 1 1 0 1 -1 0 0 -1 0 0 -2 1 1 1 -1 0 2 0 0 0 -2 0 -1 -1 0 2
0 1 0 0 0 -1 1 -1 -1 0 0 0 0 1 0 0 1 0 0 0 0 0 -1 0 0 0 0 -1 0 1 0 0
-1 1 -1 1 0 -1 2 -1 -2 0 -1 1 0 2 -1 1 0 0 0 0 0 0 -2 0 0 0 0 0 0 1 1 0
-2 12 -2 5 0 -17 5 -13 -9 -6 0 3 4 13 -3 1 6 -2 -2 -5 5 -1 -17 -1 1 2 11 4 3 4 5 -7
-1 -10 0 -1 1 14 0 9 4 5 -1 -1 -2 -7 2 0 -7 3 2 4 -4 0 12 -1 0 -2 -10 -3 -3 -3 -3 7
-1 -17 -1 -1 3 26 0 17 8 10 -3 -2 -5 -14 2 0 -12 5 5 7 -7 1 21 -1 -2 -3 -19 -6 -6 -6 -5 12
0 1 0 0 0 -2 0 -1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 -1 0 0 0 1 0 0 1 0 -1
0 -2 1 -1 -1 2 0 2 1 0 0 0 0 -1 1 1 -1 0 0 0 -1 -1 2 0 0 -1 -1 -1 0 0 0 1
-1 8 0 2 -1 -12 2 -8 -5 -5 1 2 2 8 -1 1 5 -2 -2 -4 3 -1 -11 0 1 1 8 2 3 3 3 -5
-1 -1 -1 1 1 2 1 0 -1 1 -1 0 0 0 0 0 0 1 1 1 -1 0 1 0 0 0 -2 -1 -1 0 0 1
0 5 0 1 -1 -8 1 -6 -3 -4 1 1 2 5 0 0 3 -1 -1 -3 2 -1 -7 0 1 1 6 2 2 2 2 -3
0 -16 0 -3 2 23 -2 15 8 9 -2 -3 -4 -14 3 -1 -10 5 4 7 -7 1 20 0 -1 -3 -16 -5 -5 -5 -5 11
-1 -10 0 -1 2 14 0 9 4 5 -1 -1 -2 -7 2 -1 -7 3 2 4 -4 0 12 -1 0 -2 -10 -3 -3 -3 -3 7
0 5 1 -1 -2 -9 -1 -5 -1 -4 2 1 2 4 0 0 4 -2 -2 -3 2 -1 -6 1 1 1 7 2 3 2 1 -4
0 -9 0 0 1 13 0 9 5 5 -2 -1 -2 -7 1 0 -6 3 2 3 -3 0 11 -1 -1 -2 -10 -3 -3 -3 -3 6
-1 -1 -1 1 1 2 2 0 -1 1 -1 0 0 0 0 0 0 1 1 1 -1 0 0 0 0 0 -2 -1 -1 0 0 1
-1 5 0 1 -1 -8 1 -6 -3 -3 1 1 2 5 -1 0 3 -1 -1 -2 2 -1 -7 0 1 1 6 2 2 2 2 -3
-2 5 -1 2 1 -6 2 -5 -4 -2 -1 2 1 5 -1 0 2 0 -1 -1 1 0 -6 0 1 1 3 1 1 1 2 -2
0 -11 0 -1 2 16 0 12 6 5 -2 -1 -3 -8 2 0 -8 3 2 4 -4 0 14 -1 -1 -2 -12 -4 -3 -4 -4 7
0 -1 0 0 0 1 0 1 1 0 0 0 0 -1 0 0 0 0 0 0 0 0 1 0 0 0 -1 0 0 0 -1 1
-1 -5 -1 0 1 7 1 3 0 3 -1 -1 -1 -3 1 0 -3 2 2 3 -3 0 5 0 0 -1 -5 -2 -2 -1 0 4
0 -9 0 -1 1 13 0 9 4 5 -2 -1 -2 -7 1 0 -5 3 2 4 -4 0 11 0 -1 -2 -10 -4 -3 -2 -3 6
0 -7 0 -1 1 10 0 6 3 4 -1 -1 -2 -6 1 0 -4 2 2 3 -3 0 8 0 -1 -1 -7 -3 -2 -2 -2 5
-1 -1 -1 1 1 2 2 0 -1 1 -1 0 0 0 0 0 -1 1 1 1 -1 0 1 0 0 0 -2 -1 -1 0 0 1
0 7 0 1 -1 -11 1 -7 -3 -4 1 1 2 6 -1 0 5 -2 -2 -3 3 0 -9 0 1 1 8 2 2 3 2 -5
32
-2 10 -1 4 0 -14 4 -10 -7 -5 0 3 3 11 -2 1 5 -2 -2 -4 4 -1 -14 -1 1 1 9 3 2 3 4 -6
0 8 0 1 -1 -12 0 -8 -4 -4 1 1 2 7 -1 0 5 -2 -2 -3 3 0 -10 0 1 1 9 3 2 3 3 -6
0 -5 -1 -1 1 8 -1 6 3 4 -1 -1 -2 -5 1 0 -3 1 2 3 -2 1 7 0 -1 -1 -6 -2 -2 -2 -2 3
0 -15 0 -2 2 22 -1 14 7 8 -2 -2 -4 -12 3 -1 -10 4 4 6 -6 1 18 -1 -1 -3 -15 -5 -5 -5 -4 10
0 15 1 1 -3 -22 0 -14 -7 -8 2 2 4 12 -2 1 10 -4 -4 -6 6 -1 -18 1 1 2 16 5 5 5 5 -10
0 7 0 1 -1 -11 0 -7 -3 -4 1 1 2 6 -1 0 5 -2 -2 -3 3 0 -9 0 1 1 8 3 2 3 2 -5
0 0 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 -1 1 1 2 1 0 -1 1 -1 0 0 0 0 0 -1 1 1 1 -1 0 0 0 0 0 -1 0 -1 -1 1 1
0 11 0 2 -1 -17 1 -11 -5 -6 1 2 3 10 -2 0 7 -3 -3 -5 5 0 -14 0 1 2 12 4 3 4 3 -8
0 -5 1 -2 0 7 -2 5 4 3 0 -1 -1 -5 2 -1 -3 1 1 2 -2 0 7 0 0 -1 -4 -1 -2 -2 -2 3
-1 3 0 1 0 -5 1 -3 -2 -2 0 1 1 4 0 0 1 0 -1 -1 1 0 -4 0 1 0 3 1 1 1 1 -2
-2 0 -2 3 2 1 3 -2 -3 1 -1 1 0 2 -1 0 -1 1 1 1 0 0 -2 -1 0 0 -1 0 -1 0 1 1
-1 -3 0 -1 0 4 -1 4 2 2 0 0 -1 -2 1 0 -2 0 0 2 -1 0 4 0 0 -1 -3 -1 -1 -1 -1 2
0 12 0 2 -1 -18 1 -11 -5 -6 1 2 3 10 -2 0 8 -3 -3 -5 5 0 -15 0 1 2 12 4 3 4 3 -8
-1 -5 0 0 1 8 0 4 2 3 -1 0 -1 -4 1 -1 -4 2 1 2 -2 0 6 -1 0 -1 -5 -1 -2 -2 -1 4
-1 14 0 2 -2 -21 2 -14 -8 -8 2 3 4 13 -2 1 8 -4 -4 -6 6 -1 -18 0 2 2 15 5 5 5 5 -9
0 0 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 3 -1 2 1 -5 2 -5 -3 -2 0 1 1 4 -1 0 1 0 0 -2 1 0 -6 0 1 1 4 2 1 1 2 -2
-1 -5 -2 1 2 9 1 5 1 5 -2 -1 -2 -4 0 0 -4 2 2 4 -2 1 6 -1 -1 -1 -7 -2 -3 -2 -1 4
-2 7 -2 4 1 -9 4 -7 -6 -3 -1 2 2 8 -2 1 3 -1 -1 -2 3 0 -10 -1 0 1 5 2 1 2 3 -4
0 -5 0 0 1 7 -1 5 3 3 -1 -1 -1 -4 0 0 -3 2 1 2 -1 0 6 -1 -1 -1 -5 -1 -1 -2 -2 3
0 -8 0 -2 1 11 -2 8 5 4 0 -1 -3 -7 2 -1 -5 1 2 3 -3 1 10 0 0 -1 -7 -2 -2 -3 -3 5
1 2 1 -1 -1 -3 -1 -1 0 -1 1 0 0 1 0 0 2 -1 -1 -1 1 0 -2 0 0 0 3 0 1 1 0 -2
0 2 0 1 0 -4 0 -3 -1 -1 0 0 1 2 -1 0 2 0 0 -1 1 0 -4 0 0 0 3 1 1 1 1 -2
0 8 0 1 -2 -13 1 -8 -4 -5 2 1 3 8 -1 1 5 -3 -2 -4 4 -1 -11 0 1 1 10 3 3 3 3 -6
-1 10 0 2 -1 -15 2 -9 -5 -6 1 3 3 10 -1 1 6 -3 -3 -5 4 -1 -13 0 1 2 10 3 3 3 3 -7
0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 1 1 0 0 1 0
-1 7 -1 2 0 -9 2 -8 -5 -3 0 1 2 6 -1 0 4 -1 -1 -2 2 0 -9 0 1 1 7 2 1 2 3 -4
0 -9 0 -2 1 14 -2 9 5 6 -1 -2 -3 -9 2 -1 -5 2 3 4 -4 1 12 0 -1 -1 -9 -3 -4 -3 -3 6
0 12 0 2 -1 -17 1 -12 -6 -6 1 2 3 10 -2 0 8 -3 -3 -5 5 0 -15 0 1 2 12 4 3 4 4 -8
0 4 0 1 0 -6 0 -3 -1 -2 0 1 1 4 -1 0 3 -1 -1 -2 2 0 -5 0 0 1 4 1 1 1 0 -3
0 5 0 1 0 -7 0 -5 -3 -2 0 1 1 4 -1 0 3 -1 -1 -2 2 0 -6 0 0 1 5 2 1 1 2 -3
-
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
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe