The Lattice SL2(5)2^1+6.O6-(2).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 13:13:47 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
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NAME
SL2(5)2^1+6.O6-(2).2
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DIMENSION
32
-
GRAM (floating point or integer Gram matrix)
32 0
8
4 8
4 2 8
2 2 1 8
4 3 3 2 8
4 3 3 3 4 8
4 3 3 2 4 4 8
4 3 3 4 4 4 4 8
4 3 3 2 4 4 4 4 8
4 4 2 3 4 4 4 4 4 8
2 2 1 4 2 2 2 2 2 3 8
1 1 4 3 2 0 2 2 3 1 2 8
4 3 3 3 4 4 4 4 4 4 2 3 8
2 2 2 4 3 3 3 3 3 2 4 2 3 8
2 4 4 1 2 2 2 2 2 4 1 3 2 -2 8
3 4 2 3 2 3 2 2 1 2 2 2 0 1 4 8
4 3 3 2 4 4 4 4 4 4 1 2 4 3 2 2 8
4 3 3 2 4 4 4 4 4 4 4 2 4 3 2 2 4 8
3 2 4 0 2 1 2 0 3 2 0 4 2 -1 3 3 2 2 8
4 3 3 2 4 4 4 4 4 4 2 2 4 3 2 2 4 4 2 8
2 4 1 2 1 2 2 1 0 2 2 1 1 1 2 4 3 2 2 1 8
2 1 4 1 3 0 2 1 2 1 0 4 1 1 2 2 0 2 4 1 2 8
1 1 4 2 2 1 2 1 2 1 2 4 0 2 3 4 2 2 4 2 2 4 8
3 4 2 2 2 2 1 2 2 2 1 2 2 1 4 4 3 2 1 2 2 2 2 8
3 4 2 2 2 2 2 2 2 2 2 2 2 1 4 4 4 1 1 2 4 0 2 4 8
3 4 2 2 3 2 2 2 2 2 2 2 2 1 4 4 2 2 1 4 0 0 2 4 4 8
2 2 1 4 1 2 2 2 2 3 4 2 2 4 1 2 2 2 0 3 2 1 2 2 2 1 8
2 4 1 2 3 2 3 1 0 2 2 1 1 1 2 4 1 1 2 1 4 1 2 0 2 2 2 8
1 1 1 4 0 2 2 3 2 1 0 2 1 4 -1 2 2 0 0 1 2 2 2 2 1 1 2 0 8
3 4 2 2 2 2 4 2 2 2 3 2 2 1 4 4 2 1 1 2 2 0 2 4 4 4 2 4 0 8
1 0 2 2 2 1 1 1 3 2 2 4 2 0 2 1 1 3 4 0 1 4 2 2 1 0 2 0 1 0 8
1 4 1 0 2 2 3 2 2 3 1 1 2 -1 4 2 4 2 2 2 4 0 1 4 4 2 0 2 0 4 2 8
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DIVISORS (elementary divisors)
1^16 5^16
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MINIMAL_NORM
8
-
KISSING_NUMBER
21600
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GROUP_ORDER
2^16 * 3^5 * 5^2
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GROUP_GENERATORS
2
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
-2 1 1 0 0 0 1 0 0 1 1 0 0 -2 -2 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 -1
0 -1 -1 0 -1 1 0 2 0 0 -1 0 -1 2 0 -2 -1 0 2 -1 2 0 0 1 0 2 0 0 -2 0 0 0
1 1 1 0 1 -1 -1 -2 0 0 0 0 1 -1 0 2 -1 1 -2 1 -2 0 0 -2 1 -2 0 0 2 0 0 2
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 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 1 -1 1 1 -1 -1 -2 -1 -2 0 0 0 1 3 1 0 1 -1 1 -2 0 0 -3 0 -2 0 -1 2 0 0 3
-1 1 1 0 0 0 0 0 0 1 0 0 0 -1 -2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
-2 0 2 0 -1 0 1 1 1 2 0 0 0 -1 -3 0 0 -1 0 -1 2 0 0 2 0 2 0 0 -2 -1 0 -1
-2 0 2 0 -1 0 1 1 1 2 0 0 0 -1 -3 0 0 -1 0 -1 2 0 0 1 0 2 0 0 -2 0 0 -1
2 -1 -2 0 0 0 -1 0 -1 -2 0 -1 0 3 4 0 0 0 1 0 -1 1 -1 -2 0 0 0 0 1 0 0 2
2 -1 -1 0 0 0 -1 0 0 -1 0 0 0 2 2 0 -1 0 0 0 0 0 0 -1 0 0 0 0 0 -1 0 2
1 0 -1 0 0 0 0 0 0 -1 0 0 0 1 2 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 -1 0 1
0 -1 0 0 -1 0 1 1 1 1 -1 0 0 1 -1 0 -1 -1 0 -1 2 0 0 1 0 2 0 0 -2 -1 0 0
-1 1 1 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 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 -1 -2 0 0 0 0 1 0 -2 0 -1 -1 3 4 -2 0 0 2 0 1 0 -1 0 0 0 0 0 0 0 0 0
0 -1 -1 0 0 0 0 1 0 -1 0 -1 -1 2 2 -1 0 0 2 0 1 0 -1 0 0 1 0 0 0 0 0 0
0 -2 -1 0 -1 1 0 2 0 0 -1 0 -1 3 1 -2 -1 0 2 -1 2 0 0 1 0 2 0 0 -2 0 0 0
7 -3 -8 1 1 1 -3 -1 -3 -7 0 -1 -3 9 14 -4 0 3 5 1 -4 2 -3 -4 1 -3 0 1 4 0 -2 5
-3 1 2 -1 -1 0 1 1 1 3 0 0 1 -2 -5 1 0 -1 -1 -1 2 0 1 1 0 2 0 -1 -2 1 1 -2
-1 -1 1 0 -1 0 0 1 1 2 -1 0 0 0 -3 0 -1 0 0 -1 2 0 1 1 0 2 0 0 -2 0 0 0
-1 -1 1 0 -1 0 0 1 1 1 -1 0 0 1 -2 0 -1 0 0 -1 2 0 0 1 0 2 0 0 -2 0 0 0
3 0 -2 1 3 -1 -2 -3 -1 -4 1 -1 0 1 6 0 -1 3 1 1 -4 0 -1 -3 1 -4 1 0 5 0 -2 4
2 2 0 0 2 -1 -1 -3 -1 -2 1 0 1 -1 2 2 0 1 -2 1 -3 0 0 -3 0 -3 1 -1 3 0 0 3
6 0 -4 1 4 -1 -3 -4 -3 -6 1 0 -1 3 10 0 -1 4 1 2 -6 0 -2 -5 1 -6 1 0 7 0 -2 6
2 0 -1 0 0 0 -1 -1 0 -1 0 0 0 1 2 0 0 0 -1 0 -1 1 0 -2 0 0 0 0 1 0 0 2
-1 2 2 0 0 0 0 -1 0 2 0 1 1 -3 -4 2 0 0 -3 0 0 0 1 -1 0 0 0 -1 0 1 1 0
-1 1 3 0 1 -1 0 -1 1 3 -1 1 1 -3 -5 2 -2 1 -2 -1 0 -1 1 0 1 0 1 -1 0 0 -1 1
2 2 0 1 2 -1 -1 -3 -1 -2 1 0 1 -1 2 2 0 1 -2 1 -3 0 0 -3 0 -3 0 -1 3 0 0 3
1 1 2 0 2 -1 -1 -2 0 0 0 0 1 -2 -1 2 -1 1 -2 0 -1 -1 1 -2 0 -1 1 -1 2 0 0 2
3 1 -2 1 3 -1 -2 -3 -2 -4 1 -1 0 1 6 0 0 3 1 1 -4 0 -1 -4 1 -4 1 -1 5 1 -1 3
32
-12 0 8 -2 -5 1 6 7 5 11 -1 1 1 -6 -18 0 0 -6 -1 -4 11 -1 2 10 -1 10 -1 0 -11 -1 2 -10
-7 1 6 -2 -3 0 4 3 3 7 0 1 2 -5 -12 2 0 -4 -3 -2 6 -1 2 6 -1 5 -1 0 -6 -1 2 -6
-6 0 5 -1 -2 0 3 3 3 5 0 0 1 -4 -9 0 0 -3 -1 -2 6 -1 1 5 -1 5 0 0 -5 -1 1 -5
-2 0 2 0 1 -1 1 0 1 1 0 0 1 -2 -2 1 -1 0 -1 0 1 -1 0 1 0 0 0 0 0 0 0 -1
-3 -2 -1 -1 -3 1 2 4 1 1 1 -1 -1 2 0 -3 1 -2 3 -1 3 1 -1 4 0 3 -1 2 -3 -1 0 -4
-6 0 4 -1 -3 0 3 3 3 5 0 0 1 -3 -8 0 0 -3 -1 -1 5 0 1 5 0 4 -1 1 -5 -1 1 -5
-7 2 6 -1 -2 -1 4 2 3 6 1 0 2 -6 -11 2 1 -4 -3 -1 5 -1 2 5 -1 4 -1 0 -5 -1 2 -6
-10 2 8 -2 -3 0 5 4 4 8 1 1 2 -8 -15 2 1 -5 -3 -2 7 -1 2 7 -1 6 -1 0 -7 -1 2 -8
-7 -2 2 -2 -5 1 4 7 3 5 0 -1 0 0 -7 -3 1 -5 2 -2 8 0 1 8 -1 7 -2 2 -8 -1 2 -8
-3 -1 1 -1 -2 0 2 3 1 2 0 -1 0 1 -2 -1 0 -2 1 -1 3 0 0 3 0 3 -1 1 -3 -1 1 -3
0 -2 -2 0 0 0 0 1 0 -1 0 -1 -1 3 4 -2 0 0 2 0 1 0 -1 1 0 0 -1 1 0 0 0 -1
-1 -2 0 0 -1 0 1 2 1 0 0 -1 0 1 0 -1 0 -1 1 -1 2 0 0 2 -1 2 0 1 -2 -1 0 -1
-6 -1 4 -1 -3 0 4 4 3 5 0 0 1 -2 -8 0 0 -4 0 -2 6 -1 1 6 -1 5 -1 1 -6 -2 1 -5
-1 -2 -2 0 -1 0 1 2 0 -1 0 -1 -1 3 3 -3 0 0 3 0 2 0 -1 2 0 1 -1 1 -1 0 0 -2
-1 0 2 -1 -1 0 1 1 1 2 0 0 1 -1 -3 1 0 -2 -2 -1 2 0 1 1 -1 2 0 0 -2 -1 1 -1
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
-5 -1 1 -1 -3 1 2 4 1 3 0 -1 0 0 -4 -2 1 -2 2 -1 4 1 0 4 0 4 -1 1 -4 0 1 -5
-5 -2 1 -1 -4 1 3 5 2 3 0 -1 -1 2 -3 -3 1 -4 2 -1 6 0 0 6 -1 5 -2 2 -6 -1 2 -6
-2 -1 1 0 -1 0 1 2 1 1 0 -1 0 0 -2 -1 0 -1 1 -1 2 0 0 3 0 2 0 1 -2 -1 0 -2
-6 0 4 -1 -2 0 2 3 2 5 0 0 1 -3 -8 0 0 -2 0 -2 4 0 1 4 0 4 0 0 -4 0 0 -4
0 -1 -1 0 0 0 0 0 0 -1 0 -1 0 2 2 0 0 0 1 0 0 1 -1 0 0 0 0 0 0 0 0 0
0 -2 -1 0 -1 0 1 2 1 -1 0 -1 -1 3 2 -2 0 -1 2 -1 2 0 -1 2 -1 2 0 1 -2 -1 0 -1
5 -3 -6 1 1 0 -2 0 -2 -6 0 -2 -2 7 12 -4 0 2 4 1 -2 1 -2 -2 0 -2 0 1 3 0 -1 2
-4 0 4 -1 -2 0 2 2 2 5 -1 1 1 -3 -8 1 0 -2 -2 -2 4 0 1 3 -1 4 0 0 -4 0 1 -3
-2 -1 0 -1 -1 1 1 2 0 2 0 0 0 0 -2 -1 0 -1 1 -1 2 1 0 2 0 2 0 0 -2 0 0 -2
-3 0 3 -1 -1 0 1 1 1 4 0 1 1 -3 -6 1 0 -1 -2 -1 2 0 1 2 0 2 0 0 -2 0 0 -2
0 -1 -1 0 0 0 0 1 0 0 -1 0 0 2 1 -1 -1 0 1 -1 1 0 0 0 0 1 0 0 -1 0 0 0
1 1 0 0 1 -1 0 -2 0 -1 1 0 1 -1 1 2 0 0 -2 1 -2 0 0 -1 0 -2 0 0 2 -1 0 1
-2 0 2 0 0 -1 1 0 1 1 0 0 1 -2 -3 1 0 0 -1 0 1 0 0 1 0 1 0 0 -1 0 0 -1
-4 2 5 -1 0 -1 2 0 2 5 0 1 2 -6 -9 3 0 -2 -4 -1 3 -1 2 2 -1 2 0 -1 -2 0 1 -3
1 -2 -2 0 0 0 0 1 0 -2 0 -1 -1 3 4 -2 0 0 2 0 0 0 -1 1 0 0 0 2 0 -1 0 0
-3 2 4 -1 0 -1 1 -1 1 3 1 0 2 -5 -6 3 1 -1 -3 0 0 0 1 1 0 0 0 0 0 0 1 -2
-
PROPERTIES
INTEGRAL = 1
MODULAR = 5
-
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