The Lattice SL2(5)C5D24.2
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 13:14:15 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)C5D24.2
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DIMENSION
32
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GRAM (floating point or integer Gram matrix)
32 0
6
2 6
0 -1 6
1 -1 3 6
1 1 1 2 6
1 1 1 1 0 6
0 1 3 3 3 1 6
1 3 0 -1 1 2 1 6
0 3 0 1 2 1 2 3 6
2 1 1 1 1 2 0 2 1 6
0 1 2 1 3 1 2 1 1 2 6
0 3 1 1 1 2 2 3 3 1 0 6
0 1 2 3 2 1 3 1 2 1 1 2 6
-1 0 3 1 2 0 1 2 1 2 3 1 3 6
2 1 3 2 2 1 3 0 1 0 2 1 3 1 6
2 3 1 -1 0 2 1 3 0 2 1 3 0 1 1 6
3 3 0 -1 0 0 0 0 0 1 1 0 0 0 2 3 6
3 1 1 1 1 3 1 1 1 3 1 1 1 0 2 1 1 6
1 3 0 1 0 0 1 2 2 2 1 3 1 0 1 2 2 1 6
2 0 1 1 0 0 1 0 0 1 -1 0 1 0 1 1 1 1 0 6
0 0 1 1 -1 2 0 0 -1 0 0 0 -1 0 -1 1 0 1 0 1 6
2 0 2 1 0 -1 0 0 0 2 0 0 2 2 1 0 1 1 1 3 0 6
0 1 2 1 1 1 2 2 1 -1 1 1 0 1 0 1 0 0 0 0 2 0 6
2 1 0 0 -1 0 -1 2 1 3 0 0 0 1 -1 1 1 0 1 3 0 3 1 6
2 1 1 1 1 0 0 1 1 3 0 1 1 1 0 2 2 0 1 2 0 3 0 3 6
3 2 0 0 0 2 -1 1 0 2 0 1 0 0 1 2 1 2 1 2 2 1 0 2 1 6
1 2 -1 1 1 1 1 0 3 1 0 1 1 -1 1 0 2 2 3 0 0 0 0 0 0 1 6
0 2 -1 0 0 0 0 2 2 1 -1 2 1 0 0 1 0 0 2 1 0 0 0 2 1 1 1 6
0 1 -1 0 0 0 0 1 1 -1 -1 1 1 0 0 0 0 0 0 0 0 -1 -1 -1 -1 -1 0 3 6
2 1 0 1 0 1 1 1 1 1 -1 1 2 0 1 1 1 1 1 3 1 3 0 2 2 1 1 3 2 6
0 -1 -1 0 -1 0 -1 -1 -1 0 0 -1 1 0 0 -1 0 0 0 -1 -1 1 0 0 0 0 0 1 1 2 6
0 1 0 0 1 0 0 1 2 0 0 1 1 0 1 0 0 0 1 -1 -1 1 0 -1 1 -1 1 2 2 2 1 6
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DIVISORS (elementary divisors)
1^24 11^8
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MINIMAL_NORM
6
-
KISSING_NUMBER
6720
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GROUP_ORDER
2^6 * 3^2 * 5^2
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GROUP_GENERATORS
2
32
-9 -7 -8 4 1 3 0 -6 9 2 -2 -9 0 -3 1 9 3 2 5 -7 -7 10 8 -4 -1 8 -8 0 6 3 -7 -4
-5 -3 -3 3 -1 0 0 1 2 1 1 -2 0 -3 0 2 3 1 -1 -3 -3 5 3 -3 0 4 -2 1 2 1 -3 -2
2 0 1 -2 0 0 0 -2 1 1 0 0 1 0 0 0 -1 -1 1 0 1 -1 0 0 0 -1 0 0 0 0 0 0
0 -2 -2 -2 1 2 0 -6 4 1 -2 -3 1 1 1 3 -1 0 4 -2 -1 1 3 0 0 1 -3 -1 2 1 -2 -1
1 -2 -3 -1 -2 1 1 -2 2 2 0 -1 0 1 1 0 0 -1 1 -1 -1 2 3 -3 1 1 -1 1 1 0 -2 -1
2 0 0 -2 0 0 0 -2 0 0 0 0 1 1 1 0 -2 0 1 0 1 -2 0 1 1 -1 0 0 0 0 0 0
0 -2 -1 -1 0 1 0 -3 3 1 -1 -2 1 0 0 2 0 0 2 -2 -1 1 2 -1 0 1 -2 0 1 1 -2 -1
-2 -2 -2 2 -1 0 0 1 1 1 1 -1 0 -2 0 1 2 0 -1 -2 -2 4 2 -3 0 2 -1 2 1 0 -2 -2
-1 -1 -1 1 -1 0 0 1 0 0 1 0 0 -1 0 0 1 0 -1 -1 -1 2 1 -2 1 1 0 1 0 0 -1 -1
-2 -1 -2 1 0 0 0 0 1 1 0 -1 0 -1 1 1 1 0 0 -1 -1 2 1 -1 0 1 -1 0 1 0 -1 -1
1 -1 -1 -2 0 1 0 -3 3 2 -1 -2 1 0 1 1 -1 -1 2 -1 0 1 2 -1 0 0 -2 0 1 0 -1 -1
1 1 1 0 -1 -1 0 2 -2 0 1 2 0 0 0 -2 0 0 -2 1 1 -1 -1 -1 1 -1 2 1 -1 -1 1 0
1 0 0 -1 -1 0 1 -1 0 0 0 1 0 1 0 -1 0 0 0 0 0 -1 0 0 1 0 0 0 0 0 0 0
1 1 1 0 -1 -1 0 2 -1 1 1 2 0 -1 0 -2 1 -1 -2 1 1 0 -1 -1 0 -1 1 1 -1 -1 1 0
-1 -3 -4 -1 -1 2 1 -6 5 2 -1 -4 0 1 1 3 -1 0 4 -3 -3 3 5 -3 1 3 -4 0 3 2 -4 -2
-5 -3 -3 3 0 0 0 0 3 2 0 -3 0 -3 0 3 3 1 0 -3 -3 5 3 -3 -1 4 -3 1 2 1 -3 -2
-7 -4 -4 3 1 1 0 -2 5 1 -1 -5 0 -3 0 5 3 2 2 -4 -4 6 4 -2 -1 5 -5 0 3 2 -4 -2
-4 -3 -4 2 -1 1 0 -2 3 1 0 -4 0 -1 1 3 1 1 2 -3 -4 4 4 -3 1 4 -3 0 3 2 -4 -2
-2 -1 -1 1 0 0 0 0 1 0 0 -1 0 -1 0 1 1 1 0 -1 -1 2 1 -1 0 1 -1 0 1 0 -1 -1
-6 -1 -1 4 2 0 0 1 1 -2 -1 -2 -1 -2 -1 3 3 3 0 -3 -2 3 -1 2 -1 3 -2 -1 1 1 -1 0
-4 -1 0 2 2 0 -1 0 1 -1 -1 -2 0 -2 0 2 2 2 1 -2 -1 1 0 2 -1 2 -2 -1 1 1 -1 0
-4 -1 0 2 2 0 0 0 2 -2 -1 -2 0 -2 -1 3 2 2 1 -2 -1 2 -1 2 -1 2 -2 -1 1 0 0 0
-2 -4 -1 0 1 1 -1 -2 4 1 0 -3 2 -3 -1 3 2 0 2 -3 -2 4 3 -2 -1 3 -3 1 2 1 -3 -2
-7 -3 -2 4 3 1 -1 0 4 -1 -1 -4 0 -4 -1 5 4 2 1 -4 -3 6 1 0 -2 4 -4 0 2 1 -2 -2
-4 -3 -3 1 2 2 1 -3 4 0 -2 -4 0 -1 0 4 2 1 3 -3 -2 4 2 0 -1 3 -4 0 2 0 -2 -1
-5 -3 -4 3 0 1 0 -1 3 1 0 -3 -1 -2 1 3 2 1 1 -3 -3 5 3 -2 0 4 -3 0 3 1 -3 -2
-2 -2 -2 1 -1 0 0 0 1 0 1 -1 0 -1 0 1 1 1 0 -1 -2 2 2 -2 1 2 -1 0 1 1 -2 -1
-2 0 0 3 -1 -1 0 4 -2 -1 2 2 -1 -1 -1 -2 3 1 -3 0 -1 1 -1 -1 0 1 1 1 -1 0 0 0
0 2 1 1 -1 -1 0 2 -3 -1 1 2 -1 1 0 -2 0 1 -2 1 0 -2 -1 1 1 -1 2 0 -1 0 1 1
-5 -2 -1 3 2 0 0 0 2 -2 -1 -2 0 -2 -1 3 3 3 1 -3 -2 2 0 2 -1 3 -3 -1 1 1 -1 0
1 -1 0 -2 1 1 0 -3 2 0 -1 -1 1 1 0 1 -1 0 3 0 0 -1 1 1 0 0 -2 -1 1 0 0 0
2 1 1 -1 -1 -1 1 1 -2 -1 1 2 0 1 0 -2 -1 0 -1 1 1 -2 -1 1 1 -1 2 0 -1 -1 1 1
32
-6 -6 -7 2 1 4 0 -6 8 3 -2 -8 0 -2 1 7 2 0 5 -5 -6 9 8 -5 -1 6 -7 1 5 2 -6 -4
-5 -5 -6 1 0 3 0 -6 7 3 -2 -7 0 -1 1 6 1 0 5 -5 -6 7 8 -5 0 6 -6 0 5 3 -6 -4
2 2 2 -1 0 -1 0 2 -3 0 1 3 0 0 0 -3 0 -1 -2 2 2 -2 -2 1 0 -2 2 0 -1 -1 2 1
0 0 1 1 0 -1 -1 3 -1 1 1 2 0 -2 0 -1 2 -1 -3 1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 0
-3 -1 -1 2 0 0 0 1 1 0 0 -1 -1 -1 0 1 2 1 -1 -1 -2 2 1 -1 0 2 -1 0 1 1 -1 -1
2 0 0 -2 0 1 0 -2 1 1 -1 -1 1 1 0 0 -1 -1 2 1 0 -1 1 -1 0 -1 -1 0 0 0 0 0
0 0 0 0 0 0 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
-4 -3 -4 0 1 3 1 -6 5 1 -3 -6 0 0 1 5 0 1 5 -4 -4 4 5 -1 0 4 -5 -1 4 2 -4 -2
-7 -3 -2 3 2 1 -1 -1 4 0 -2 -5 0 -3 0 5 3 2 2 -4 -4 5 3 -1 -1 5 -4 -1 3 2 -3 -2
-1 -1 -2 -1 0 2 0 -4 2 1 -1 -3 0 1 1 2 -1 0 3 -1 -2 1 3 -1 1 1 -2 0 2 1 -2 -1
0 -2 -2 -1 -1 1 1 -3 2 1 0 -2 0 1 0 1 0 0 2 -1 -2 1 3 -2 1 2 -2 0 2 1 -2 -1
2 1 0 -2 -1 0 0 -1 -1 1 0 1 0 1 1 -1 -2 -1 0 1 0 -1 1 -1 1 -1 1 0 0 0 0 0
1 1 1 0 -1 -1 0 3 -2 1 1 2 0 -1 0 -2 1 -1 -3 1 1 0 -1 -1 0 -1 2 1 -1 -1 1 0
3 2 2 -2 -1 -1 1 1 -3 0 1 3 0 1 0 -3 -1 -1 -2 2 2 -3 -2 1 1 -2 3 0 -1 -1 2 1
0 -1 -1 0 -1 0 0 1 0 2 1 0 0 -1 0 -1 1 -1 -1 0 -1 2 2 -3 0 1 0 1 1 0 -1 -1
1 -1 -3 -2 -1 2 1 -5 2 2 -1 -2 0 2 1 1 -2 -1 3 -1 -2 1 4 -2 1 1 -2 0 2 1 -2 -1
-3 -4 -5 0 1 3 0 -6 6 2 -2 -6 0 0 1 5 0 0 5 -4 -4 5 6 -3 0 4 -5 0 4 2 -4 -3
-1 -2 -3 0 -1 2 0 -2 2 2 0 -3 0 0 1 1 0 -1 2 -1 -3 3 4 -4 1 2 -2 1 2 1 -3 -2
1 -2 -3 -3 0 3 0 -7 4 2 -2 -4 0 2 2 3 -3 -1 5 -2 -2 2 5 -2 1 1 -3 0 3 1 -3 -2
-3 0 0 2 2 1 0 1 0 -1 -1 -1 -1 -1 -1 1 2 1 0 -1 -1 2 -1 1 -1 1 -1 0 0 0 0 0
2 1 1 -1 0 0 0 0 -1 0 0 1 0 1 0 -1 -1 -1 0 1 1 -1 -1 0 0 -2 1 0 -1 0 1 0
0 1 1 -1 2 1 0 -1 0 -1 -1 -1 0 0 0 1 -1 0 1 0 1 0 -1 2 0 -1 0 0 0 -1 1 0
-5 -3 -3 2 2 2 0 -3 5 0 -2 -5 0 -2 0 5 2 1 3 -4 -3 5 3 -1 -1 4 -5 -1 3 2 -3 -2
-7 -4 -4 2 3 3 0 -5 6 0 -3 -7 0 -2 0 7 2 2 5 -5 -4 6 4 0 -1 5 -6 -1 4 2 -4 -2
-5 -1 -1 2 3 1 -1 -2 3 -1 -2 -4 0 -2 0 5 1 2 2 -3 -2 3 1 2 -1 2 -3 -1 2 1 -1 -1
-1 -2 -3 0 -1 2 0 -3 3 2 0 -3 0 0 0 2 0 -1 2 -1 -3 4 4 -4 0 2 -2 1 2 1 -3 -2
-2 -2 -2 0 1 2 -1 -3 4 1 -2 -4 0 0 1 3 0 0 3 -2 -2 3 3 -2 0 2 -3 0 2 1 -2 -2
-2 0 -1 1 0 0 0 0 0 1 -1 -1 -1 0 1 1 0 0 0 -1 -1 1 1 0 0 1 0 -1 1 1 -1 0
1 1 0 0 -1 -1 1 2 -2 1 0 2 -1 1 1 -2 0 -1 -2 1 1 -1 -1 0 0 -1 2 0 -1 -1 1 1
-1 0 0 0 2 1 0 -1 1 0 -2 -2 0 0 0 2 0 0 1 -1 0 1 0 1 -1 0 -1 0 0 0 0 0
3 1 1 -2 0 0 0 -1 0 0 0 0 1 1 0 0 -2 -1 0 1 2 -2 -1 1 0 -2 1 0 -1 -1 1 1
0 2 2 1 0 -1 0 3 -2 -1 0 1 -1 0 0 -1 0 0 -2 1 1 -1 -2 1 0 -1 2 0 -1 -1 2 1
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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