The Lattice 4.L3(4).2^2b
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 13:14:26 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
URL (links to other sites for this lattice)
LAST_LINE
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NAME
4.L3(4).2^2b
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DIMENSION
32
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GRAM (floating point or integer Gram matrix)
32 0
4
2 4
2 2 4
2 2 1 4
2 2 2 2 4
2 2 1 2 2 4
2 2 1 2 2 2 4
2 1 2 2 2 2 2 4
2 2 2 2 2 2 2 2 4
2 1 1 2 2 1 2 2 2 4
2 2 2 1 2 2 2 1 1 1 4
2 2 1 2 1 2 2 1 2 2 1 4
2 1 2 2 2 1 2 2 2 2 1 2 4
2 1 1 1 1 2 2 2 1 1 1 2 1 4
2 2 1 2 2 2 2 2 1 2 2 1 1 1 4
2 2 2 1 1 1 1 1 2 1 1 1 1 1 1 4
2 1 1 1 1 2 1 1 1 1 2 1 1 1 2 1 4
2 1 1 2 2 1 2 1 1 2 1 2 2 1 1 1 1 4
2 1 1 1 1 2 1 1 1 1 1 2 1 2 2 1 2 1 4
2 2 2 1 2 1 1 1 1 1 2 1 2 0 2 1 2 1 1 4
2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 1 2 2 1 2 4
2 1 1 0 1 1 0 0 1 1 1 1 0 1 1 2 1 1 1 1 1 4
2 1 1 2 1 1 1 1 2 2 0 2 2 1 1 2 1 2 1 1 1 2 4
2 1 2 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 4
2 1 1 1 1 1 1 1 2 2 1 1 1 1 1 2 1 1 1 0 1 2 2 1 4
2 2 2 1 1 1 1 1 2 1 1 2 2 1 1 1 1 1 1 2 1 1 2 2 1 4
2 1 2 2 2 2 1 2 2 1 1 1 2 1 1 2 2 2 1 1 2 1 2 1 1 1 4
2 1 2 2 2 2 2 2 2 1 2 1 2 1 1 1 1 2 1 1 2 0 1 1 1 1 2 4
2 1 1 2 2 2 2 2 2 2 1 2 2 2 2 1 2 2 2 1 2 1 2 1 1 1 2 2 4
2 1 2 1 1 2 1 1 1 1 2 1 1 1 1 1 2 1 1 1 2 1 1 1 1 1 2 2 1 4
2 2 2 2 2 2 2 1 2 1 2 2 2 1 1 1 1 2 1 1 2 1 1 1 1 2 2 2 1 2 4
1 1 2 2 1 1 1 2 1 1 1 1 2 1 1 1 1 1 1 1 1 -1 1 1 0 1 2 1 1 1 1 4
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DIVISORS (elementary divisors)
1^32
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MINIMAL_NORM
4
-
KISSING_NUMBER
146880
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GROUP_ORDER
2^10 * 3^2 * 5 * 7
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GROUP_GENERATORS
2
32
-2 -3 3 8 -1 2 2 2 2 -2 4 -4 3 -1 -3 1 -1 5 3 -2 -1 2 -4 -2 -1 5 -1 -7 0 3 -6 -4
-3 -1 2 7 -2 1 1 3 2 -1 4 -4 3 0 -3 1 -1 5 3 -1 -2 2 -4 -2 -1 4 0 -6 0 3 -5 -4
-2 -2 3 7 -2 2 2 2 1 -1 4 -4 3 -1 -3 1 -1 4 3 -2 -1 2 -3 -2 -1 4 0 -6 0 2 -5 -4
-1 3 -1 -2 -1 -1 -3 0 4 0 0 0 3 2 3 -2 1 2 -1 0 -3 1 0 1 -1 -3 0 1 -2 1 0 0
-1 1 1 1 -2 0 -1 1 3 0 2 -2 2 1 0 -1 0 3 1 0 -2 0 0 0 -1 -1 0 -2 -1 1 -1 -2
-1 -4 3 6 1 2 4 1 -3 0 2 -3 -1 -2 -5 2 -1 0 3 -1 2 1 -2 -2 0 6 0 -4 1 0 -3 -2
-1 -3 3 6 -1 2 3 1 -1 0 3 -3 0 -1 -4 1 -2 2 3 0 0 1 -3 -2 0 5 1 -5 1 1 -4 -3
-2 -1 2 6 -1 1 2 2 1 -1 3 -3 3 -1 -3 0 0 3 3 -2 -1 3 -3 -2 -1 4 0 -4 -1 2 -5 -3
-2 -2 2 6 -1 1 2 2 1 -1 3 -3 2 -1 -3 1 -1 3 3 -1 -1 2 -3 -2 -1 4 0 -5 0 2 -4 -3
-1 2 0 0 -2 -1 -3 1 5 -1 2 -1 3 2 2 -2 0 4 0 0 -3 0 0 0 -1 -2 0 -2 -1 2 -1 -2
-1 -4 4 7 -1 3 4 1 -2 0 3 -4 0 -2 -5 2 -2 2 3 -1 1 1 -3 -2 0 6 0 -6 2 1 -4 -3
-2 -2 2 6 0 1 2 2 0 -1 3 -3 2 -1 -3 1 -1 3 3 -2 0 2 -3 -2 -1 5 0 -5 0 2 -5 -3
-1 1 0 1 -2 0 -2 1 4 -1 3 -2 3 1 1 -1 -1 4 1 0 -2 0 0 0 -1 -1 0 -3 -1 2 -2 -2
-2 -4 3 9 0 2 4 2 -1 -1 4 -4 2 -2 -5 2 -1 3 4 -3 1 3 -5 -3 -1 8 0 -6 0 2 -7 -4
-1 1 0 0 -1 0 -1 1 2 0 1 -1 1 1 0 -1 0 2 0 1 -2 0 0 0 0 -1 0 -1 0 1 0 -1
-2 -2 2 6 -2 1 0 3 3 -2 4 -3 3 0 -1 1 -1 5 2 -1 -2 1 -3 -2 -1 3 -1 -6 0 3 -4 -4
0 -3 2 3 0 2 2 0 -1 0 1 -2 -1 -1 -2 1 -1 1 1 0 1 0 -1 -1 0 3 0 -3 1 0 -1 -1
0 -2 3 3 -1 2 1 0 0 0 1 -2 0 0 -1 0 -1 2 1 0 0 0 -1 -1 0 2 0 -3 0 0 -2 -2
0 -1 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 -2 2 4 -1 2 2 1 -1 0 2 -3 0 -1 -3 1 -1 2 2 0 0 0 -1 -1 0 3 0 -4 1 1 -2 -2
-2 -3 4 7 -2 3 3 1 -1 0 3 -4 1 -1 -4 1 -2 3 3 0 0 1 -3 -2 0 5 1 -6 1 1 -4 -4
-1 -4 3 6 0 2 3 1 -1 -1 2 -3 0 -1 -3 2 -1 2 2 -1 1 0 -2 -2 0 5 -1 -5 1 1 -3 -3
0 1 0 -1 -1 0 -3 0 4 -1 1 -1 2 2 3 -1 0 3 -1 0 -2 -1 1 0 -1 -2 -1 -1 -1 1 0 -1
-2 1 0 4 -2 0 0 2 3 -1 3 -3 4 0 -1 -1 0 4 2 -2 -2 3 -3 -1 -1 2 0 -3 -1 2 -4 -2
-1 -1 1 3 -1 0 -1 1 4 -2 2 -1 3 1 1 0 0 4 0 -1 -2 1 -2 -1 -1 1 -1 -3 -1 2 -3 -2
-2 -1 1 6 -1 1 1 3 2 -2 4 -4 3 -1 -3 1 -1 5 3 -2 -1 2 -3 -2 -1 4 -1 -6 0 3 -5 -3
-1 -1 2 3 -1 1 0 1 2 -1 2 -2 2 0 0 0 0 3 1 -1 -1 1 -1 -1 -1 1 -1 -3 -1 1 -2 -2
0 -3 3 4 -1 3 2 0 -1 0 2 -3 0 -1 -3 1 -2 1 2 0 1 0 -1 -1 0 3 0 -4 1 0 -2 -2
-1 -1 1 3 -1 1 1 1 1 0 2 -3 1 0 -2 0 -1 2 2 0 0 1 -1 -1 -1 2 0 -3 0 1 -2 -2
0 -3 3 4 0 2 2 0 -1 -1 2 -2 0 -1 -2 1 -1 1 1 -1 1 0 -1 -1 0 3 0 -4 1 0 -2 -2
-1 -2 2 4 0 1 2 1 0 -1 2 -2 1 -1 -2 1 -1 2 2 -1 0 1 -2 -1 0 3 0 -4 0 1 -3 -2
-1 0 1 3 0 0 1 1 0 0 1 -1 2 -1 -1 0 1 1 1 -2 -1 3 -2 -1 -1 2 0 -1 -1 1 -3 -1
32
0 -1 0 1 0 0 2 0 -1 0 -1 0 -1 -1 -1 0 0 -1 0 1 0 1 -1 0 1 1 0 0 1 0 0 1
-1 -1 1 3 0 0 3 1 -2 0 0 0 0 -2 -2 0 1 -1 1 -1 0 3 -2 -1 0 3 0 0 0 0 -2 0
-1 0 -1 1 1 -1 1 1 0 -1 -1 1 1 -1 0 0 2 0 0 -1 -1 3 -2 0 0 1 -1 1 -1 1 -1 1
-1 -1 1 3 1 0 3 1 -2 0 -1 0 0 -2 -2 0 1 -1 1 -1 0 3 -2 -1 0 3 0 0 0 0 -2 0
0 0 0 0 1 0 1 0 -1 0 -1 0 0 -1 0 0 1 -1 0 -1 0 1 0 0 0 1 -1 1 0 0 0 1
1 -1 0 -1 1 0 2 -1 -3 1 -2 0 -3 -1 -1 0 0 -3 0 1 2 0 1 0 1 1 0 2 1 -2 2 2
1 -1 1 0 0 1 2 -2 -3 2 -2 0 -2 -1 -1 0 0 -3 0 1 1 0 0 0 1 1 1 2 1 -2 1 1
0 0 -1 0 1 -1 0 0 0 0 -1 0 0 0 0 0 1 -1 0 0 0 1 0 0 0 0 -1 1 0 0 1 1
-1 -4 2 6 2 1 6 0 -4 0 -1 -1 -1 -3 -4 2 1 -2 2 -2 2 4 -4 -2 0 7 0 -1 0 0 -4 0
0 1 0 0 1 -1 1 -1 0 0 -2 1 1 0 1 -1 2 -1 -1 -1 -1 2 -1 0 0 0 0 2 -1 0 -1 1
1 -1 1 0 0 1 2 -1 -3 1 -2 0 -2 -1 -1 0 0 -2 0 1 1 0 0 0 1 1 0 1 1 -1 1 1
-1 3 -2 -2 0 -3 0 0 1 0 -2 2 1 0 2 -2 2 -1 -1 0 -2 3 -1 1 0 -2 1 4 -1 0 0 2
-1 0 0 1 1 -1 2 0 -1 0 -2 1 1 -1 0 0 2 -1 0 -1 -1 3 -2 0 0 1 0 2 -1 0 -1 1
0 4 -3 -4 -2 -2 -4 0 4 0 0 0 1 2 3 -2 0 1 -1 2 -2 -1 2 2 0 -5 0 2 0 0 3 1
0 -1 1 3 0 0 1 1 0 -1 1 -1 1 -1 -1 0 0 1 1 -1 0 1 -1 -1 0 2 -1 -2 0 1 -2 -1
-1 -3 2 6 0 1 4 1 -1 -1 1 -1 0 -2 -3 1 0 1 2 -1 0 3 -4 -2 0 5 0 -3 0 1 -4 -1
0 -6 4 8 1 3 6 1 -5 -1 1 -3 -2 -3 -6 3 -1 0 3 -1 3 1 -3 -3 1 8 -1 -5 2 0 -4 -2
0 1 0 0 0 0 1 0 0 0 -1 0 1 -1 0 -1 1 0 0 -1 -1 2 -1 0 0 0 0 1 0 0 -1 1
-1 3 -2 -2 -2 -2 -4 1 6 -2 1 0 3 2 4 -2 0 4 -1 1 -3 0 0 1 0 -4 -1 0 -1 2 0 0
-1 -2 1 4 1 0 3 1 -2 -1 0 0 1 -2 -2 1 1 0 1 -2 0 3 -3 -1 0 4 -1 -1 0 1 -3 0
0 -4 2 5 3 1 7 0 -7 0 -2 0 -2 -4 -5 2 1 -4 2 -2 3 4 -3 -2 1 7 0 0 1 -1 -3 1
0 -2 1 4 0 1 3 1 -1 -1 2 -2 0 -2 -3 1 -1 1 2 -1 1 1 -2 -1 0 4 0 -4 1 1 -3 -1
-1 -1 1 4 0 0 2 1 1 -1 1 -1 2 -1 -1 0 1 2 1 -2 -1 3 -3 -1 -1 3 0 -2 -1 1 -4 -1
0 0 0 1 -1 0 -1 1 2 -1 1 -1 1 0 0 0 0 2 0 0 -1 0 -1 0 0 0 -1 -2 1 1 0 -1
-1 -4 4 8 -1 3 5 1 -2 0 2 -4 0 -2 -5 2 -1 2 3 -1 1 2 -4 -3 0 7 0 -6 1 1 -5 -3
-1 0 0 2 0 -1 1 1 1 -1 0 0 2 -1 0 0 2 1 0 -2 -1 3 -2 0 -1 1 -1 0 -1 1 -2 0
0 -2 0 2 2 0 3 1 -2 -1 -1 0 -1 -2 -2 1 1 -1 1 -1 1 2 -1 -1 0 3 -1 0 0 0 -1 1
0 -3 2 3 1 2 4 -1 -4 1 -2 -1 -2 -2 -3 1 0 -2 1 0 2 2 -2 -1 1 4 0 0 1 -1 -1 1
-1 -1 1 4 0 0 2 1 0 -1 1 -2 1 -1 -2 0 0 1 2 -1 0 2 -2 -1 0 3 0 -2 0 1 -3 -1
2 -3 1 -1 3 1 4 -2 -6 1 -4 2 -5 -2 -2 1 1 -5 -1 1 3 0 1 0 2 2 0 3 1 -3 2 3
1 -2 1 0 2 1 4 -1 -5 1 -3 1 -3 -3 -2 1 1 -4 0 0 2 1 0 0 1 2 0 2 1 -2 1 2
-1 5 -4 -5 0 -4 -4 1 5 -1 -2 3 3 2 5 -3 3 1 -2 0 -4 2 1 2 -1 -6 -1 5 -3 1 2 2
-
PROPERTIES
INTEGRAL = 1
MODULAR = 1
-
REFERENCES
G. Nebe, Finite quaternionic matrix groups,
Representation Theory 2, 106-223 (April 1998)
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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