The Lattice L_20,4
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 13:17:53 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
GRAM
DIVISORS
MINIMAL_NORM
KISSING_NUMBER
GROUP_ORDER
GROUP_NAME
GROUP_GENERATORS
PROPERTIES
REFERENCES
NOTES
LAST_LINE
-
NAME
L_20,4
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DIMENSION
20
-
GRAM
20 0
6
-2 6
1 0 6
-2 2 1 6
1 -1 0 1 6
-2 2 1 1 -3 6
-2 3 1 3 1 2 6
0 -1 -2 -3 1 -3 -3 6
-1 2 -2 0 -1 1 2 -1 6
1 -1 -2 -2 -2 1 -2 1 0 6
1 2 -2 1 -1 1 1 -2 2 2 6
2 2 1 -2 -1 0 -1 0 1 -1 0 6
-3 0 2 1 -2 3 2 -1 -1 0 -1 -3 6
1 2 -2 -2 0 0 1 1 1 2 1 1 -1 6
-1 -1 -3 1 -1 0 0 0 0 3 1 -2 0 0 6
1 2 2 1 -2 2 0 -1 -2 2 2 1 1 0 0 6
-1 1 -2 1 -2 2 -1 0 2 1 2 -1 0 -1 0 0 6
-1 0 2 2 -1 2 1 -1 1 -2 -2 -1 2 -2 -1 -1 2 6
1 -2 0 0 0 -3 -1 1 -2 -2 -2 -1 0 -1 0 -1 -1 1 6
1 2 0 1 -1 -1 1 0 2 -2 0 2 -1 1 -1 0 0 2 2 6
-
DIVISORS
2^10 11^4
-
MINIMAL_NORM
6
-
KISSING_NUMBER
1320
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GROUP_ORDER
2^6 * 3^2 * 5 * 11
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GROUP_NAME
(SL_2(11) o SL_2(3) ).2
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GROUP_GENERATORS
3
20 20
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 0 0 0 0 0 0 -1 0
0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0
1 0 -1 1 -1 0 1 1 -1 1 0 0 0 -1 -1 -1 -1 0 -1 0
1 1 -1 0 -1 0 1 0 -1 1 0 0 0 -1 -1 -1 -1 0 0 0
-1 -1 1 0 1 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0
0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0
0 1 0 -1 0 0 -1 -1 0 -1 0 -1 0 0 0 0 0 0 0 0
0 0 0 0 1 -1 0 -1 0 1 0 1 1 0 0 0 1 0 0 0
0 0 1 0 0 0 -1 0 0 -1 0 0 0 1 1 0 1 0 0 0
0 -1 -1 1 -1 -1 1 0 -1 1 0 1 0 0 -1 0 0 1 -1 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
-1 -1 1 -1 1 0 0 0 0 -1 0 0 0 1 1 1 1 0 0 0
-1 0 3 -1 2 2 -2 0 1 -1 1 0 0 1 2 0 1 -1 1 1
0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 -1 0 1 -1 0 0 1 0 -1 0 0 0 1 0 0 0 0 -1 0
0 0 -1 0 0 -1 0 -1 -1 0 0 0 0 0 0 0 0 1 -1 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 -1 0 1 -1 0 -1 0 0 0 1 -1 0 0 0
0 0 1 0 1 1 -1 0 1 0 0 -1 0 0 0 0 0 -1 0 1
20 20
-2 -2 2 -1 1 0 0 0 0 -1 1 0 -1 1 1 1 1 0 0 1
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 -1 1 0
0 0 0 0 0 0 0 0 0 -1 0 0 0 0 1 0 0 0 0 0
1 1 -1 0 0 1 -1 0 0 -1 0 -1 0 0 0 0 -1 0 0 0
-1 0 3 -1 2 2 -2 0 1 -1 1 -1 -1 1 2 0 1 -1 1 1
1 0 -2 1 -1 -1 1 0 0 0 -1 1 1 0 -1 0 0 0 0 -1
1 0 0 1 0 2 0 1 0 0 0 0 0 0 0 -1 0 -1 1 0
-1 0 1 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0
0 0 0 -1 0 0 1 0 -1 0 0 0 0 0 0 0 1 0 0 0
-1 -1 -1 0 0 -1 1 0 0 1 0 1 0 0 -1 1 0 1 0 0
0 -1 -1 0 0 0 1 0 0 0 0 0 0 0 -1 1 0 0 0 0
-1 -1 1 -1 0 -1 0 -1 0 -1 0 0 0 1 1 1 1 0 0 0
2 1 -2 2 -1 0 1 1 0 1 -1 1 1 -1 -1 -1 -1 0 0 -1
-1 -1 1 0 1 1 0 0 0 1 0 1 0 0 0 0 1 -1 1 1
0 0 -1 0 0 0 0 0 0 1 0 0 0 0 -1 0 -1 1 0 0
0 -1 -2 1 -1 -1 1 0 0 0 0 1 0 0 -1 1 -1 1 0 -1
0 0 -1 0 -1 -1 1 0 -1 0 0 0 0 0 -1 0 0 0 -1 0
0 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 0 0 0 0
0 0 1 1 0 1 -1 1 0 0 1 0 0 0 0 -1 -1 0 0 0
0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0
20 20
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 -1 0 0 1 0 -1 1 0 0 0 -1 0 -1 0 0 0 0
0 0 0 0 0 -1 0 0 0 0 0 1 1 0 0 0 0 0 0 0
0 0 -1 0 0 -1 0 0 0 0 0 1 1 0 0 0 0 1 0 -1
1 0 -2 1 0 0 0 0 0 0 0 1 1 0 -1 0 -1 1 0 -1
-1 0 1 -1 1 0 0 0 0 0 0 0 0 0 1 0 1 -1 0 1
-1 0 1 0 1 1 0 1 0 1 1 1 0 0 0 -1 0 0 1 0
0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0
-1 -1 1 0 0 1 1 1 -1 1 1 0 -1 0 0 -1 0 0 0 1
0 0 1 -1 0 1 0 0 0 -1 0 -1 -1 0 1 0 1 -1 0 1
0 0 1 -1 0 1 0 1 0 -1 1 -1 -1 0 1 0 0 0 0 0
1 0 -1 0 -1 -1 2 0 -1 1 -1 0 0 -1 -1 0 0 0 -1 0
-2 0 3 -1 2 1 -2 0 1 -1 1 0 0 1 2 0 1 -1 1 1
0 1 1 -1 1 2 0 0 0 1 0 -1 -1 -1 0 -1 0 -1 1 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 1 -1 0 0 0 0 0 -1 0 0 0 0 1 0 1 -1 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 1 0 -1 0 0 0 1 0 1 1 0 0 -1 0 0 0 0
0 0 1 1 0 0 -1 0 1 0 0 0 0 1 0 0 0 0 1 -1
0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0
-
PROPERTIES
-
REFERENCES
W. Plesken, G. Nebe, Finite rational matrix groups.
AMS-Memoir No. 556, vol. 116 (1995), p. 49.
G. Nebe, Some cyclo-quaternionic lattices, J. Alg. 199 (1998), 472-498.
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NOTES
CycloQuaternionic lattice of type Delta4
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe