The Lattice dim16mod11
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 Tue Aug 22 10:23:25 CEST 2017
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DIVISORS
MINIMAL_NORM
KISSING_NUMBER
GROUP_ORDER
GROUP_NAME
GROUP_GENERATORS
GRAM
PROPERTIES
REMARKS
LAST_LINE
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NAME
dim16mod11
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DIMENSION
16
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DIVISORS
1 1 1 1 1 1 1 1 11 11 11 11 11 11 11 11
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MINIMAL_NORM
8
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KISSING_NUMBER
720
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GROUP_ORDER
2^8 * 3^2 * 5^2
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GROUP_NAME
SL2(5) o SL2(5) . 2^2
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GROUP_GENERATORS
3
16 16
0 0 0 0 0 0 0 0 0 0 1 1 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 1 1 0 1 0 0 0 0
0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 0
0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
-1 0 0 1 -1 1 1 0 0 0 0 0 0 0 0 0
0 1 1 -1 1 -1 -1 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
1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 -1 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0
1 -1 0 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 0 0 0
16 16
0 0 0 0 0 0 0 0 0 -1 0 -1 0 -1 1 1
0 0 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0
0 0 0 0 0 0 0 0 -1 -1 0 0 0 -1 0 1
0 0 0 0 0 0 0 0 0 0 -1 0 0 0 -1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1
0 0 0 0 0 0 0 0 0 -1 0 -1 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 0 1
0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0
1 0 1 -1 1 -2 -1 -1 0 0 0 0 0 0 0 0
-1 1 -1 0 0 1 1 1 0 0 0 0 0 0 0 0
-1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 -1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 -1 1 -1 -1 0 0 0 0 0 0 0 0 0
0 -1 -1 1 -1 2 1 1 0 0 0 0 0 0 0 0
0 0 -1 1 -1 1 1 1 0 0 0 0 0 0 0 0
0 0 -1 1 0 1 1 1 0 0 0 0 0 0 0 0
16 16
1 -1 0 -1 1 -1 -1 -1 0 0 0 0 0 0 0 0
1 0 1 -1 1 -2 -1 -1 0 0 0 0 0 0 0 0
0 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 -1 1 0 0 -1 -1 -1 0 0 0 0 0 0 0 0
0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0
1 -1 0 0 1 -1 -1 0 0 0 0 0 0 0 0 0
-1 0 0 0 0 1 0 0 0 0 0 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 -1 -1 -1 -1 -1 -1 0 0
0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0
0 0 0 0 0 0 0 0 0 -1 1 -1 0 0 1 1
0 0 0 0 0 0 0 0 1 1 0 1 0 1 -1 -1
0 0 0 0 0 0 0 0 -1 -1 0 0 0 -1 1 0
0 0 0 0 0 0 0 0 1 1 0 1 1 1 -1 0
0 0 0 0 0 0 0 0 0 1 0 1 1 1 -1 -1
0 0 0 0 0 0 0 0 1 1 0 1 1 1 0 -1
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GRAM
16 16
8 4 2 2 0 4 0 0 3 0 0 0 0 0 0 0
4 8 -2 4 0 4 -4 -4 0 3 0 0 0 0 0 0
2 -2 8 2 4 2 4 2 0 0 3 0 0 0 0 0
2 4 2 8 4 4 -2 -4 0 0 0 3 0 0 0 0
0 0 4 4 8 4 2 -2 0 0 0 0 3 0 0 0
4 4 2 4 4 8 -2 -4 0 0 0 0 0 3 0 0
0 -4 4 -2 2 -2 8 2 0 0 0 0 0 0 3 0
0 -4 2 -4 -2 -4 2 8 0 0 0 0 0 0 0 3
3 0 0 0 0 0 0 0 8 -4 0 -2 4 -6 -4 -4
0 3 0 0 0 0 0 0 -4 8 2 -2 0 0 2 2
0 0 3 0 0 0 0 0 0 2 8 -4 0 -4 -4 -4
0 0 0 3 0 0 0 0 -2 -2 -4 8 -4 4 4 4
0 0 0 0 3 0 0 0 4 0 0 -4 8 -6 -4 -2
0 0 0 0 0 3 0 0 -6 0 -4 4 -6 12 6 6
0 0 0 0 0 0 3 0 -4 2 -4 4 -4 6 8 4
0 0 0 0 0 0 0 3 -4 2 -4 4 -2 6 4 8
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PROPERTIES
INTEGRAL =1
MODULAR = 11
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REMARKS
Found by Gabriele Nebe using the convenient construction described in Bachoc/Nebe (Crelle 1998)
If F is the GramMatrix of the extremal 5-modular lattice with
automorphism group SL2(5)oSL2(5):2 of dimension 8
then the GramMatrix of this lattice is the block matrix
2F 3I8
3I8 10F^-1
Its automorphism group is diag(g,g^{-tr}) (the obvious subgroup) with g in Aut(F)
extended by the isometry between F and 5 F^-1.
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe