The Lattice dim12mod11
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 11:54:37 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
dim12mod11
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DIMENSION
12
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DIVISORS
1 1 1 1 1 1 11 11 11 11 11 11
-
MINIMAL_NORM
6
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KISSING_NUMBER
100
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GROUP_ORDER
2^5 * 3 * 5
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GROUP_NAME
2 x S5 .2
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GROUP_GENERATORS
3
12 12
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 -1 1 0 -1 0 0
0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 1 0 -1 0 1 0
0 0 0 0 0 0 0 -1 1 0 0 -1
1 0 0 -1 -1 0 0 0 0 0 0 0
0 -1 0 -1 0 1 0 0 0 0 0 0
0 0 0 -1 0 0 0 0 0 0 0 0
0 0 1 0 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 -1 0 0 0 0 0 0
12 12
0 0 0 0 0 0 0 0 0 -1 1 -1
0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 -1 0
0 0 0 0 0 0 0 -1 1 0 0 -1
0 0 0 0 0 0 1 0 -1 0 1 0
0 0 0 0 0 0 0 0 1 0 0 0
0 0 0 -1 0 0 0 0 0 0 0 0
0 -1 0 -1 0 1 0 0 0 0 0 0
1 0 0 -1 -1 0 0 0 0 0 0 0
0 -1 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 0 0 0 0 0 0
12 12 .
-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 1 0 0 0 0 0 0 0 0 0
0 -1 0 -1 0 1 0 0 0 0 0 0
0 0 -1 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 0 -1 0 0 0 0 0
0 0 0 0 0 0 -1 1 0 -1 0 0
0 0 0 0 0 0 -1 0 1 0 -1 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 1 -1 1
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GRAM
12 12
6 -2 -2 2 2 0 3 0 0 0 0 0
-2 6 -2 -2 0 2 0 3 0 0 0 0
-2 -2 6 0 -2 -2 0 0 3 0 0 0
2 -2 0 6 -2 2 0 0 0 3 0 0
2 0 -2 -2 6 -2 0 0 0 0 3 0
0 2 -2 2 -2 6 0 0 0 0 0 3
3 0 0 0 0 0 6 2 2 -2 -2 0
0 3 0 0 0 0 2 6 2 2 0 -2
0 0 3 0 0 0 2 2 6 0 2 2
0 0 0 3 0 0 -2 2 0 6 2 -2
0 0 0 0 3 0 -2 0 2 2 6 2
0 0 0 0 0 3 0 -2 2 -2 2 6
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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 odd extremal 5-modular lattice with
automorphism group 2xS5 dimension 6
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