The Lattice M6,2
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 13:19:31 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
GRAM
DIVISORS
MINIMAL_NORM
KISSING_NUMBER
GROUP_ORDER
GROUP_NAME
GROUP_GENERATORS
NOTES
REFERENCES
PROPERTIES
LAST_LINE
-
NAME
M6,2
-
DIMENSION
6
-
GRAM
6 6
3 -1 -1 1 1 0
-1 3 -1 -1 0 1
-1 -1 3 0 -1 -1
1 -1 0 3 -1 1
1 0 -1 -1 3 -1
0 1 -1 1 -1 3
-
DIVISORS
1 1 1 5 5 5
-
MINIMAL_NORM
3
-
KISSING_NUMBER
20
-
GROUP_ORDER
240
-
GROUP_NAME
C2 x S5
-
GROUP_GENERATORS
2
6
0 0 0 -1 0 0
0 0 0 0 -1 0
-1 0 0 1 1 0
0 0 0 0 0 -1
0 -1 0 -1 0 1
0 0 -1 0 -1 -1
6
-1 0 0 0 0 0
0 0 0 1 0 0
0 0 0 0 1 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 0 0 1
-
NOTES
Called F_15 by Plesken & Pohst, Q_6(4)^{+2} in LDL II (see references)
The "shorter" associate of Q8(1).
-
REFERENCES
E. M. Rains and N. J. A. Sloane,
The Shadow Theory of Modular and Unimodular Lattices,
J. Number Theory, 73 (1998), pp. 359-389;
http://neilsloane.com/doc/shad.pdf or shad.ps
Plesken & Pohst, Math. Comp. 31 (1977), 552-573.
Conway-Sloane, "Low-Dimensional Lattices II: Subgroups of GL(n,Z)",
Proc. Royal Soc. London, A 419 (1988), 29-68.
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PROPERTIES
INTEGRAL=1
MODULAR=5
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe