The Lattice Q1762
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 13:25:51 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DET
DIVISORS
MINIMAL_NORM
KISSING_NUMBER
GRAM
PROPERTIES
NOTES
REFERENCES
THETA_SERIES
GROUP_ORDER
GROUP_NAME
LAST_LINE
-
NAME
Q1762
-
DIMENSION
17
-
DET
50331648
-
DIVISORS
1 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 12
-
MINIMAL_NORM
7
-
KISSING_NUMBER
816
-
GRAM
17 17
7 -1 -3 1 1 -1 1 3 -3 -3 3 1 -1 1 1 -3 -1
-1 7 -1 -3 1 1 -1 1 3 -3 -3 3 1 -1 1 1 -3
-3 -1 7 -1 -3 1 1 -1 1 3 -3 -3 3 1 -1 1 1
1 -3 -1 7 -1 -3 1 1 -1 1 3 -3 -3 3 1 -1 1
1 1 -3 -1 7 -1 -3 1 1 -1 1 3 -3 -3 3 1 -1
-1 1 1 -3 -1 7 -1 -3 1 1 -1 1 3 -3 -3 3 1
1 -1 1 1 -3 -1 7 -1 -3 1 1 -1 1 3 -3 -3 3
3 1 -1 1 1 -3 -1 7 -1 -3 1 1 -1 1 3 -3 -3
-3 3 1 -1 1 1 -3 -1 7 -1 -3 1 1 -1 1 3 -3
-3 -3 3 1 -1 1 1 -3 -1 7 -1 -3 1 1 -1 1 3
3 -3 -3 3 1 -1 1 1 -3 -1 7 -1 -3 1 1 -1 1
1 3 -3 -3 3 1 -1 1 1 -3 -1 7 -1 -3 1 1 -1
-1 1 3 -3 -3 3 1 -1 1 1 -3 -1 7 -1 -3 1 1
1 -1 1 3 -3 -3 3 1 -1 1 1 -3 -1 7 -1 -3 1
1 1 -1 1 3 -3 -3 3 1 -1 1 1 -3 -1 7 -1 -3
-3 1 1 -1 1 3 -3 -3 3 1 -1 1 1 -3 -1 7 -1
-1 -3 1 1 -1 1 3 -3 -3 3 1 -1 1 1 -3 -1 7
-
PROPERTIES
INTEGRAL=1
-
NOTES
Called F_4(vi) by Plesken, Q_17(6)^{+6} in LDL II (see references)
-
REFERENCES
Plesken, J. Algebra, vol. 97 (1985) pp. 286-312
Conway-Sloane, "Low-Dimensional Lattices II: Subgroups of GL(n,Z)",
Proc. Royal Soc. London, A 419 (1988), 29-68.
-
THETA_SERIES
0 1
1 0
2 0
3 0
4 0
5 0
6 0
7 816
8 2040
9 0
10 0
11 20400
12 41956
13 0
14 0
15 236912
16 362406
-
GROUP_ORDER
32640
-
GROUP_NAME
C2 x L(2,16):C4
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe