The Lattice Q1766
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 13:25:55 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
Q1766
-
DIMENSION
17
-
DET
722204136308736
-
DIVISORS
1 6 6 6 6 6 6 6 6 12 12 12 12 12 12 12 12
-
MINIMAL_NORM
17
-
KISSING_NUMBER
240
-
GRAM
17 17
17 -1 -1 -1 -7 -1 -7 5 5 5 5 -7 -1 -7 -1 -1 -1
-1 17 -1 -1 -1 -7 -1 -7 5 5 5 5 -7 -1 -7 -1 -1
-1 -1 17 -1 -1 -1 -7 -1 -7 5 5 5 5 -7 -1 -7 -1
-1 -1 -1 17 -1 -1 -1 -7 -1 -7 5 5 5 5 -7 -1 -7
-7 -1 -1 -1 17 -1 -1 -1 -7 -1 -7 5 5 5 5 -7 -1
-1 -7 -1 -1 -1 17 -1 -1 -1 -7 -1 -7 5 5 5 5 -7
-7 -1 -7 -1 -1 -1 17 -1 -1 -1 -7 -1 -7 5 5 5 5
5 -7 -1 -7 -1 -1 -1 17 -1 -1 -1 -7 -1 -7 5 5 5
5 5 -7 -1 -7 -1 -1 -1 17 -1 -1 -1 -7 -1 -7 5 5
5 5 5 -7 -1 -7 -1 -1 -1 17 -1 -1 -1 -7 -1 -7 5
5 5 5 5 -7 -1 -7 -1 -1 -1 17 -1 -1 -1 -7 -1 -7
-7 5 5 5 5 -7 -1 -7 -1 -1 -1 17 -1 -1 -1 -7 -1
-1 -7 5 5 5 5 -7 -1 -7 -1 -1 -1 17 -1 -1 -1 -7
-7 -1 -7 5 5 5 5 -7 -1 -7 -1 -1 -1 17 -1 -1 -1
-1 -7 -1 -7 5 5 5 5 -7 -1 -7 -1 -1 -1 17 -1 -1
-1 -1 -7 -1 -7 5 5 5 5 -7 -1 -7 -1 -1 -1 17 -1
-1 -1 -1 -7 -1 -7 5 5 5 5 -7 -1 -7 -1 -1 -1 17
-
PROPERTIES
INTEGRAL=1
-
NOTES
Called F_6(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 0
8 0
9 0
10 0
11 0
12 0
13 0
14 0
15 0
16 0
17 240
18 0
19 0
20 1020
21 816
21 0
23 0
24 2040
25 0
26 0
27 0
28 0
29 17952
30 0
-
GROUP_ORDER
32640
-
GROUP_NAME
C2 x L(2,16):C4
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe