The Lattice S3 x ((PSL(2,7) x D8).C2)
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 13:24:06 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
GRAM
DIVISORS
MINIMAL_NORM
KISSING_NUMBER
GROUP_ORDER
GROUP_NAME
GROUP_GENERATORS
LAST_LINE
-
NAME
S3 x ((PSL(2,7) x D8).C2)
-
DIMENSION
24
-
GRAM
24
16 -4 -8 8 -4 -6 2 6 8 -8 8 8 8 -2 -4
4 -2 -3 1 3 4 -4 4 4
-4 16 8 -4 -6 8 6 -8 -2 4 -2 -2 -2 8 4
-2 -3 4 3 -4 -1 2 -1 -1
-8 8 16 -2 2 6 6 -6 0 2 -8 -8 -4 4 8
-1 1 3 3 -3 0 1 -4 -4
8 -4 -2 16 -4 0 6 0 0 0 8 6 4 -2 -1
8 -2 0 3 0 0 0 4 3
-4 -6 2 -4 16 2 -8 0 0 0 -4 -2 -2 -3 1
-2 8 1 -4 0 0 0 -2 -1
-6 8 6 0 2 16 4 -8 -2 4 -2 -4 -3 4 3
0 1 8 2 -4 -1 2 -1 -2
2 6 6 6 -8 4 16 -6 2 2 -2 -4 1 3 3
3 -4 2 8 -3 1 1 -1 -2
6 -8 -6 0 0 -8 -6 16 8 -4 0 6 3 -4 -3
0 0 -4 -3 8 4 -2 0 3
8 -2 0 0 0 -2 2 8 16 -8 0 0 4 -1 0
0 0 -1 1 4 8 -4 0 0
-8 4 2 0 0 4 2 -4 -8 16 0 -2 -4 2 1
0 0 2 1 -2 -4 8 0 -1
8 -2 -8 8 -4 -2 -2 0 0 0 16 8 4 -1 -4
4 -2 -1 -1 0 0 0 8 4
8 -2 -8 6 -2 -4 -4 6 0 -2 8 16 4 -1 -4
3 -1 -2 -2 3 0 -1 4 8
8 -2 -4 4 -2 -3 1 3 4 -4 4 4 16 -4 -8
8 -4 -6 2 6 8 -8 8 8
-2 8 4 -2 -3 4 3 -4 -1 2 -1 -1 -4 16 8
-4 -6 8 6 -8 -2 4 -2 -2
-4 4 8 -1 1 3 3 -3 0 1 -4 -4 -8 8 16
-2 2 6 6 -6 0 2 -8 -8
4 -2 -1 8 -2 0 3 0 0 0 4 3 8 -4 -2
16 -4 0 6 0 0 0 8 6
-2 -3 1 -2 8 1 -4 0 0 0 -2 -1 -4 -6 2
-4 16 2 -8 0 0 0 -4 -2
-3 4 3 0 1 8 2 -4 -1 2 -1 -2 -6 8 6
0 2 16 4 -8 -2 4 -2 -4
1 3 3 3 -4 2 8 -3 1 1 -1 -2 2 6 6
6 -8 4 16 -6 2 2 -2 -4
3 -4 -3 0 0 -4 -3 8 4 -2 0 3 6 -8 -6
0 0 -8 -6 16 8 -4 0 6
4 -1 0 0 0 -1 1 4 8 -4 0 0 8 -2 0
0 0 -2 2 8 16 -8 0 0
-4 2 1 0 0 2 1 -2 -4 8 0 -1 -8 4 2
0 0 4 2 -4 -8 16 0 -2
4 -1 -4 4 -2 -1 -1 0 0 0 8 4 8 -2 -8
8 -4 -2 -2 0 0 0 16 8
4 -1 -4 3 -1 -2 -2 3 0 -1 4 8 8 -2 -8
6 -2 -4 -4 6 0 -2 8 16
-
DIVISORS
1 1 1 1 1 1 1 1 1 1 1 1 42 42 42 42 42 42 42 42 42 42
42 42
-
MINIMAL_NORM
16
-
KISSING_NUMBER
1008
-
GROUP_ORDER
16128
-
GROUP_NAME
S3 x ((PSL(27) x D8).C2)
-
GROUP_GENERATORS
3
24
-2 1 -1 0 1 -1 2 1 0 -1 1 0 2 -1 1
0 -1 1 -2 -1 0 1 -1 0
0 0 0 0 0 0 -1 -1 1 0 0 0 0 0 0
0 0 0 1 1 -1 0 0 0
1 0 0 0 0 0 -1 -1 0 0 -1 0 -1 0 0
0 0 0 1 1 0 0 1 0
0 -1 0 -1 0 0 1 0 0 0 0 1 0 1 0
1 0 0 -1 0 0 0 0 -1
0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0
1 0 0 -1 0 0 0 0 0 0 0 0 -1 0 0
1 0 0 0 0 0 0 0 0
-2 2 -2 2 1 -1 1 1 0 -1 0 -1 2 -2 2
-2 -1 1 -1 -1 0 1 0 1
-2 2 -2 1 1 -1 1 1 0 -1 0 -1 2 -2 2
-1 -1 1 -1 -1 0 1 0 1
2 -2 1 -1 -1 1 -1 -1 0 1 0 0 -2 2 -1
1 1 -1 1 1 0 -1 0 0
0 -2 1 -1 -1 0 0 -1 1 1 0 1 0 2 -1
1 1 0 0 1 -1 -1 0 -1
-1 -1 0 0 -1 0 0 -1 1 0 0 1 1 1 0
0 1 0 0 1 -1 0 0 -1
0 0 0 0 0 0 0 0 0 0 0 0 2 -1 1
0 -1 1 -2 -1 0 1 -1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 1 -1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0
0 0 0 1 1 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 0 -1 0 0 0 0 -1
0 0 0 0 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 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 0 0 0 0 -1 0 0
1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 2 -2 2
-2 -1 1 -1 -1 0 1 0 1
0 0 0 0 0 0 0 0 0 0 0 0 2 -2 2
-1 -1 1 -1 -1 0 1 0 1
0 0 0 0 0 0 0 0 0 0 0 0 -2 2 -1
1 1 -1 1 1 0 -1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 2 -1
1 1 0 0 1 -1 -1 0 -1
0 0 0 0 0 0 0 0 0 0 0 0 1 1 0
0 1 0 0 1 -1 0 0 -1
24
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 -1 0 -2 -1 1 1 -1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1
0 1 0 1 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0
-1 0 0 1 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 1 -1 1
0 -1 0 -2 -2 1 1 -1 1
0 0 0 0 0 0 0 0 0 0 0 0 1 -1 1
-1 -1 0 0 0 -1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
-1 0 0 0 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 1 0 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 0 0 0 0 0 0 0 0 0 0 0 -1 0
0 -1 0 -1 -1 1 1 -1 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 1
-1 1 0 1 1 -1 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 2 -1 1
0 -1 1 -2 -1 0 1 -1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 0 -1 0 0 0 -1 0
0 0 0 -1 1 0 2 1 -1 -1 1 0 0 0 0
1 -1 0 -2 -1 1 1 -1 0
0 -1 1 0 -1 0 -1 -1 0 0 0 0 0 1 -1
0 1 0 1 1 0 0 0 0
0 1 0 1 0 0 -1 0 0 0 0 -1 0 -1 0
-1 0 0 1 0 0 0 0 1
-1 1 -1 0 1 0 2 2 -1 -1 1 -1 1 -1 1
0 -1 0 -2 -2 1 1 -1 1
-1 1 -1 1 1 0 0 0 1 0 0 0 1 -1 1
-1 -1 0 0 0 -1 0 0 0
-1 0 0 1 0 0 0 0 0 0 0 0 1 0 0
-1 0 0 0 0 0 0 0 0
1 -1 1 -1 -1 1 0 0 -1 0 0 0 -1 1 -1
1 1 -1 0 0 1 0 0 0
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 1 0 1 1 -1 -1 1 0 0 -1 0
0 -1 0 -1 -1 1 1 -1 0
-1 0 -1 1 -1 0 -1 -1 1 0 -1 0 1 0 1
-1 1 0 1 1 -1 0 1 0
-2 1 -1 0 1 -1 2 1 0 -1 1 0 2 -1 1
0 -1 1 -2 -1 0 1 -1 0
0 -1 0 -1 0 0 1 0 0 0 1 0 0 1 0
1 0 0 -1 0 0 0 -1 0
24
0 0 0 1 -1 0 -2 -1 1 0 -1 0 0 0 0
0 0 0 0 0 0 0 0 0
0 -1 0 -1 0 0 1 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 -1 1 0 2 1 -1 -1 1 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 1 -1 0 -1 -1 1 0 -1 0 0 0 0
0 0 0 0 0 0 0 0 0
-1 1 0 0 1 0 1 1 -1 -1 1 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 -1 0 0 1 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 -1 0 0 0 0
0 0 0 0 0 0 0 0 0
2 -2 2 -1 -2 1 -2 -1 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0
1 -1 1 -1 -1 1 -1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 1 -1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
-1 0 -1 1 -1 0 -1 -1 1 0 -1 0 0 0 0
0 0 0 0 0 0 0 0 0
1 -2 1 0 -2 1 -2 -2 1 1 -1 1 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 -1 0 -2 -1 1 0 -1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0
-1 0 0 1 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 1 0 2 1 -1 -1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 -1 0 -1 -1 1 0 -1 0
0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0
0 1 0 1 1 -1 -1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 0 0 1 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 -1 0
0 0 0 0 0 0 0 0 0 0 0 0 2 -2 2
-1 -2 1 -2 -1 0 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 -1 1
-1 -1 1 -1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 1 -1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 -1 0 -1
1 -1 0 -1 -1 1 0 -1 0
0 0 0 0 0 0 0 0 0 0 0 0 1 -2 1
0 -2 1 -2 -2 1 1 -1 1
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe