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 13:24:05 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
8 -2 -4 0 2 0 2 0 -2 4 -2 2 4 -1 -2
0 1 0 1 0 -1 2 -1 1
-2 8 2 -4 4 -2 -2 0 2 0 0 0 -1 4 1
-2 2 -1 -1 0 1 0 0 0
-4 2 8 2 0 0 2 2 0 0 4 -2 -2 1 4
1 0 0 1 1 0 0 2 -1
0 -4 2 8 -4 -2 4 0 -2 0 4 -2 0 -2 1
4 -2 -1 2 0 -1 0 2 -1
2 4 0 -4 8 0 0 0 0 4 -2 2 1 2 0
-2 4 0 0 0 0 2 -1 1
0 -2 0 -2 0 8 -2 2 0 0 0 2 0 -1 0
-1 0 4 -1 1 0 0 0 1
2 -2 2 4 0 -2 8 0 2 2 4 2 1 -1 1
2 0 -1 4 0 1 1 2 1
0 0 2 0 0 2 0 8 -2 0 0 2 0 0 1
0 0 1 0 4 -1 0 0 1
-2 2 0 -2 0 0 2 -2 8 0 2 4 -1 1 0
-1 0 0 1 -1 4 0 1 2
4 0 0 0 4 0 2 0 0 8 2 4 2 0 0
0 2 0 1 0 0 4 1 2
-2 0 4 4 -2 0 4 0 2 2 8 2 -1 0 2
2 -1 0 2 0 1 1 4 1
2 0 -2 -2 2 2 2 2 4 4 2 8 1 0 -1
-1 1 1 1 1 2 2 1 4
4 -1 -2 0 1 0 1 0 -1 2 -1 1 8 -2 -4
0 2 0 2 0 -2 4 -2 2
-1 4 1 -2 2 -1 -1 0 1 0 0 0 -2 8 2
-4 4 -2 -2 0 2 0 0 0
-2 1 4 1 0 0 1 1 0 0 2 -1 -4 2 8
2 0 0 2 2 0 0 4 -2
0 -2 1 4 -2 -1 2 0 -1 0 2 -1 0 -4 2
8 -4 -2 4 0 -2 0 4 -2
1 2 0 -2 4 0 0 0 0 2 -1 1 2 4 0
-4 8 0 0 0 0 4 -2 2
0 -1 0 -1 0 4 -1 1 0 0 0 1 0 -2 0
-2 0 8 -2 2 0 0 0 2
1 -1 1 2 0 -1 4 0 1 1 2 1 2 -2 2
4 0 -2 8 0 2 2 4 2
0 0 1 0 0 1 0 4 -1 0 0 1 0 0 2
0 0 2 0 8 -2 0 0 2
-1 1 0 -1 0 0 1 -1 4 0 1 2 -2 2 0
-2 0 0 2 -2 8 0 2 4
2 0 0 0 2 0 1 0 0 4 1 2 4 0 0
0 4 0 2 0 0 8 2 4
-1 0 2 2 -1 0 2 0 1 1 4 1 -2 0 4
4 -2 0 4 0 2 2 8 2
1 0 -1 -1 1 1 1 1 2 2 1 4 2 0 -2
-2 2 2 2 2 4 4 2 8
-
DIVISORS
1 1 1 1 1 1 1 1 1 1 1 1 6 6 6 6 6 6 6 6 42 42 42 42
-
MINIMAL_NORM
8
-
KISSING_NUMBER
1008
-
GROUP_ORDER
16128
-
GROUP_NAME
S3 x ((PSL(27) x D8).C2)
-
GROUP_GENERATORS
3
24
-1 0 -2 -1 0 0 1 1 0 1 1 -2 1 0 2
1 0 0 -1 -1 0 -1 -1 2
1 -2 1 0 2 -1 -2 0 1 -1 1 0 -1 2 -1
0 -2 1 2 0 -1 1 -1 0
1 0 1 1 0 0 -1 0 1 0 -1 0 -1 0 -1
-1 0 0 1 0 -1 0 1 0
0 1 0 0 -1 0 1 0 0 0 -1 0 0 -1 0
0 1 0 -1 0 0 0 1 0
1 -2 0 0 2 -1 -2 1 1 -1 2 -1 -1 2 0
0 -2 1 2 -1 -1 1 -2 1
0 0 0 0 -1 0 0 0 0 1 0 0 0 0 0
0 1 0 0 0 0 -1 0 0
0 0 -1 0 0 0 0 1 1 0 0 -1 0 0 1
0 0 0 0 -1 -1 0 0 1
0 0 0 0 0 0 0 1 1 1 0 -1 0 0 0
0 0 0 0 -1 -1 -1 0 1
1 -1 0 0 1 0 -1 0 1 -1 1 0 -1 1 0
0 -1 0 1 0 -1 1 -1 0
0 -1 -1 0 1 0 0 1 1 0 1 -2 0 1 1
0 -1 0 0 -1 -1 0 -1 2
0 0 0 1 0 0 0 0 1 0 -1 0 0 0 0
-1 0 0 0 0 -1 0 1 0
0 -1 -1 0 1 0 0 1 1 0 1 -1 0 1 1
0 -1 0 0 -1 -1 0 -1 1
0 0 0 0 0 0 0 0 0 0 0 0 1 0 2
1 0 0 -1 -1 0 -1 -1 2
0 0 0 0 0 0 0 0 0 0 0 0 -1 2 -1
0 -2 1 2 0 -1 1 -1 0
0 0 0 0 0 0 0 0 0 0 0 0 -1 0 -1
-1 0 0 1 0 -1 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0
0 1 0 -1 0 0 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 -1 2 0
0 -2 1 2 -1 -1 1 -2 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 -1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
0 0 0 0 -1 -1 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 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 1 0 -1 1 -1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 1
0 -1 0 0 -1 -1 0 -1 2
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 0 0 0 0 -1 0 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 1
0 -1 0 0 -1 -1 0 -1 1
24
-1 0 0 -1 0 0 1 0 -1 0 0 0 0 0 0
0 0 0 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 0 0 0 0
1 0 1 1 0 0 -1 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
1 0 1 0 0 0 0 0 0 -1 0 1 0 0 0
0 0 0 0 0 0 0 0 0
-1 1 0 0 -1 1 1 -1 -1 1 -1 0 0 0 0
0 0 0 0 0 0 0 0 0
-1 1 -1 0 -1 0 1 0 -1 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0
1 0 1 0 0 0 0 0 0 -1 0 0 0 0 0
0 0 0 0 0 0 0 0 0
1 -1 1 -1 0 -1 -1 0 0 0 1 0 0 0 0
0 0 0 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 0 0 0 0
-1 1 0 0 -1 1 1 0 -1 1 -1 0 0 0 0
0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 -1 0 0 -1 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 0 0 0 0 0 0 -1 0 0
-1 0 0 1 0 -1 0 0 0
0 0 0 0 0 0 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 0 0 0 0 1 0 1
1 0 0 -1 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 1
0 0 0 0 0 0 -1 0 1
0 0 0 0 0 0 0 0 0 0 0 0 -1 1 0
0 -1 1 1 -1 -1 1 -1 0
0 0 0 0 0 0 0 0 0 0 0 0 -1 1 -1
0 -1 0 1 0 -1 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 1
0 0 0 0 0 0 -1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 -1 1
-1 0 -1 -1 0 0 0 1 0
0 0 0 0 0 0 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 0 0 0 0 -1 1 0
0 -1 1 1 0 -1 1 -1 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 1
1 0 0 -1 0 0 -1 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
24
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 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 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 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 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 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 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 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 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 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 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 0
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 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 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 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 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 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 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 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 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 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 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
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe