The Lattice (PSL(2,7) x W(F4)).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 13:23:49 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
(PSL(2,7) x W(F4)).C2
-
DIMENSION
24
-
GRAM
24 24
8 1 1 -3 0 0 2 4 1 0 0 -1 2 -2 -2
1 2 -1 2 2 4 -2 0 -3
1 8 4 0 0 2 0 0 -1 0 0 0 -2 0 0
-2 2 -4 -2 0 0 2 2 -3
1 4 8 -2 -1 2 2 0 0 0 1 0 -2 0 -1
2 2 0 -2 1 0 -2 2 -3
-3 0 -2 8 -2 0 -4 -3 -1 -3 1 0 -3 1 2
-2 -2 -3 -1 -1 -4 4 0 4
0 0 -1 -2 8 0 0 -2 0 4 1 1 2 -1 3
0 3 -2 -2 -2 -1 -1 -3 0
0 2 2 0 0 8 -2 2 -2 -1 0 -2 -1 2 -2
-2 -1 0 0 4 -2 0 3 2
2 0 2 -4 0 -2 8 0 1 0 -1 0 2 -3 -1
2 1 2 -2 -3 4 -4 1 -4
4 0 0 -3 -2 2 0 8 2 -1 -2 -3 1 0 -4
-1 -1 1 4 4 4 -1 3 0
1 -1 0 -1 0 -2 1 2 8 0 0 -2 0 0 -2
-1 2 -1 0 0 3 -3 0 2
0 0 0 -3 4 -1 0 -1 0 8 1 2 -1 -2 2
1 0 -1 0 -1 -1 0 -1 -2
0 0 1 1 1 0 -1 -2 0 1 8 2 0 0 0
2 2 -2 -2 2 -2 2 -4 -1
-1 0 0 0 1 -2 0 -3 -2 2 2 8 0 -4 4
4 0 0 -1 -3 -3 0 -4 -2
2 -2 -2 -3 2 -1 2 1 0 -1 0 0 8 0 -2
2 4 2 -1 -1 2 -2 -4 -2
-2 0 0 1 -1 2 -3 0 0 -2 0 -4 0 8 -4
-2 0 2 0 4 0 2 0 2
-2 0 -1 2 3 -2 -1 -4 -2 2 0 4 -2 -4 8
1 0 -3 0 -4 -4 1 -2 0
1 -2 2 -2 0 -2 2 -1 -1 1 2 4 2 -2 1
8 2 4 -1 -1 -1 -4 -4 -2
2 2 2 -2 3 -1 1 -1 2 0 2 0 4 0 0
2 8 -2 -3 -1 1 -2 -4 -2
-1 -4 0 -3 -2 0 2 1 -1 -1 -2 0 2 2 -3
4 -2 8 1 1 1 -4 0 0
2 -2 -2 -1 -2 0 -2 4 0 0 -2 -1 -1 0 0
-1 -3 1 8 4 0 1 1 1
2 0 1 -1 -2 4 -3 4 0 -1 2 -3 -1 4 -4
-1 -1 1 4 8 0 1 1 1
4 0 0 -4 -1 -2 4 4 3 -1 -2 -3 2 0 -4
-1 1 1 0 0 8 -2 2 -2
-2 2 -2 4 -1 0 -4 -1 -3 0 2 0 -2 2 1
-4 -2 -4 1 1 -2 8 0 0
0 2 2 0 -3 3 1 3 0 -1 -4 -4 -4 0 -2
-4 -4 0 1 1 2 0 8 1
-3 -3 -3 4 0 2 -4 0 2 -2 -1 -2 -2 2 0
-2 -2 0 1 1 -2 0 1 8
-
DIVISORS
1 1 1 1 1 1 1 1 1 1 1 1 7 7 7 7 7 7 7 7 7 7 7 7
-
MINIMAL_NORM
8
-
KISSING_NUMBER
4032
-
GROUP_ORDER
387072
-
GROUP_NAME
(PSL(27) x W(F4)).C2
-
GROUP_GENERATORS
2
24
0 -1 0 -1 0 0 0 0 0 0 0 1 0 1 0
0 0 -1 0 0 0 0 1 0
0 0 0 0 0 0 0 0 -1 0 1 1 1 2 0
0 -1 -2 1 -1 0 -2 1 0
0 0 0 0 0 0 0 -1 0 0 0 1 1 1 0
1 0 -1 1 0 0 0 2 0
1 1 1 2 0 -1 1 1 0 1 1 0 1 0 2
-2 0 3 -1 1 0 0 0 1
-1 -1 -1 0 0 1 0 0 0 0 0 0 0 1 -1
2 0 -3 1 -1 0 -1 1 -1
0 -1 0 -1 1 0 0 -1 0 -1 -1 0 -1 -1 -2
1 0 -1 0 0 -1 1 0 0
0 0 -1 0 0 0 -1 0 0 0 1 1 0 1 0
0 1 0 1 -1 0 -1 2 -1
0 0 1 -1 0 0 0 0 0 0 0 0 0 -1 0
-1 0 1 0 0 0 1 -1 1
0 0 0 -1 1 1 -1 -1 2 -1 -1 -1 0 -1 0
2 -1 0 0 0 0 2 0 -1
-1 -1 -1 -1 0 1 0 0 0 -1 -1 0 -1 0 -1
2 0 -3 0 0 0 0 0 -1
1 0 0 -1 -1 -1 1 1 0 0 0 0 0 1 1
-1 0 0 -1 0 -2 0 0 1
-1 -1 -1 0 0 1 0 0 0 -1 0 0 -1 1 -1
1 0 -2 1 -1 0 -1 0 -2
0 0 0 0 -1 0 0 0 0 1 0 0 0 0 0
-1 0 0 0 0 0 -1 -1 0
1 1 1 1 0 -1 1 0 0 1 -1 0 1 -1 1
-1 0 2 -1 2 0 1 -1 2
-1 0 -1 1 0 1 0 0 0 0 1 0 0 1 0
1 0 -1 1 -1 1 -1 1 -1
0 0 0 1 -1 0 1 1 0 1 0 1 0 1 1
-1 1 1 0 0 0 0 0 0
0 0 0 0 -1 0 0 0 0 1 0 0 1 1 1
0 -1 -1 0 0 0 -1 0 0
0 0 0 0 0 0 0 0 0 0 -1 0 -1 -1 -1
0 1 1 0 0 0 1 -1 0
0 0 1 0 0 0 0 0 0 0 0 0 0 -1 0
-1 0 1 0 0 1 1 -1 1
1 0 1 -1 0 -1 1 0 0 0 -1 0 0 -1 0
-1 0 1 -1 1 -1 2 -1 2
0 0 0 -1 0 0 -1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
1 1 1 1 -1 -1 1 1 -1 1 1 0 1 0 2
-3 0 2 -1 1 0 -1 -1 2
0 0 0 -1 1 0 -1 -1 0 -1 0 0 0 -1 -1
1 0 0 0 0 0 1 1 0
0 0 1 1 1 0 0 0 1 0 -1 -1 0 -2 0
0 0 2 -1 1 0 2 -1 0
24
0 0 0 0 0 0 0 0 0 0 1 1 0 1 0
0 1 0 1 -1 0 0 1 0
0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
-1 1 1 0 0 0 0 0 0
0 1 0 1 0 -1 0 1 0 0 1 1 1 1 1
-1 0 1 0 0 0 -1 1 0
0 0 0 -1 1 1 0 -1 1 -1 -2 -1 -1 -2 -1
1 -1 0 -1 1 0 2 -2 0
-1 -1 0 0 0 0 0 1 -1 0 0 0 -1 1 -1
0 0 -2 1 -1 0 -2 -1 -1
0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0
1 0 0 -1 1 0 1 0 0
0 1 0 2 0 0 0 0 0 1 2 1 1 1 1
-1 1 2 2 -1 1 -1 2 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 0 0 1 1 0
-1 -1 -1 0 1 1 0 0 0 -1 0 0 -1 1 -1
2 0 -2 1 -1 0 0 1 -2
-1 -1 0 0 0 -1 0 1 -2 0 1 1 0 2 -1
0 0 -3 1 -1 0 -3 1 0
0 0 0 0 0 0 0 1 0 0 1 0 0 1 1
-1 0 0 0 -1 0 -1 0 0
1 1 1 1 -2 -1 1 2 -2 2 2 1 1 2 2
-4 0 1 0 -1 0 -3 -1 2
0 0 0 0 -1 0 0 0 0 1 0 0 0 0 1
-1 1 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 -1 -1 0 -2 1
0 0 2 -2 2 0 2 -1 0
0 0 0 0 0 0 0 0 -1 0 0 0 0 1 -1
0 -1 -2 1 -1 0 -2 -1 0
1 1 0 0 -1 -1 0 1 -1 1 2 1 1 2 2
-2 0 1 0 -1 0 -2 1 1
-1 -1 -1 -1 0 1 -1 0 0 -1 0 0 -1 1 -1
1 0 -2 1 -2 0 -1 0 -2
1 1 0 0 -1 -1 0 0 0 1 1 0 1 0 2
-1 0 2 -1 1 0 0 1 1
0 0 0 0 0 0 0 -1 0 0 0 0 1 0 0
1 0 -1 0 1 0 0 1 0
0 0 0 0 0 0 0 0 1 0 0 0 1 0 1
1 0 0 -1 1 0 1 1 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 1 1 1 -1 0 1 1 0
0 0 1 0 0 0 0 0 0 0 -1 -1 0 -2 0
-1 0 1 -1 1 0 1 -2 1
0 0 0 0 1 0 0 -1 1 -1 -1 0 0 -1 -1
2 0 0 0 1 0 2 1 0
0 -1 0 -1 1 1 0 -1 1 -1 -2 -1 -1 -1 -1
2 -1 -1 -1 1 0 2 -1 -1
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe