The Lattice W(F4) x S5
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 13:23:43 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
W(F4) x S5
-
DIMENSION
24
-
GRAM
24
6 0 -3 -3 2 0 -1 -1 0 0 0 0 -2 0 1
1 2 0 -1 -1 -2 0 1 1
0 6 3 3 0 2 1 1 0 0 0 0 0 -2 -1
-1 0 2 1 1 0 -2 -1 -1
-3 3 6 3 -1 1 2 1 0 0 0 0 1 -1 -2
-1 -1 1 2 1 1 -1 -2 -1
-3 3 3 6 -1 1 1 2 0 0 0 0 1 -1 -1
-2 -1 1 1 2 1 -1 -1 -2
2 0 -1 -1 6 0 -3 -3 2 0 -1 -1 2 0 -1
-1 0 0 0 0 -2 0 1 1
0 2 1 1 0 6 3 3 0 2 1 1 0 2 1
1 0 0 0 0 0 -2 -1 -1
-1 1 2 1 -3 3 6 3 -1 1 2 1 -1 1 2
1 0 0 0 0 1 -1 -2 -1
-1 1 1 2 -3 3 3 6 -1 1 1 2 -1 1 1
2 0 0 0 0 1 -1 -1 -2
0 0 0 0 2 0 -1 -1 6 0 -3 -3 2 0 -1
-1 2 0 -1 -1 2 0 -1 -1
0 0 0 0 0 2 1 1 0 6 3 3 0 2 1
1 0 2 1 1 0 2 1 1
0 0 0 0 -1 1 2 1 -3 3 6 3 -1 1 2
1 -1 1 2 1 -1 1 2 1
0 0 0 0 -1 1 1 2 -3 3 3 6 -1 1 1
2 -1 1 1 2 -1 1 1 2
-2 0 1 1 2 0 -1 -1 2 0 -1 -1 6 0 -3
-3 -2 0 1 1 0 0 0 0
0 -2 -1 -1 0 2 1 1 0 2 1 1 0 6 3
3 0 -2 -1 -1 0 0 0 0
1 -1 -2 -1 -1 1 2 1 -1 1 2 1 -3 3 6
3 1 -1 -2 -1 0 0 0 0
1 -1 -1 -2 -1 1 1 2 -1 1 1 2 -3 3 3
6 1 -1 -1 -2 0 0 0 0
2 0 -1 -1 0 0 0 0 2 0 -1 -1 -2 0 1
1 6 0 -3 -3 2 0 -1 -1
0 2 1 1 0 0 0 0 0 2 1 1 0 -2 -1
-1 0 6 3 3 0 2 1 1
-1 1 2 1 0 0 0 0 -1 1 2 1 1 -1 -2
-1 -3 3 6 3 -1 1 2 1
-1 1 1 2 0 0 0 0 -1 1 1 2 1 -1 -1
-2 -3 3 3 6 -1 1 1 2
-2 0 1 1 -2 0 1 1 2 0 -1 -1 0 0 0
0 2 0 -1 -1 6 0 -3 -3
0 -2 -1 -1 0 -2 -1 -1 0 2 1 1 0 0 0
0 0 2 1 1 0 6 3 3
1 -1 -2 -1 1 -1 -2 -1 -1 1 2 1 0 0 0
0 -1 1 2 1 -3 3 6 3
1 -1 -1 -2 1 -1 -1 -2 -1 1 1 2 0 0 0
0 -1 1 1 2 -3 3 3 6
-
DIVISORS
1 1 1 1 1 1 1 1 1 1 1 1 10 10 10 10 10 10 10 10 10 10
10 10
-
MINIMAL_NORM
6
-
KISSING_NUMBER
240
-
GROUP_ORDER
138240
-
GROUP_NAME
W(F4) x S5
-
GROUP_GENERATORS
3
24
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 -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
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 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 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 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 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 -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 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 1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 -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 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 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 -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 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 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 -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 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
24
-1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 1 0 -1 0 -1 0
0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 -1
0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0
0 0 0 -1 1 0 0 1 -1
0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0
0 0 -1 0 1 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 -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 1 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 -1
0 0 0 0 0 0 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 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 1 -1 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 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 0 0 0 0 0 0 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
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 1 -1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 -1 0 0 0 0
0 0 0 0 0 0 0 0 -1 0 -1 0 1 0 1
0 1 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0
1 0 0 0 1 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 0 1 0 -1 0 -1 0
1 0 -1 0 1 0 0 0 0
0 0 0 0 1 0 1 0 -1 0 -1 0 0 0 0
0 0 0 0 0 1 0 1 0
0 0 0 0 0 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 -1 1 0 0 1 -1 0 0 0
0 0 0 0 0 0 0 -1 1
0 0 0 0 0 -1 0 1 0 1 0 -1 0 0 0
0 0 0 0 0 0 -1 0 1
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 0 -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 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 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
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 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
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 0 -1
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 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 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 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 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 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 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 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 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 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 0 0 0 0 0 0 0 0
0 0 0 0 0 0 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 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe