The Lattice SL2(5)^4:S4.2
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 13:14:23 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
GRAM (floating point or integer Gram matrix)
DIVISORS (elementary divisors)
MINIMAL_NORM
KISSING_NUMBER
GROUP_ORDER
GROUP_GENERATORS
PROPERTIES
REFERENCES
NOTES
URL (links to other sites for this lattice)
LAST_LINE
-
NAME
SL2(5)^4:S4.2
-
DIMENSION
32
-
GRAM (floating point or integer Gram matrix)
32 0
4
0 4
0 0 4
0 1 1 4
0 2 -2 0 4
0 1 0 1 1 4
-1 -2 -1 0 -1 0 4
0 0 0 0 -1 -1 0 4
-2 0 0 1 0 0 1 1 4
0 0 1 1 -1 0 0 0 0 4
0 -1 0 -1 -1 -1 1 0 -1 -1 4
0 1 1 -1 0 0 -2 2 0 -1 0 4
1 0 0 -2 0 0 -1 0 -2 0 1 1 4
2 1 1 1 0 1 -1 -1 -1 0 0 0 0 4
0 -1 -1 0 0 -1 1 -1 0 1 0 -2 0 -1 4
-1 -1 -1 0 0 -1 2 0 1 1 0 -2 0 -2 2 4
0 1 1 0 0 -1 -1 0 0 0 0 0 0 0 0 0 4
0 0 1 0 0 0 -1 0 0 0 -1 1 0 -1 0 0 2 4
-1 0 1 1 0 1 0 0 1 1 -1 0 -1 -1 0 1 1 2 4
1 0 0 0 0 0 0 -1 -1 1 1 -1 1 1 2 0 1 0 0 4
1 0 0 -1 0 -2 -1 0 -2 0 1 1 1 0 -1 -1 0 0 -1 0 4
0 1 1 1 0 0 0 0 1 2 -1 -1 0 0 0 1 1 0 1 0 0 4
0 0 -1 1 0 0 2 0 1 1 -1 -2 -1 0 1 2 -1 -1 0 -1 -1 2 4
1 1 0 1 1 1 -1 -1 -1 -1 0 0 0 2 -2 -2 -1 -1 -1 -1 1 0 0 4
0 1 -2 0 2 1 0 -1 0 1 -1 -1 1 0 1 1 -1 -1 0 1 0 1 1 0 4
0 1 -2 0 1 0 0 1 0 1 -1 0 1 -1 1 1 -1 -1 -1 0 0 0 1 -1 2 4
0 -1 0 0 0 1 1 -1 0 0 0 -1 -1 0 -1 0 0 1 1 -1 0 1 1 1 0 -2 4
0 -2 0 0 -1 -1 1 -1 0 1 1 -2 0 0 2 1 0 0 0 2 0 0 0 -1 0 0 0 4
0 1 1 0 -1 0 -1 2 0 0 0 2 0 0 -2 -1 1 1 0 -2 0 0 0 0 -2 0 0 -2 4
0 1 1 0 0 0 -2 0 -1 0 0 1 1 1 0 -1 1 0 1 1 0 -1 -2 0 0 0 -2 0 0 4
0 -2 1 -1 -2 -2 1 0 0 0 2 -1 0 0 1 1 1 0 0 1 0 0 0 -1 -2 -2 0 2 0 0 4
0 1 -1 0 2 2 0 -1 0 0 -1 0 0 0 -1 0 -1 0 0 -1 0 1 1 1 2 0 2 -2 0 -2 -2 4
-
DIVISORS (elementary divisors)
-
MINIMAL_NORM
-
KISSING_NUMBER
-
GROUP_ORDER
2^13 * 3^5 * 5^4
-
GROUP_GENERATORS
4
32
-1 -1 2 -1 1 3 -1 1 0 0 0 0 -1 1 1 1 1 0 0 0 2 -1 0 1 2 2 1 -2 0 -2 2 -3
0 0 0 1 1 4 -2 0 1 1 0 0 1 -1 0 0 1 -1 -1 -1 3 -2 2 -2 2 -2 1 -2 -1 -2 1 -5
0 1 0 1 1 1 0 0 1 1 0 -1 2 1 0 -1 0 0 0 -2 1 -1 0 -2 0 0 1 -1 -1 -1 1 -2
1 1 0 0 -1 1 0 0 1 1 0 1 1 -1 0 0 2 -1 0 -1 1 -2 2 0 0 -2 -1 2 -1 0 -1 1
0 -1 1 0 1 3 -1 0 0 0 0 1 -1 -1 1 1 1 -1 -1 0 2 -1 1 0 3 -2 0 -1 1 -2 0 -4
0 0 1 0 1 2 -1 0 0 1 0 0 1 -1 0 -1 1 -1 0 -1 1 -2 2 -1 3 -3 -1 -1 0 -3 0 -4
1 0 -2 -1 -2 -5 2 -1 -1 0 0 2 -1 -2 -2 0 0 0 0 2 -4 2 1 2 -3 -2 -3 5 1 4 -4 7
1 1 -2 1 -1 -3 2 -1 0 0 -1 1 1 -1 -1 -1 -1 0 0 1 -2 1 -1 0 -3 1 1 2 0 3 0 4
2 1 -2 1 -1 -3 2 -1 -1 1 0 2 0 -3 -2 -1 0 0 -1 0 -3 1 1 0 -1 -3 -2 4 0 3 -2 4
0 1 -1 1 -1 0 0 0 0 1 0 1 1 0 0 -1 1 0 0 -2 0 -1 1 -1 -1 0 0 1 -2 1 1 2
0 0 -1 0 -1 -3 2 -1 0 -1 0 0 -1 1 -1 0 -2 2 0 1 -2 3 -3 1 -3 5 1 -1 -1 3 2 4
0 0 0 1 1 1 0 0 1 0 0 -1 1 0 0 -1 -1 1 -1 0 1 0 0 -1 -1 2 2 -2 -1 1 2 -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 -2 2 1 -1 -1 1 1 1
0 -1 1 0 1 2 -1 -1 0 0 0 1 -1 -1 -1 1 0 0 -1 1 1 0 1 0 2 0 0 -1 1 -1 1 -3
0 0 0 -1 -1 0 0 1 0 0 1 0 -1 1 1 0 1 0 1 -1 0 0 0 1 -1 1 -1 1 -1 1 0 3
1 0 -2 0 -2 -4 2 -1 -1 0 0 2 -1 -1 -1 0 0 0 0 1 -3 2 0 1 -3 0 -1 3 0 4 -2 6
0 1 -1 1 0 -1 1 -1 -1 0 0 1 0 0 -1 0 -1 0 0 0 -1 1 -1 -1 0 0 1 0 0 0 0 -1
-1 1 1 0 1 2 0 1 0 0 0 -2 1 2 2 -1 0 0 1 -2 2 -1 -1 -1 2 0 1 -2 0 -3 1 -4
0 1 0 0 0 -1 1 0 0 0 0 -1 1 1 1 -1 -1 0 1 -1 0 0 -1 -1 1 -1 0 0 1 -1 -1 -1
0 0 0 -1 -1 1 0 0 0 0 1 1 -2 0 0 1 0 1 -1 0 0 1 0 1 -1 2 0 0 -1 2 1 2
-1 -1 1 -1 0 2 -1 1 1 -1 0 -1 -1 1 1 2 0 1 -1 1 2 0 0 1 -1 2 1 -1 0 1 0 0
1 1 -1 1 0 -1 1 -1 -1 1 -1 2 1 -2 -1 0 1 -2 0 -1 -1 -1 1 -1 1 -4 -1 3 1 0 -2 0
1 0 -1 0 -1 -3 1 -1 -1 0 -1 2 0 -2 -1 0 1 -2 1 1 -2 0 1 1 0 -3 -2 4 2 1 -3 3
-1 0 2 0 2 4 -2 1 1 0 -1 -2 2 1 2 1 1 -2 1 -1 4 -3 0 -1 4 -3 0 -2 2 -6 0 -7
1 -1 0 -1 -1 1 -1 0 0 1 1 2 -2 -3 -1 1 2 0 -2 1 0 -1 4 1 -1 -2 -2 2 -1 3 -2 3
1 0 -1 0 -2 -1 0 0 0 0 0 2 -1 -2 -1 0 1 0 -1 1 -1 0 2 1 -3 1 0 2 -2 4 0 5
-1 0 1 0 2 1 0 0 -1 0 -1 -1 1 1 1 0 0 -1 1 -1 1 -1 -1 -1 5 -4 -1 -1 3 -5 -1 -6
0 0 0 -1 -1 -1 1 0 -1 -1 0 0 -2 1 0 1 -1 1 0 0 -1 2 -2 1 0 1 -1 1 1 1 0 2
0 1 -1 2 0 -2 1 -1 0 0 -1 0 2 0 -1 -2 -1 0 1 0 -1 0 -1 -1 -1 2 2 -1 -1 0 2 0
0 0 0 0 0 1 -1 0 1 0 1 -1 0 1 0 0 -1 1 0 0 1 0 0 -1 -1 2 1 -2 -1 0 1 -1
0 0 -1 0 -1 -4 2 -1 -1 -1 0 0 -1 1 -1 0 -2 1 1 1 -3 3 -3 1 -2 3 0 1 1 2 0 4
0 -1 1 0 1 2 -1 0 0 1 0 1 0 -2 0 0 2 -1 -1 0 1 -2 3 0 2 -3 -1 0 0 -1 -1 -2
32
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
-1 1 1 0 2 3 -1 1 0 0 -1 -2 1 2 2 0 -1 -1 1 -2 3 -1 -2 -2 4 -2 1 -3 1 -5 2 -7
1 1 0 0 -1 -1 0 0 0 1 0 1 0 -2 -1 0 2 -1 0 0 -1 -2 2 1 -1 -1 -1 2 -1 1 -1 3
0 1 0 1 0 0 1 -1 0 0 -1 1 0 1 1 0 -1 0 0 -1 0 1 -3 0 1 2 2 -2 0 -1 3 -2
-1 0 0 0 1 2 -1 1 0 0 0 -2 1 2 1 -1 -1 0 1 -2 2 0 -1 -2 2 -1 0 -2 0 -3 1 -4
1 0 0 0 0 -1 1 -1 0 0 0 1 -1 -2 -2 0 -1 1 -2 1 -1 1 1 0 -1 0 0 1 0 3 0 2
0 -1 0 0 -1 -2 1 -1 0 -1 0 1 -1 0 -1 1 -1 1 -1 2 -2 2 -1 1 -2 3 1 0 0 3 0 3
0 0 0 0 1 1 -1 0 1 1 0 0 1 0 0 0 1 -1 0 0 1 -2 2 -1 0 -2 0 0 0 -1 -1 -2
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 1 0 -1 1 -1 -1 -1 -1 1 0 0 0 0 -1 0 0 0 -1 1 -2 0 2 1 1 -1 1 -1 2 -2
0 -1 1 -1 0 1 -1 1 0 1 1 0 0 -1 0 0 2 0 0 0 0 -2 3 1 0 -2 -2 1 -1 0 -2 1
0 0 0 0 2 3 -2 1 1 2 0 -1 2 -1 0 0 2 -2 0 -1 3 -4 4 -2 2 -7 -2 1 1 -3 -3 -4
1 0 -1 0 -1 -1 0 0 0 1 1 0 0 -2 -2 -1 1 1 -1 0 -1 -1 3 0 -2 -1 -2 2 -2 3 -1 4
0 0 1 0 1 1 0 1 0 0 0 -1 0 1 1 0 0 0 0 -1 1 0 -1 0 1 0 0 -1 0 -1 1 -1
0 0 0 0 -2 -1 1 0 0 -1 0 1 -1 0 0 0 0 1 0 1 -1 1 -1 2 -1 4 1 0 -1 2 2 3
0 0 -1 0 -2 -3 1 -1 -1 -1 0 1 -1 0 -1 0 -1 1 0 1 -3 2 -1 1 -1 2 0 1 0 2 0 3
-1 1 1 0 1 3 -1 2 0 1 0 -2 1 2 2 -1 1 0 1 -3 2 -2 -1 -1 2 1 1 -3 -2 -4 3 -4
0 1 -1 1 0 0 0 0 0 1 0 0 1 0 0 -1 0 0 0 -1 0 -1 0 -1 0 0 1 -1 -1 -1 1 -1
0 1 0 1 1 -1 1 -1 -1 0 -1 0 1 0 0 -1 -1 -1 1 -1 -1 0 -2 -1 3 -1 1 -1 2 -3 1 -4
0 0 1 0 0 2 0 1 0 0 0 0 0 0 1 0 1 0 0 -1 1 -1 0 1 1 1 0 -1 -1 -1 2 -1
-1 0 0 1 2 2 -1 0 -1 0 -1 -1 2 2 2 0 0 -2 2 -2 2 -1 -2 -2 4 -3 0 -2 2 -6 0 -7
0 1 0 1 0 -1 1 -1 -1 -1 -1 0 0 1 0 -1 -1 0 1 -1 -1 1 -3 -1 2 2 1 -2 0 -2 3 -2
0 0 -1 1 -1 -4 2 -2 -1 -2 -1 1 -1 1 -1 0 -3 1 0 2 -3 4 -4 0 -1 4 2 -1 1 2 2 2
0 0 0 0 1 1 0 0 0 0 0 -1 0 1 1 0 -1 0 0 -1 1 1 -2 -1 1 -1 0 -1 1 -1 0 -2
0 1 -1 1 0 -2 2 -1 -1 -1 -1 0 1 1 0 -1 -2 0 1 -1 -1 2 -3 -1 1 0 0 0 1 -1 1 -1
0 0 -1 1 0 0 0 -1 0 0 0 1 0 0 -1 0 -1 1 -1 0 0 1 0 -1 0 1 1 -1 -1 1 2 -1
0 1 -1 1 0 -3 2 -1 -1 -1 -1 0 1 1 0 -1 -2 0 1 0 -2 2 -3 -1 -1 1 1 0 1 0 0 1
0 0 0 1 -1 0 0 0 0 0 1 1 0 0 0 -1 1 1 0 -1 -1 0 0 1 -1 4 1 -1 -3 1 3 2
0 0 0 0 1 0 -1 0 0 1 0 0 0 -1 -1 0 0 0 -1 1 0 -1 2 -1 0 -2 0 0 0 0 -1 -1
0 1 1 0 1 1 0 1 0 1 0 -1 1 0 1 -1 1 -1 1 -2 1 -2 0 0 2 -1 0 0 0 -2 1 -2
0 -1 1 -1 -1 0 -1 1 0 0 1 0 -1 -1 0 0 2 0 0 1 -1 -1 2 2 -1 1 -1 1 -1 1 -1 3
0 0 -1 0 0 -2 1 -1 -1 -1 -1 0 0 0 -1 0 -2 0 0 1 -1 2 -1 -1 0 -2 -1 1 2 0 -2 0
32
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 1 -1 0 0 0 0 0 0 1 0 0 0 0 -1 0 -1 1 -1 0 0 0 1 -1 -1 -1 0 0 -1 1 0 0
0 0 1 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 -1 1 1 0 -1 1 0 0 0 0 1 1 0 -1 1
-1 0 0 1 1 0 0 0 0 -1 -1 -1 1 2 1 0 -2 0 1 0 1 1 -2 -1 1 0 1 -2 1 -2 1 -3
0 1 -1 0 -1 1 0 1 0 1 0 0 0 0 0 0 0 1 -1 -1 0 0 0 0 -1 0 0 0 -2 1 1 1
0 1 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 -1 1 0 0 -1 0 0 0 -1 0 1 0 -1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 -1 1 -1 0 0 0 0 0 -1 -1 1 0 -1 -1 0
0 0 1 0 2 2 -1 1 1 1 0 -1 1 0 1 0 1 -1 0 -1 2 -2 1 -1 1 -2 0 -1 0 -2 0 -3
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
-1 0 1 0 1 0 0 0 0 -1 -1 -1 1 2 2 0 -1 -1 2 0 1 0 -2 0 2 1 1 -2 2 -3 1 -3
1 0 -1 0 -1 -3 1 -1 -1 1 1 2 0 -2 -2 -1 1 0 0 0 -3 0 2 1 -2 -1 -2 3 -1 2 -2 4
0 1 1 0 1 2 -1 1 1 1 0 -1 1 0 1 0 1 -1 0 -1 2 -3 1 -1 1 -2 0 0 0 -2 0 -2
1 0 0 0 0 1 0 0 0 2 1 1 0 -2 -1 -1 2 0 -1 -1 0 -2 3 0 0 -1 -1 1 -2 1 0 1
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 -1 0 0 -1 -1 0 0 0 0 1 0 -1 0 -1 -1 0 2 0 0 -1 1 0 1 -1 4 0 -1 -2 2 2 3
0 0 0 0 0 -1 1 0 -1 0 0 0 0 0 0 -1 0 0 1 -1 -1 1 -1 0 1 0 -1 0 0 -1 0 0
-1 0 0 0 1 2 -1 1 0 0 0 -2 1 2 1 -1 0 0 1 -2 2 -1 0 -2 2 -1 0 -2 0 -3 1 -4
-1 1 1 0 1 4 -2 2 1 0 0 -3 2 2 3 -1 1 -1 2 -3 4 -3 0 -2 3 -2 0 -2 0 -5 1 -5
-1 1 1 0 1 0 0 1 0 -1 -1 -3 2 2 2 -1 -1 -1 3 -1 1 -1 -2 -1 2 -1 0 -1 2 -4 0 -3
0 -1 0 0 0 1 -1 0 0 1 1 0 0 0 -1 -1 1 1 0 -1 0 -1 2 0 0 1 -1 -1 -2 0 1 0
0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 -1 0 1 0 0 0 0 -1 0 0 1 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 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 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 1 -1 0 -1 1 0 1 0 0 -1 -2 0 1 1 1 -2 0
0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 -1 -1 0 0 0 0 1 0 0 -1 -1 0 1 -1
0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 1 -1 0 1 0 0 0 -1 2 1 -2 -2 1 2 0
-1 1 1 0 1 2 -1 1 0 -1 -1 -2 2 2 3 0 0 -2 2 -2 2 -1 -2 -1 3 -2 1 -1 2 -5 0 -5
0 -1 0 0 -1 0 0 0 1 0 1 0 0 0 0 -1 1 1 0 0 0 0 1 1 -2 3 0 -1 -2 2 1 3
0 1 0 0 1 0 0 0 0 0 -1 0 1 0 1 0 0 -2 1 0 1 -1 0 -1 1 -3 0 1 2 -2 -1 -2
0 0 0 0 0 -2 1 0 0 0 0 -1 0 0 -1 -1 -1 1 0 1 -1 0 0 0 -1 1 0 0 0 2 0 2
1 -1 -1 0 -1 -3 1 -1 -1 0 1 2 -1 -2 -2 -1 1 0 0 1 -3 1 2 1 -2 0 -2 3 0 3 -2 5
0 1 0 0 0 1 0 0 -1 0 -1 1 0 0 1 1 0 -1 0 -1 0 0 -1 0 2 -2 0 1 1 -2 0 -2
32
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 -1 0 -1 -1 0 0 0 0 1 0 0 0 -1 -1 0 1 0 0 -1 1 1 0 -2 1 -1 1 -2 2 0 3
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 0 0
-1 0 0 1 1 0 0 0 0 -1 -1 -1 1 2 1 0 -2 0 1 0 1 1 -2 -1 1 0 1 -2 1 -2 1 -3
0 0 -1 0 0 1 -1 1 1 1 1 -1 1 0 0 -1 1 0 0 -1 1 -1 2 -1 -2 -1 -1 1 -2 1 -1 2
0 1 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 -1 1 0 0 -1 0 0 0 -1 0 1 0 -1 0 0
0 1 0 0 0 -1 1 0 0 0 -1 0 1 0 0 0 0 -1 1 0 0 -1 0 0 0 -1 0 1 1 -1 -1 0
0 0 1 0 0 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 1 -1 0 1 0 2 1 -1 -1 0 2 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 -2 1 -1 -1 0 0 1 -1 0 -1 0 -1 1 0 1 -2 2 -1 1 0 2 0 -1 0 1 1 1
0 1 0 0 0 -1 0 0 0 0 0 0 1 0 0 0 0 -1 1 0 0 -1 0 0 0 -1 0 1 1 -1 -1 0
1 0 0 0 -1 0 0 0 0 1 1 2 -1 -2 -1 0 2 0 -1 0 -1 -1 2 1 -1 0 -1 2 -2 2 0 3
0 1 1 0 1 3 -1 1 0 1 0 -1 1 0 1 0 1 -1 0 -2 2 -2 0 -1 3 -2 0 -1 0 -3 1 -4
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 -1 0 0 -1 0 0 0 0 0 0 -1 0 0 1 -1 -1 0 0 0 1 0 -1 0 0 -1 0 0
-1 0 1 0 1 3 -1 1 1 0 0 -2 1 2 2 0 0 0 1 -2 3 -1 -1 -1 2 1 1 -3 0 -3 2 -4
-1 0 0 0 1 2 -1 1 0 0 0 -2 1 2 1 -1 0 0 1 -2 2 0 -1 -2 2 -1 0 -2 0 -3 1 -4
0 0 0 0 0 2 -1 1 0 1 1 -1 0 0 0 -1 1 1 0 -2 1 -1 1 -1 1 -1 -1 -1 -2 -1 1 -1
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 -1 0 0 -1 0 0 0 0 0 -1 -1 0 0 1 0 -1 0 0 0 1 0 -1 0 0 -1 0 0
1 -1 -1 0 -1 -2 1 -1 -1 0 1 2 -2 -2 -2 1 0 1 -2 2 -2 2 1 1 -2 0 -1 2 0 4 -2 4
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 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 -1 0 -1 1 0 1 0 0 -1 -2 0 1 1 1 -2 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 0 0 0 0 0 0 0 1 0 -1 -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 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 -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 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 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 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 1 0 0 0 1
-
PROPERTIES
INTEGRAL = 1
MODULAR = 1
-
REFERENCES
G. Nebe, Finite quaternionic matrix groups,
Representation Theory 2, 106-223 (April 1998)
-
NOTES
-
URL (links to other sites for this lattice)
All the quaternionic matrix groups
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe