The Lattice SL2(7)SL2(3)C3.2
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 13:13:58 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
GRAM (floating point or integer Gram matrix)
DIVISORS (elementary divisors)
MINIMAL_NORM
GROUP_ORDER
GROUP_GENERATORS
PROPERTIES
REFERENCES
NOTES
URL (links to other sites for this lattice)
LAST_LINE
-
NAME
SL2(7)SL2(3)C3.2
-
DIMENSION
32
-
GRAM (floating point or integer Gram matrix)
32 0
12
4 12
2 4 12
4 4 4 12
2 6 6 2 12
2 -2 2 4 -1 12
2 4 2 5 0 2 12
1 6 6 2 4 1 2 12
4 4 4 6 4 4 6 2 12
1 2 6 2 6 1 0 6 2 12
4 4 4 0 6 1 0 3 2 1 12
2 3 4 2 3 1 3 6 1 2 4 12
2 2 1 2 6 4 2 2 4 3 6 3 12
3 4 4 0 2 0 3 2 3 2 2 2 1 12
6 6 2 2 6 -1 4 2 4 4 2 2 4 6 12
2 0 4 2 2 1 4 3 4 3 2 6 3 1 2 12
3 6 6 2 2 -1 4 6 2 0 3 6 -1 6 4 3 12
2 4 2 5 4 2 6 4 6 2 2 2 6 2 4 4 2 12
4 4 1 4 2 2 6 3 2 2 4 3 6 3 6 3 2 4 12
1 0 6 1 3 1 2 4 3 6 2 6 2 1 1 6 2 1 1 12
2 3 6 4 4 -1 2 4 2 6 3 3 3 2 3 5 2 4 3 5 12
6 3 2 4 1 -1 4 2 2 4 1 4 0 2 4 6 4 2 3 3 6 12
2 0 4 2 2 1 4 4 6 4 2 2 1 2 2 4 4 2 1 3 2 4 12
-1 4 6 4 3 2 4 6 2 4 3 2 2 4 1 0 4 2 6 2 2 0 3 12
1 2 4 3 2 2 6 0 6 0 2 2 2 3 0 3 4 4 0 4 1 2 2 2 12
-1 2 6 2 2 2 4 6 4 4 2 6 3 2 0 5 4 4 3 6 4 1 2 4 4 12
1 1 2 4 0 4 6 0 2 2 2 3 4 3 3 4 2 4 5 0 4 6 3 2 3 2 12
3 4 2 1 4 0 2 2 5 4 4 -1 2 4 4 1 0 1 2 1 1 2 3 2 0 0 1 12
0 4 2 4 2 3 6 4 6 2 0 3 2 3 2 4 2 4 4 1 0 2 4 6 3 3 4 3 12
3 3 6 0 3 0 0 6 2 4 6 6 3 1 2 5 4 2 1 6 6 4 3 0 0 5 2 2 -2 12
3 5 4 2 3 0 2 6 4 2 2 4 0 4 2 3 6 2 2 3 -2 2 4 6 2 3 -2 2 6 2 12
2 6 6 1 6 1 1 6 2 4 3 3 3 6 4 0 4 3 2 3 2 0 0 5 2 3 0 2 3 4 6 12
-
DIVISORS (elementary divisors)
1^12 2^4 14^16
-
MINIMAL_NORM
12
-
GROUP_ORDER
2^8 * 3^3 * 7
-
GROUP_GENERATORS
5
32
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 -1 0 2 0 1 1 0 0 -1 -1 0 0 -1 0 1 -1 0 0 0 -1 -1 0 0 0 1 0 0 1 0 0
-1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 0 -2 0 0 0 0 0 0 1 0
1 -1 -1 0 2 -1 2 1 2 2 0 -1 0 1 -3 0 2 -1 0 1 -1 -1 -2 -1 -2 -1 2 -1 0 0 0 0
-1 0 1 0 -1 0 0 0 0 0 1 0 0 -1 1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 -1 0 1
0 -1 -1 1 1 -1 1 1 1 1 1 -1 0 1 -1 0 1 -1 0 1 -1 0 -1 -1 -1 0 1 -1 0 0 0 0
2 -2 -2 -1 2 -2 2 1 5 3 0 -1 0 0 -4 0 4 -1 0 1 -1 -1 -3 0 -3 -1 3 -1 -1 -1 -1 1
-1 0 1 0 0 0 0 1 0 -1 0 0 0 0 1 0 -1 0 0 0 -1 1 0 0 0 0 0 0 -1 0 0 0
1 -2 -1 0 1 -2 2 1 4 3 1 -1 0 0 -3 0 4 -1 0 1 -1 -1 -3 -1 -3 -1 2 -1 0 -1 -1 1
0 0 -1 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 1 0 0 1 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 0 0 0 0 0 0 1
0 2 0 0 0 1 -1 0 -2 -2 -1 0 0 0 2 1 -2 0 -1 0 0 0 2 1 1 1 0 0 -1 0 0 0
-1 0 1 0 -1 0 0 0 0 0 1 0 0 -1 1 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 -1 0 1
0 0 1 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 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 0 0 0 0 0 0 0 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 0 2 0 -1 0 0 1 0 -1 0 0 1 0 1 -1 -1 0 0 0 0 1 0 -1 0 0 0 0 -1 -1 1 0
1 -3 0 -1 1 -3 3 2 7 4 2 -1 0 0 -4 0 4 -1 0 1 -2 0 -5 -1 -4 -2 3 -2 -1 -2 -1 1
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 -1 1
0 1 0 0 0 0 0 0 -1 -1 0 0 0 0 1 0 -1 0 -1 0 0 0 1 0 0 1 0 0 0 0 0 0
1 0 -1 0 2 0 0 0 0 0 -1 0 -1 0 -1 0 0 0 0 0 0 -1 0 0 0 0 1 0 0 1 0 0
1 0 -1 0 1 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 0 0 -1 0 1 0 0 1 0 0 1 0 0
-1 1 1 0 -2 0 -1 -1 0 0 0 1 0 -1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 -1 -1 0 1
-1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 -1 1 0 -1 0 0 0 0 0 0 0 0
0 -2 1 -1 -1 -2 2 1 5 3 2 0 1 -1 -2 -1 3 -1 0 0 0 0 -3 -2 -3 -1 2 -1 -1 -3 1 1
1 -2 -1 0 2 -2 2 2 4 2 1 -2 0 1 -3 0 3 -1 0 1 -2 0 -3 -1 -3 -1 2 -2 0 0 -1 0
1 0 -1 0 1 0 0 -1 0 1 -1 0 0 0 -1 0 1 0 0 0 0 -1 0 0 0 0 1 0 0 1 0 0
2 -1 -3 0 3 0 1 -1 0 1 -1 -1 -1 0 -2 0 3 0 0 1 0 -2 -1 1 -1 0 1 0 1 2 -1 0
0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 -1 0 0 0 0 0 0 0 0 0 -1 0
0 0 0 0 1 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
-2 0 3 0 -2 0 0 1 0 -1 1 0 1 0 2 -1 -1 0 0 0 -1 2 0 -1 0 0 -1 0 0 -1 0 0
-2 0 3 0 -1 0 0 1 0 -1 1 0 1 0 1 -1 -1 0 1 0 -1 2 0 -2 0 0 -1 0 0 -1 0 0
32
-4 3 4 0 -4 3 -3 -2 -5 -3 0 2 1 -1 5 -1 -4 2 1 -1 1 3 4 -1 3 1 -4 2 0 -1 1 0
0 0 -1 1 1 0 0 0 -1 0 0 -1 0 0 0 0 1 0 0 1 -1 0 0 0 0 0 0 0 1 1 -1 0
0 1 -1 1 0 1 -1 -2 -3 -1 -1 0 0 0 1 0 0 1 0 0 0 0 2 1 1 1 -2 1 1 2 -1 0
-2 1 2 0 -3 0 -1 -1 0 0 1 1 1 -1 2 0 -1 1 0 0 -1 2 1 0 0 0 -2 0 0 -1 -1 1
0 0 -1 1 1 1 0 -1 -3 -1 -1 -1 0 0 1 0 0 0 0 0 0 0 1 0 1 1 -1 1 1 2 0 0
-1 0 1 -1 -2 0 -1 0 2 0 1 1 0 -1 1 0 0 1 0 0 0 1 0 0 -1 0 0 0 -1 -2 0 1
-1 2 1 0 -1 1 -2 -1 -2 -2 -1 1 0 -1 2 0 -2 1 0 0 0 1 2 1 1 1 -1 1 0 0 0 0
2 -1 -2 0 2 -1 0 0 1 1 -1 -1 0 0 -2 0 3 0 0 1 -1 -1 -1 1 -1 0 1 0 1 1 -2 0
-2 2 2 0 -3 1 -2 -1 -2 -2 0 1 1 -1 3 0 -2 1 0 0 0 2 2 0 1 1 -2 1 0 -1 0 1
1 1 -1 0 1 1 -1 -2 -3 -1 -2 0 0 0 0 0 0 1 0 0 0 0 2 1 1 1 -1 1 1 2 -1 0
-1 0 0 1 0 1 -1 0 -2 -2 0 0 0 0 2 0 -1 0 0 0 0 1 1 0 1 1 -1 1 0 0 0 0
1 -1 -1 0 1 -1 0 1 1 0 0 -1 0 0 -1 0 1 0 0 1 -1 0 -1 1 -1 0 1 0 0 0 -1 0
0 0 0 0 0 1 -1 0 -2 -2 -1 0 0 -1 2 0 -1 0 0 0 1 0 1 0 1 1 0 1 0 0 1 0
1 1 -2 1 2 1 0 -1 -3 -1 -1 -1 0 1 0 0 0 0 -1 1 0 -1 1 1 0 1 0 0 1 2 0 -1
-1 3 0 1 0 3 -2 -2 -7 -3 -2 0 0 0 3 0 -3 1 0 0 1 0 4 0 3 2 -2 2 1 2 1 -1
0 3 0 0 -1 2 -3 -2 -5 -3 -2 1 0 -1 3 1 -3 1 0 -1 1 0 4 2 3 2 -2 2 0 1 0 0
1 0 -2 1 2 0 0 0 -1 0 -1 -1 0 1 -1 0 1 0 0 1 -1 -1 0 1 0 0 0 0 1 2 -1 -1
1 1 -2 0 1 1 -1 -1 -2 -1 -2 0 0 -1 1 1 0 0 -1 0 1 -1 1 2 1 1 0 1 0 1 0 0
-1 2 1 1 0 2 -2 -1 -5 -3 -1 0 0 0 3 0 -3 1 0 0 0 1 3 0 2 2 -2 1 1 1 0 -1
0 1 0 0 0 1 -1 -1 -3 -2 -1 0 0 0 1 0 -1 1 0 0 0 1 2 1 1 1 -2 1 1 1 -1 0
-1 2 1 1 -2 2 -2 -2 -6 -3 -1 1 1 -1 4 0 -3 1 -1 -1 1 1 4 1 3 2 -3 2 1 1 0 0
-2 3 3 0 -3 2 -3 -2 -5 -3 -1 2 1 -1 4 0 -4 2 0 -1 0 2 4 1 3 1 -3 2 0 0 0 0
-1 2 2 0 -2 1 -2 -1 -2 -2 -1 1 1 0 2 0 -2 1 0 0 -1 2 2 1 1 1 -2 1 0 0 -1 0
1 -1 -1 1 2 -1 1 0 1 1 0 -1 0 1 -2 0 2 0 0 1 -2 0 -1 0 -2 0 0 -1 1 1 -2 0
0 0 -1 0 1 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0
2 -1 -2 0 2 -1 0 0 1 0 -1 -1 0 0 -2 0 2 0 0 1 0 -1 -1 1 -1 0 1 0 1 1 -1 0
0 2 0 0 -1 1 -2 -1 -2 -2 -1 1 0 -1 2 1 -2 1 -1 0 0 0 2 2 1 1 0 1 -1 0 0 0
-1 2 1 0 -2 1 -2 -2 -2 -1 0 1 0 -1 2 0 -1 1 0 0 0 1 2 0 1 1 -1 1 0 -1 0 1
1 0 -1 0 1 -1 0 0 2 1 0 -1 0 0 -2 1 2 0 0 1 -2 0 -1 1 -2 0 1 -1 0 0 -2 1
0 1 0 0 -1 1 -2 -1 -3 -2 -1 1 0 -1 2 0 -1 1 0 0 1 0 2 1 2 1 -1 2 0 0 0 0
1 -1 -1 0 2 -1 1 0 2 2 0 -1 0 1 -3 0 3 0 1 1 -2 0 -2 0 -2 -1 0 -1 1 1 -2 0
2 -1 -3 0 3 0 1 -1 0 1 -1 -1 -1 0 -2 0 3 0 0 1 0 -2 -1 1 -1 0 1 0 1 2 -1 0
32
-3 0 3 1 -3 0 0 1 -1 -1 2 1 1 0 3 -1 -3 0 0 -1 0 2 1 -2 1 0 -2 0 0 -1 1 0
0 -1 -1 1 1 -1 1 1 1 0 1 -1 0 1 0 0 0 -1 -1 1 -1 0 -1 0 -1 0 1 -1 0 0 0 0
-1 0 1 0 0 0 0 0 0 -1 0 0 0 0 1 0 -1 0 0 0 0 1 0 0 0 0 -1 0 0 0 0 0
-1 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 -1 0 0 0 -1 1 0 -1 -1 0 -1 -1 0 0 0 0
-1 1 0 1 0 1 -1 -1 -3 -2 -1 0 0 0 2 0 -2 0 0 0 1 0 2 0 2 1 -1 1 0 1 1 0
0 0 0 0 1 0 1 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 -1 0 0 1 -1 2 1 3 2 1 0 0 1 -2 0 1 -1 0 0 -1 0 -2 -1 -2 -1 1 -1 -1 -1 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 1 0 0 0 0 0 1 0 0
0 -1 0 1 1 -1 2 1 1 1 1 -1 0 1 -1 0 0 -1 0 0 -1 0 -1 -1 -1 0 0 -1 0 0 0 0
-1 0 1 0 0 0 0 -1 0 0 0 0 0 0 0 -1 0 0 1 0 0 1 0 -1 0 0 -1 0 1 1 0 0
0 2 -1 1 0 1 -1 -1 -4 -2 -1 0 0 0 2 1 -2 0 -1 0 1 -1 3 1 2 1 -1 1 0 1 0 0
0 0 -1 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 1 -1 0 0 0 0 1 0 -1 0 1 0
-1 1 0 1 0 1 0 -1 -3 -1 0 0 0 0 1 0 -1 0 0 0 1 0 2 -1 1 1 -1 1 0 0 1 0
-2 0 3 0 -2 0 0 1 0 -1 2 0 1 0 2 -1 -2 0 0 0 0 2 0 -2 0 0 -1 0 0 -2 1 0
-3 1 3 1 -3 1 -1 0 -3 -2 1 1 1 0 4 -1 -4 0 0 -1 1 2 2 -2 2 1 -2 1 0 -1 2 0
1 -2 -2 0 3 -1 2 1 2 2 0 -1 -1 1 -3 0 2 -1 1 0 0 -1 -2 -1 -1 -1 1 -1 0 1 0 0
-1 0 1 0 -1 0 0 1 0 -1 1 0 0 0 2 0 -2 0 -1 0 0 1 0 0 0 0 0 0 -1 -1 1 0
-1 0 1 1 0 0 1 0 -1 0 1 0 0 1 0 0 -1 0 0 0 -1 1 0 -1 0 0 -1 0 0 0 0 0
-2 2 1 1 -1 2 -1 -1 -4 -2 0 1 0 0 3 0 -3 0 0 -1 1 1 3 -1 2 1 -2 1 0 0 1 0
-1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 1 0 -1 0 0 -1 0 0 0 0 0
-2 1 2 0 -2 0 -1 -1 0 0 1 1 0 0 1 0 -1 1 1 0 -1 2 1 -1 0 0 -2 0 0 -1 -1 1
-1 -1 1 0 0 -1 1 1 2 1 1 0 0 1 -1 -1 0 0 1 0 -1 1 -1 -2 -1 -1 0 -1 0 0 0 0
0 0 0 0 0 0 1 -1 0 1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 0 0 1 0 0
-1 1 1 0 0 1 0 -1 -1 -1 0 0 0 0 1 0 -1 0 0 0 0 1 1 0 0 0 -1 0 0 0 0 0
0 -1 0 0 1 -1 2 2 3 1 1 -1 0 1 -2 0 1 -1 0 1 -1 0 -2 -1 -2 -1 1 -1 -1 -1 0 0
0 0 0 0 1 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 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0 0
1 0 -1 1 2 0 0 0 -2 -1 -1 -1 0 1 0 0 -1 -1 0 0 0 -1 1 0 1 1 0 0 1 2 0 -1
1 -1 -2 0 3 0 2 0 1 1 0 -1 -1 1 -2 0 1 -1 0 0 0 -1 -1 0 -1 0 1 -1 0 1 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 -2 0 0 1 -1 2 1 2 1 1 -1 0 0 -1 -1 1 -1 0 0 0 0 -2 -1 -1 -1 1 -1 0 0 1 0
-2 0 2 0 -1 0 0 0 0 -1 1 0 1 0 1 -1 -1 0 0 0 0 2 0 -1 0 0 -1 0 0 -1 1 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
3 -2 -3 -1 2 -3 2 1 7 4 1 -1 -1 0 -5 1 5 -1 0 2 -2 -2 -4 1 -4 -2 4 -2 -1 -1 -2 1
1 -2 -1 0 1 -2 1 2 4 2 1 -1 0 1 -2 0 2 -1 0 1 -2 0 -3 0 -2 -1 2 -2 0 0 -1 0
3 -2 -4 0 4 -2 2 2 4 2 0 -2 -1 1 -4 1 3 -2 0 1 -1 -2 -3 1 -2 -1 3 -2 0 1 -1 0
2 -1 -3 1 2 -1 1 1 1 1 0 -1 -1 1 -1 1 1 -1 -1 1 -1 -2 -1 1 -1 0 2 -1 0 1 -1 0
0 -2 0 0 1 -1 2 2 2 1 1 -1 0 1 -2 -1 1 -1 1 0 0 0 -2 -2 -1 -1 1 -1 0 0 1 0
1 0 -1 -1 1 -1 0 1 3 1 0 0 -1 0 -2 0 1 0 1 1 0 -1 -1 0 -1 -1 2 -1 -1 -1 0 0
2 -3 -2 0 2 -3 2 2 5 3 1 -2 0 1 -4 0 4 -1 0 2 -2 -1 -4 0 -3 -2 3 -2 0 0 -1 0
2 -2 -2 0 2 -2 2 2 4 2 1 -1 -1 1 -3 0 2 -1 0 1 -1 -1 -3 0 -2 -1 2 -2 0 0 -1 0
0 -2 -1 1 1 -1 1 2 2 1 1 -1 0 1 -1 0 1 -1 0 1 -1 0 -2 -1 -1 -1 1 -1 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 0 0 0 0
0 1 0 0 -1 0 -1 0 -1 0 0 0 0 0 1 0 -1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0
0 1 -1 1 0 1 -1 0 -3 -2 -1 0 -1 0 2 0 -2 0 0 0 1 -1 2 0 2 1 0 1 0 1 1 0
0 -1 1 -1 0 -1 1 1 3 1 1 0 0 0 -1 -1 1 0 0 1 -1 1 -2 -1 -2 -1 1 -1 0 -1 0 0
1 0 -1 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 1 0 -1 0 0 0 0 1 0 0 0 0 0
1 0 -2 0 1 0 -1 0 0 0 -1 0 -1 0 0 0 0 0 0 0 1 -1 0 1 1 0 1 0 0 1 0 0
1 0 0 -1 0 -1 0 0 2 1 0 0 0 0 -1 0 1 0 0 1 -1 0 -1 1 -1 -1 1 -1 0 0 -1 0
2 -2 -2 0 2 -2 1 2 3 1 0 -1 -1 0 -2 0 2 -1 0 1 0 -2 -2 0 -1 -1 3 -1 0 0 0 0
1 0 -2 0 2 0 0 0 0 0 -1 -1 -1 0 -1 0 1 0 1 1 0 -1 0 0 0 0 1 0 0 1 0 0
0 0 0 0 -1 0 -1 1 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 0 -2 0 1 0 -1 0 0 0 -1 0 -1 0 0 1 0 0 0 0 0 -1 0 1 1 0 1 0 0 1 0 0
1 1 -2 0 1 1 -1 -1 -1 0 -1 0 -1 0 0 1 0 0 0 0 1 -1 1 1 1 0 0 0 0 1 0 0
0 0 0 1 1 0 0 1 -1 -1 0 -1 0 2 0 0 -1 0 0 1 -1 1 0 0 0 0 -1 -1 1 1 -1 -1
1 -2 -2 0 2 -2 2 2 4 2 1 -2 0 1 -3 0 3 -1 0 2 -2 0 -3 0 -3 -1 2 -2 0 0 -1 0
0 0 1 -1 -2 -1 0 1 3 1 1 1 0 -1 0 0 0 0 0 0 0 0 -1 0 -1 -1 1 -1 -1 -2 0 1
-1 -1 1 0 -1 -1 0 1 2 1 1 0 0 0 0 -1 0 0 1 0 -1 1 -1 -1 0 -1 0 -1 0 0 0 0
-1 1 0 0 0 1 -1 0 -1 -1 0 0 -1 0 1 0 -1 0 1 0 1 0 1 -1 1 0 0 0 0 0 1 0
2 -2 -3 0 3 -1 2 1 3 2 0 -1 -1 1 -3 0 3 -1 0 1 0 -2 -3 0 -2 -1 2 -1 0 1 0 -1
2 -2 -3 0 3 -2 2 2 4 2 1 -2 -1 1 -4 0 3 -1 0 2 -1 -1 -3 0 -3 -1 3 -2 0 0 -1 0
0 0 0 0 -1 0 -1 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
2 -2 -2 0 2 -2 2 2 4 2 1 -2 0 1 -3 0 3 -1 -1 2 -2 0 -3 1 -3 -1 2 -2 0 0 -2 0
2 -2 -2 0 2 -2 2 2 4 2 1 -2 0 1 -3 0 3 -1 -1 2 -2 -1 -3 0 -3 -1 3 -2 0 0 -1 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 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 1 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 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 -1 0 0 -1 0 0 0 -1 0 1 0 0 0 1 -1 0 1 0 0 0 0 0 1 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
-1 0 1 0 -2 0 0 -1 1 1 1 1 0 -1 1 0 0 0 0 -1 0 1 0 0 0 0 -1 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 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 -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 1 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 -1 0 0 0 0 0
0 1 1 -1 -1 1 -1 -2 -1 0 -1 1 0 -1 1 0 0 1 0 -1 1 0 1 1 1 0 -1 1 0 0 0 0
1 0 -2 0 2 1 0 -1 0 0 -1 0 -1 0 -1 0 1 0 0 0 1 -1 0 1 0 0 0 0 0 1 0 0
0 1 0 0 0 1 -1 -1 -2 -1 -1 0 0 -1 1 0 0 0 0 0 1 0 1 0 1 1 0 1 0 0 1 0
1 0 -1 0 1 0 0 -1 0 0 -1 0 0 0 -1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0
2 1 -2 0 1 0 0 -1 0 1 -1 0 -1 0 -1 1 1 0 -1 0 0 -2 0 2 0 0 1 0 0 1 -1 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 0
1 -1 -1 0 1 -1 1 0 3 2 0 0 0 0 -2 0 2 -1 0 0 0 -1 -2 0 -1 -1 1 -1 0 0 0 0
0 1 0 0 0 1 0 -1 -1 -1 0 0 0 0 1 0 -1 0 -1 0 0 1 1 1 0 1 -1 0 0 0 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 0 0 0 0 0 0 0 0
0 0 1 -1 -1 -1 0 0 3 1 1 1 0 -1 -1 0 1 0 0 0 0 0 -1 0 -1 -1 1 0 -1 -2 0 1
0 0 1 -1 -2 -1 0 0 3 1 1 1 0 -1 0 0 1 0 0 0 0 0 -1 0 -1 -1 1 0 -1 -2 0 1
-1 0 1 1 -1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 -1 1 0 0 0 0 -1 0 0 0 -1 0
-1 1 1 0 0 1 0 -1 -1 -1 0 0 0 0 1 0 -1 0 0 0 0 1 1 0 0 1 -1 0 0 0 0 0
-1 0 1 0 -2 0 0 0 1 1 1 1 0 -1 1 0 0 0 0 -1 1 0 0 -1 0 0 0 0 -1 -2 1 1
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 -1 0 0
-1 0 1 -1 -2 0 0 0 3 1 1 1 0 -1 0 0 1 0 0 0 0 1 -1 0 -1 -1 0 0 -1 -2 0 1
0 1 0 1 0 1 -1 -1 -3 -2 -1 0 0 0 1 0 -1 0 0 0 1 0 2 0 1 1 -1 1 1 1 0 0
0 0 0 0 0 0 1 -1 1 1 0 0 0 0 -1 0 1 0 0 0 0 0 -1 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 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0
0 1 0 1 1 1 0 -1 -3 -1 -1 -1 0 1 1 0 -1 0 0 0 0 0 1 0 1 1 -1 0 1 2 0 -1
1 -1 -1 0 2 0 1 0 0 0 -1 -1 0 0 -1 0 1 -1 0 0 1 -1 -1 0 0 0 1 0 0 1 1 0
-
PROPERTIES
INTEGRAL = 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