The Lattice 2.U4(3).4SS3.2
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 13:14:43 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
2.U4(3).4SS3.2
-
DIMENSION
40
-
GRAM (floating point or integer Gram matrix)
40 0 /2
12
2 12
0 0 12
4 4 0 12
0 0 2 0 12
-2 -2 0 0 4 12
4 0 -2 0 -2 2 12
4 0 0 0 -2 -4 0 12
0 0 0 0 4 2 -2 2 12
4 0 0 2 4 0 2 2 4 12
4 0 0 0 2 0 0 4 0 0 12
2 0 -2 -2 0 4 2 0 2 0 0 12
0 2 2 4 0 -2 -2 0 4 0 0 0 12
0 0 2 0 0 -4 0 0 0 0 0 0 4 12
2 0 0 0 4 4 -2 0 4 2 0 2 0 0 12
0 0 4 0 2 -2 -2 2 2 0 0 0 0 2 2 12
0 2 4 0 2 0 0 4 0 2 0 2 -2 0 0 2 12
0 0 4 0 2 0 -2 4 2 0 0 -4 0 0 2 4 0 12
0 0 4 -2 4 0 0 0 0 2 4 -4 2 0 0 0 0 4 12
0 0 2 2 2 0 0 0 0 4 2 -2 4 0 0 0 0 2 6 12
4 4 0 4 -2 -4 0 4 0 2 2 -2 0 0 0 0 4 0 -2 2 12
2 0 0 4 4 2 0 2 0 2 4 0 0 0 4 0 0 4 2 4 0 12
4 4 0 0 4 0 0 0 0 0 4 4 0 4 4 4 0 0 0 0 0 4 12
4 4 -2 2 0 0 4 2 2 0 4 2 0 2 0 0 0 0 0 0 4 0 4 12
4 0 -4 0 2 2 2 0 2 0 2 4 0 2 2 -4 0 -4 -2 -4 0 0 4 4 12
0 0 -2 0 4 4 0 -4 0 0 0 0 -4 0 2 2 -2 0 -4 -2 0 2 4 0 0 12
0 0 -2 0 0 4 4 -4 -2 2 4 0 0 0 0 -4 -4 -2 2 4 -2 2 0 2 0 2 12
4 2 4 4 0 -4 0 0 0 4 0 -2 4 0 0 0 0 0 2 4 4 2 0 0 -4 0 0 12
0 0 4 0 2 0 -4 4 4 2 0 0 0 0 4 4 4 4 0 0 4 0 0 0 0 0 -4 0 12
0 0 -4 0 2 0 2 0 2 4 2 2 0 0 2 -4 0 -4 0 0 -2 4 0 0 4 -2 4 0 -2 12
2 0 2 4 0 4 4 0 2 4 0 2 2 0 0 0 0 2 2 4 0 4 0 4 0 0 4 4 0 2 12
2 0 0 0 0 0 0 0 0 0 2 2 0 2 2 2 -4 2 0 0 0 4 4 0 0 0 0 -2 -2 0 0 12
0 2 4 0 4 -4 -4 0 0 0 2 0 4 4 0 4 0 0 4 2 0 2 4 0 0 0 -2 4 4 0 0 0 12
0 0 2 -2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 12
0 -2 0 0 4 4 0 0 0 0 4 2 -4 -2 0 2 2 0 0 0 0 4 2 0 0 4 0 -2 0 0 0 2 0 2 12
-2 2 2 -2 -4 -2 0 0 0 0 -4 0 2 2 0 0 2 0 0 0 0 -4 -2 -2 -2 -4 0 0 0 0 0 0 -2 4 -2 12
2 4 -2 2 -2 -4 0 0 0 0 -2 0 4 4 0 0 -2 0 0 0 0 -2 2 2 2 -2 0 0 0 0 0 0 2 2 -4 6 12
-2 0 0 -2 0 -4 0 2 0 2 0 -4 0 0 -4 0 0 2 4 2 0 -2 -4 0 -4 -4 0 0 -2 0 -2 0 0 2 0 4 2 12
0 0 2 2 -2 0 0 4 0 2 0 -2 2 0 0 0 4 2 2 4 4 0 -4 0 0 -4 0 0 4 0 4 -2 0 2 0 4 2 2 12
2 4 0 2 -2 -2 0 4 0 0 4 0 2 -2 -4 0 2 0 0 0 4 0 0 0 0 -2 0 0 0 0 0 2 0 2 2 4 2 4 4 12
-
DIVISORS (elementary divisors)
1^20 3^20
-
MINIMAL_NORM
6
-
KISSING_NUMBER
3360
-
GROUP_ORDER
2^12 * 3^7 * 5 * 7
-
GROUP_GENERATORS
4
40
-1 1 2 0 1 -3 0 0 -1 1 1 2 0 0 1 0 -2 -1 1 0 0 1 -2 0 1 1 -1 -1 0 -1 1 -1 -2 0 0 0 0 0 0 0
3 0 -1 -3 1 4 -2 -1 0 0 -2 -1 0 2 -3 2 -1 -1 0 -1 1 3 0 2 -2 -2 0 1 0 1 -2 -1 -1 0 -1 0 0 -1 1 1
24 0 -18 -21 1 41 -11 -6 5 -7 -12 -21 -2 13 -23 12 5 -5 -9 -4 1 12 7 5 -12 -23 4 19 8 7 -12 3 0 -1 -2 -3 4 -3 5 2
-4 1 4 2 1 -8 1 1 -2 2 2 4 1 -2 4 -1 -2 -1 2 0 0 0 -3 0 2 4 -1 -4 -1 -2 3 -1 -2 0 0 0 0 0 -1 0
7 1 -5 -6 1 12 -3 -2 1 -2 -2 -5 -1 4 -7 4 0 -1 -3 -1 1 4 1 1 -3 -7 0 5 2 2 -3 0 0 0 -1 0 1 -1 1 0
17 0 -13 -15 1 29 -7 -5 4 -5 -8 -15 -2 9 -16 8 3 -3 -8 -3 1 9 6 3 -9 -18 3 13 5 4 -8 1 1 -1 -1 -2 3 -2 4 1
-7 0 6 6 0 -12 3 2 -2 2 3 6 1 -4 6 -3 -2 1 3 1 0 -3 -2 -1 4 7 -1 -5 -2 -2 3 -1 -1 0 1 1 -1 1 -1 -1
-11 0 9 10 0 -20 4 4 -3 3 4 11 2 -6 10 -5 -3 1 7 1 0 -5 -4 -2 6 12 -1 -9 -3 -3 5 -1 -2 1 1 1 -2 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 1 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 0 0 0 0 0
15 0 -12 -12 1 24 -6 -4 4 -5 -7 -13 -2 8 -14 6 4 -2 -6 -2 0 6 5 2 -8 -15 3 11 5 4 -6 2 1 0 -1 -2 2 -2 3 1
13 0 -10 -12 1 21 -5 -4 3 -4 -6 -12 -1 7 -11 5 3 -2 -7 -2 0 6 5 2 -7 -14 2 10 4 3 -5 1 1 -1 0 -2 2 -1 3 1
15 -1 -12 -12 0 24 -6 -4 4 -5 -7 -14 -1 7 -13 5 6 -2 -7 -2 -1 5 6 3 -8 -14 3 11 5 4 -6 3 2 -1 -1 -2 2 -1 3 1
2 0 -2 -1 0 2 0 -1 1 -1 0 -2 0 1 -1 0 2 0 -1 0 -1 0 0 0 -1 -1 0 1 1 0 0 1 1 0 0 0 0 0 0 0
1 0 0 -1 1 2 -1 0 0 0 -1 1 -1 1 -2 2 -2 -1 1 -1 1 3 -1 1 0 -1 0 1 0 0 -2 -1 -1 0 -1 1 0 -1 1 0
-2 1 2 1 1 -2 0 2 -1 0 0 2 0 0 1 1 -2 -1 2 0 0 0 -2 0 2 2 0 0 0 0 0 0 -2 0 0 0 0 0 0 0
25 1 -18 -23 2 42 -12 -6 4 -7 -13 -20 -1 14 -24 14 3 -6 -8 -5 3 15 6 5 -12 -24 4 19 8 7 -12 1 -2 -1 -2 -3 4 -3 5 2
-5 0 4 4 0 -7 1 2 -1 1 1 5 0 -2 3 -1 -2 0 4 0 0 -1 -2 0 3 5 0 -2 -1 -1 0 0 -2 0 0 0 0 0 0 0
23 -1 -18 -18 0 39 -10 -6 6 -7 -11 -20 -3 12 -22 10 6 -3 -9 -3 0 10 8 5 -12 -22 4 18 7 7 -12 3 2 -1 -2 -2 3 -3 5 2
-1 -1 1 3 -1 -3 1 1 1 0 0 1 0 -2 1 -2 1 1 1 0 0 -2 1 0 0 2 1 -2 -1 0 0 1 2 0 0 1 -1 0 0 -1
4 1 -2 -5 1 7 -3 0 0 -1 -4 -2 0 3 -5 4 -1 -3 1 -1 1 5 -1 2 -1 -3 1 4 2 1 -3 0 -3 0 -1 -1 1 -1 1 1
-14 0 11 13 0 -25 6 4 -3 4 7 13 1 -8 13 -7 -3 3 6 2 0 -7 -5 -3 7 14 -2 -12 -5 -4 7 -1 0 1 1 2 -2 1 -3 -2
-15 0 12 14 0 -26 7 4 -3 5 8 14 1 -8 14 -8 -4 4 6 2 0 -8 -5 -3 7 15 -3 -13 -6 -4 7 -2 1 1 1 3 -3 1 -3 -2
-1 1 1 -1 1 -1 0 0 -1 1 0 1 0 1 0 1 -2 -1 1 0 0 2 -2 1 1 0 -1 0 0 -1 0 -1 -2 0 0 0 0 -1 0 1
3 1 -2 -3 0 4 -1 -2 0 0 0 -2 0 2 -2 1 0 0 -2 0 0 2 0 0 -1 -3 -1 1 1 0 0 -1 0 0 0 0 0 0 0 0
-18 1 14 15 0 -29 8 5 -4 5 9 16 1 -9 16 -7 -5 3 7 3 0 -8 -7 -4 10 17 -3 -13 -6 -5 8 -2 -1 1 1 2 -2 2 -4 -2
20 -1 -16 -16 0 32 -7 -6 6 -7 -9 -19 -3 10 -17 7 7 -2 -10 -2 -1 7 8 3 -11 -20 4 15 6 5 -8 3 3 -1 -1 -3 3 -2 4 2
-4 0 3 3 0 -6 1 2 -1 1 1 3 0 -2 3 -1 0 0 2 1 -1 -2 -2 0 3 4 0 -1 -1 -1 1 1 -1 0 0 0 0 0 -1 0
4 0 -2 -4 0 8 -3 0 0 -1 -4 -2 0 3 -5 4 -1 -2 1 -1 1 4 0 2 -1 -3 1 4 2 2 -4 0 -2 0 -1 -1 1 -1 1 1
3 0 -2 -2 0 3 -1 -1 0 -1 -1 -2 0 1 -2 1 1 0 -1 0 0 1 1 0 -1 -2 0 1 1 1 0 0 0 0 0 0 0 0 0 0
9 0 -7 -8 0 15 -4 -2 2 -3 -5 -9 -1 5 -8 4 3 -2 -4 -1 -1 4 3 2 -4 -9 2 8 3 2 -4 2 0 -1 0 -2 2 -1 2 1
2 0 -2 -1 1 2 0 -1 1 -1 0 -2 -1 1 -1 -1 1 0 -2 0 -1 0 1 0 -2 -2 0 1 1 0 0 1 1 0 0 0 0 0 1 0
9 0 -7 -7 0 15 -4 -2 2 -3 -4 -8 -1 5 -8 4 3 -1 -4 0 -1 3 2 2 -4 -8 1 7 3 3 -4 2 1 0 -1 -1 1 -1 1 1
-14 -1 11 13 -2 -22 6 4 -3 5 6 12 1 -8 13 -7 -2 4 6 2 0 -8 -4 -2 7 14 -2 -11 -6 -3 5 -1 2 1 1 2 -2 1 -3 -1
6 1 -4 -6 1 11 -3 -1 1 -2 -4 -5 -1 4 -6 4 0 -2 -2 -1 1 4 1 1 -3 -7 1 5 2 2 -3 0 -1 0 0 -2 2 -1 1 1
13 -1 -9 -11 0 22 -6 -3 3 -4 -8 -11 -1 7 -12 6 3 -3 -4 -3 1 7 5 3 -7 -12 3 10 4 4 -7 1 0 -1 -1 -2 2 -1 3 2
-5 -1 5 5 -1 -9 2 1 -1 2 2 5 1 -3 5 -3 -1 1 3 0 0 -2 -1 0 2 6 -1 -5 -2 -1 2 -1 0 0 0 1 -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 0 0 0 0 0 0 0 0 0 0 0 0 1
21 0 -15 -18 0 35 -10 -5 4 -6 -12 -17 -1 11 -20 11 4 -5 -6 -4 1 12 6 5 -10 -19 4 16 7 6 -11 2 -1 -1 -2 -3 3 -2 5 2
6 0 -4 -5 0 9 -3 -1 1 -2 -4 -5 0 3 -5 2 2 -1 -2 -1 0 2 2 1 -3 -5 2 4 2 2 -2 1 0 0 0 -2 1 0 1 1
40
-19 -1 13 18 -2 -32 9 5 -3 5 9 15 2 -11 18 -11 -1 5 7 3 -2 -12 -4 -4 9 19 -2 -14 -6 -5 9 0 2 1 2 2 -3 2 -4 -2
-39 0 30 35 -2 -65 17 11 -8 11 19 34 3 -21 36 -19 -8 8 16 6 -1 -21 -12 -8 20 39 -6 -30 -13 -10 18 -3 0 2 3 5 -6 4 -8 -4
-3 1 3 1 0 -4 0 1 -2 2 1 3 1 -1 2 0 -2 0 2 0 1 0 -2 0 2 3 -1 -2 -1 0 1 -1 -2 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 0 0 0 0 -1 0 0
-8 -1 5 8 -1 -13 4 2 -1 2 4 6 0 -4 9 -6 0 3 2 2 -1 -7 -1 -2 3 7 -1 -6 -3 -2 4 0 2 0 1 0 -1 1 -2 0
-16 0 12 14 0 -28 7 4 -4 5 8 14 1 -8 16 -8 -4 3 6 3 -1 -8 -6 -3 8 15 -3 -13 -5 -5 8 -2 0 1 1 2 -3 1 -4 0
7 0 -5 -6 1 10 -3 -2 2 -2 -3 -5 0 3 -7 3 1 -2 -2 -2 1 5 2 1 -4 -6 1 4 2 1 -3 0 0 0 -1 0 1 -1 2 0
-4 0 3 3 -1 -6 1 2 -1 0 0 3 1 -2 3 -1 0 0 3 1 -1 -2 -1 0 3 5 0 -1 0 0 1 1 -2 0 1 -1 0 1 -1 0
-8 0 6 6 -1 -12 3 2 -2 2 3 6 0 -3 8 -3 -1 1 3 2 -1 -4 -3 -1 5 7 -1 -4 -2 -2 3 0 -1 0 1 -1 0 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 0 0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0
-7 -1 4 7 -1 -12 4 2 0 1 3 4 0 -4 8 -6 1 3 1 2 -2 -7 0 -2 3 6 0 -4 -2 -2 4 1 2 0 2 0 -1 1 -2 0
-4 -2 3 5 -1 -6 2 1 0 1 1 3 0 -3 3 -3 0 2 2 0 0 -3 1 0 1 4 0 -3 -2 0 0 0 2 0 0 1 -1 0 0 0
7 0 -5 -7 0 12 -3 -3 2 -2 -3 -7 -1 4 -6 3 2 -1 -4 -1 0 3 3 1 -4 -8 1 6 2 2 -3 1 0 -1 0 -2 2 -1 2 1
18 -1 -13 -15 0 31 -8 -5 5 -5 -9 -15 -2 9 -18 8 4 -3 -7 -3 1 9 7 4 -10 -17 3 14 5 6 -10 2 1 -1 -2 -2 3 -2 5 1
-36 0 27 32 -2 -61 16 9 -8 11 18 31 3 -19 34 -18 -7 7 14 6 -2 -19 -11 -7 18 35 -6 -28 -11 -10 17 -3 0 2 3 4 -6 4 -8 -3
-3 0 2 2 -1 -3 0 1 -1 1 0 3 0 -1 1 0 -1 0 3 0 0 0 -1 1 2 3 0 0 0 0 -1 0 -2 0 0 0 0 0 0 0
-7 0 6 6 0 -11 2 3 -2 2 2 7 1 -4 5 -2 -3 0 5 0 1 -2 -2 -1 4 8 -1 -5 -2 -1 2 -1 -2 0 0 1 -1 1 -1 -1
-17 1 13 13 -1 -27 6 5 -5 5 7 15 2 -8 15 -6 -4 2 8 3 -1 -7 -7 -2 10 17 -3 -11 -4 -4 7 -1 -3 1 1 1 -2 2 -4 -1
-26 0 20 22 -1 -44 11 7 -6 8 12 22 3 -14 25 -13 -5 5 10 4 -1 -14 -8 -5 13 25 -4 -20 -8 -7 13 -2 -1 1 3 2 -3 3 -6 -2
-4 0 3 3 0 -7 2 0 -1 2 3 3 0 -2 5 -3 -1 2 0 1 0 -3 -1 -1 1 3 -2 -4 -2 -1 3 -1 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-23 0 17 20 -1 -38 10 6 -5 7 11 20 2 -12 21 -11 -5 5 9 4 -1 -12 -7 -4 12 22 -4 -17 -7 -6 10 -2 0 1 2 3 -4 2 -5 -2
-25 -1 18 23 -2 -40 11 7 -4 7 11 21 1 -13 22 -13 -4 6 10 4 -2 -14 -6 -4 12 24 -3 -17 -8 -6 9 -1 1 1 2 3 -4 2 -4 -2
4 -1 -4 -3 0 7 -1 -1 2 -2 -2 -5 -1 2 -3 0 3 0 -3 0 -1 0 2 1 -3 -4 1 4 1 1 -2 2 2 0 0 -1 1 -1 1 1
-7 -1 4 7 -1 -11 4 2 0 1 3 4 0 -4 7 -5 1 2 1 2 -2 -6 0 -2 3 6 0 -4 -2 -2 3 1 2 0 1 0 -1 1 -1 0
6 0 -6 -4 0 10 -2 -2 2 -2 -2 -5 -2 4 -5 2 2 0 -3 0 -1 2 1 1 -3 -6 1 5 2 1 -3 1 2 0 -1 0 0 -1 1 1
8 0 -7 -6 1 11 -2 -3 3 -3 -2 -8 -2 4 -5 1 3 0 -6 0 -1 1 3 0 -5 -9 1 5 2 1 -1 1 3 0 0 -1 1 -1 1 1
16 1 -12 -15 1 27 -7 -5 3 -4 -7 -14 -1 9 -15 8 3 -3 -7 -3 1 9 4 3 -8 -16 2 12 5 4 -7 1 0 -1 -1 -2 3 -2 3 1
3 0 -2 -3 -1 6 -2 0 0 -1 -3 -3 0 2 -3 2 1 -1 0 0 0 1 1 1 -1 -2 1 3 2 2 -2 1 -1 0 0 -2 1 0 0 1
-3 0 2 3 0 -5 2 1 0 0 2 2 0 -2 3 -2 0 1 0 1 0 -3 0 -2 2 2 0 -2 -1 -1 2 0 1 0 1 0 0 1 -1 -1
0 1 0 -2 1 1 -1 0 -1 0 -1 0 0 1 -1 2 -1 -1 0 0 0 2 -2 1 1 -1 0 2 1 0 -1 0 -2 0 0 -1 1 -1 0 1
-42 -1 32 37 -2 -70 18 11 -9 13 20 37 4 -23 38 -20 -9 9 17 6 -1 -21 -12 -7 21 41 -6 -32 -14 -11 18 -4 0 2 3 6 -7 4 -8 -4
10 -1 -8 -8 -1 18 -4 -3 3 -3 -5 -10 -1 5 -9 3 4 0 -5 -1 0 2 5 2 -6 -10 2 8 3 4 -5 2 2 -1 0 -2 2 -1 2 1
17 1 -13 -15 1 27 -7 -5 3 -5 -7 -15 -1 9 -15 7 4 -3 -8 -2 -1 8 5 3 -8 -16 2 13 6 4 -7 2 0 -1 -1 -2 2 -1 4 1
0 -1 -1 1 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 1 0 0 1 -1 0 0 0
-2 1 2 1 1 -4 0 1 -1 0 1 2 0 -1 1 0 -1 -1 1 0 0 0 -1 -1 2 2 0 -1 0 -1 2 0 -2 0 0 0 0 1 0 -1
15 0 -12 -13 1 25 -6 -4 4 -6 -7 -14 -2 8 -14 6 5 -3 -7 -2 -1 6 6 2 -8 -15 3 13 6 4 -6 3 0 -1 -1 -3 3 -1 4 1
16 0 -12 -14 1 26 -7 -4 3 -5 -7 -14 -1 8 -14 7 4 -3 -7 -2 0 7 5 3 -8 -15 2 12 5 4 -6 2 0 -1 -1 -2 3 -1 3 1
-4 1 3 2 0 -7 1 1 -2 1 2 3 1 -2 4 -1 -1 0 1 1 -1 -2 -2 -1 3 4 -1 -2 0 -1 3 0 -2 0 1 -1 0 1 -1 0
-15 0 11 13 -1 -25 6 5 -3 3 6 12 1 -8 14 -7 -2 3 6 3 -2 -9 -4 -3 9 15 -1 -9 -4 -4 7 0 -1 0 2 1 -2 2 -3 -1
40
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
-3 1 3 1 0 -4 0 1 -2 2 1 3 1 -1 2 1 -2 -1 2 0 1 1 -3 0 3 3 -1 -2 -1 -1 1 -1 -2 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 -1 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 0 0
11 0 -8 -10 1 19 -5 -3 2 -3 -5 -9 -1 6 -10 5 1 -2 -5 -2 1 6 4 2 -6 -11 1 8 3 3 -5 0 0 -1 -1 -1 2 -1 3 1
8 0 -6 -8 1 14 -4 -2 2 -3 -5 -8 -1 5 -7 4 2 -2 -4 -1 -1 4 3 2 -4 -9 2 8 3 2 -4 1 -1 -1 0 -2 2 -1 2 2
-20 0 16 17 -1 -33 8 6 -5 6 9 18 2 -10 18 -8 -5 3 9 3 -1 -9 -7 -3 11 20 -3 -14 -6 -5 8 -2 -2 1 1 2 -3 2 -4 -1
-1 0 0 1 1 -2 1 0 0 0 1 1 -1 0 1 -1 0 0 0 0 0 -1 0 -1 0 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0
29 -1 -22 -25 1 49 -12 -8 7 -9 -14 -26 -3 15 -26 12 7 -5 -13 -4 1 13 11 5 -16 -29 5 22 9 8 -13 3 2 -2 -2 -4 5 -3 6 3
11 -1 -8 -8 0 17 -4 -3 3 -3 -5 -9 -1 5 -9 3 3 -1 -5 -2 0 4 5 2 -7 -10 2 7 3 3 -5 1 2 -1 -1 -1 1 -1 3 1
-8 0 6 7 0 -14 4 2 -1 2 4 7 0 -4 8 -4 -2 1 3 1 0 -4 -2 -2 4 7 -1 -6 -3 -3 4 -1 0 0 1 1 -1 1 -1 -1
18 0 -15 -16 1 30 -7 -5 5 -6 -8 -18 -3 10 -15 7 6 -3 -10 -1 -2 7 6 3 -9 -19 3 15 6 4 -7 3 2 -1 -1 -3 3 -2 3 3
-6 0 4 5 0 -9 3 1 -1 2 3 5 0 -3 5 -2 -2 1 2 1 0 -2 -2 -1 3 5 -1 -4 -2 -2 2 -1 0 0 0 1 -1 0 -1 0
2 0 -1 -2 0 4 -1 -1 0 0 -1 -1 0 1 -3 2 -1 -1 0 -1 1 3 1 1 -1 -2 0 1 1 1 -2 -1 -1 0 -1 0 0 0 1 0
33 -1 -25 -28 1 55 -14 -9 8 -10 -16 -29 -3 17 -30 14 8 -5 -14 -5 1 15 12 6 -17 -32 6 25 10 9 -15 3 2 -2 -2 -4 5 -3 7 3
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 -1 1 1 0 0 0 0 1 -1 -1 1 0 0 0 0 -2 0 0 0 0 -1 0 -2 0 1 0 -1 1 0 0 0 0 0 0 0 0 0
1 -1 -1 0 0 1 0 -1 0 0 0 -1 0 0 0 -1 1 1 -1 0 0 -1 1 0 -1 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
-12 0 9 10 0 -20 5 3 -3 4 6 11 1 -6 11 -5 -4 2 5 1 0 -5 -4 -2 6 11 -2 -9 -4 -4 5 -2 -1 0 1 2 -2 1 -2 -1
-2 0 1 2 1 -5 2 -1 0 1 3 2 0 -1 3 -2 -1 1 -1 0 0 -1 -1 -1 0 1 -1 -3 -1 -2 2 -1 1 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
5 -1 -5 -2 0 7 -1 -2 2 -2 -1 -5 -1 2 -3 0 3 1 -4 0 -1 -1 3 0 -3 -5 1 3 1 1 -1 1 3 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-8 0 6 6 -1 -12 3 2 -2 2 3 6 0 -3 8 -3 -1 1 3 2 -1 -4 -3 -1 5 7 -1 -4 -2 -2 3 0 -1 0 1 -1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
3 0 -1 -3 0 5 -2 0 0 -1 -3 -2 1 1 -3 2 0 -1 0 -1 1 2 1 1 -1 -2 1 2 1 2 -2 0 -1 0 0 -1 1 0 1 0
-6 0 5 5 -1 -11 3 1 -1 2 3 5 1 -3 7 -3 -1 1 2 1 -1 -3 -2 -1 3 6 -1 -5 -2 -2 3 -1 0 0 1 0 -1 1 -1 0
2 -1 -2 0 -1 3 0 0 1 -1 -1 -2 0 0 -1 0 2 1 -1 0 0 -1 1 0 -1 -1 1 1 0 1 -1 1 2 0 0 0 0 0 0 0
19 -1 -15 -16 1 31 -8 -5 5 -6 -10 -17 -2 10 -17 7 5 -3 -8 -3 1 8 8 3 -11 -19 4 14 6 5 -8 2 1 -1 -1 -3 3 -2 4 2
0 -1 0 2 -1 -1 1 0 1 0 1 0 0 -1 1 -2 1 1 -1 0 0 -2 2 -1 -1 1 0 -2 -1 0 1 0 3 0 0 1 -1 1 0 -1
-26 -1 19 24 -2 -44 12 7 -5 7 12 21 2 -14 26 -14 -3 6 9 5 -3 -16 -7 -5 13 25 -3 -19 -8 -7 12 -1 1 1 3 2 -4 3 -6 -1
-2 -1 2 3 -1 -4 1 0 0 1 1 2 0 -2 2 -2 0 1 1 1 -1 -2 0 1 1 3 -1 -2 -1 0 0 0 1 0 0 1 -1 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 0 0 0
18 0 -14 -16 1 30 -8 -4 4 -7 -10 -16 -2 10 -17 9 5 -4 -7 -2 -1 9 5 4 -8 -17 4 16 7 5 -9 3 -1 -1 -1 -3 3 -2 4 2
2 0 -2 -1 1 2 -1 0 1 -2 -1 -2 -1 1 -1 0 1 -1 -1 0 -1 0 1 0 -1 -2 1 2 1 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 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 0 0 0 0 -1 0 0 0 0
-5 0 4 4 0 -8 2 1 -2 2 3 5 0 -2 5 -2 -2 1 2 1 0 -2 -3 0 2 5 -2 -4 -2 -1 2 -1 0 0 0 1 -1 0 -1 0
-23 0 17 20 0 -39 10 6 -5 7 11 20 2 -12 21 -11 -5 4 9 3 -1 -11 -7 -4 11 22 -3 -17 -7 -7 10 -2 -1 1 2 3 -4 2 -4 -2
-24 1 18 20 0 -40 10 7 -6 7 11 21 2 -12 22 -10 -6 3 10 4 -1 -11 -9 -4 13 23 -4 -17 -7 -7 11 -2 -2 1 2 3 -4 2 -5 -2
40
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
-16 0 12 14 -1 -26 7 5 -3 4 7 13 1 -8 15 -8 -3 3 6 3 -1 -9 -4 -3 8 15 -2 -11 -5 -4 7 -1 0 0 2 1 -2 2 -3 -1
-3 0 3 2 0 -4 0 1 -1 1 0 4 0 -1 1 0 -2 0 3 0 1 0 -1 0 2 3 0 -1 -1 0 0 -1 -2 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 0 0
2 1 -1 -3 1 4 -2 1 -1 -1 -3 -1 0 2 -3 3 -1 -2 1 0 0 3 -1 1 0 -2 1 3 2 1 -2 0 -3 0 0 -1 1 -1 0 1
6 0 -4 -5 1 10 -3 -1 1 -2 -4 -4 -1 4 -6 4 0 -2 -1 -1 1 4 1 1 -3 -6 1 4 2 2 -3 0 -1 0 -1 -1 1 -1 1 1
1 0 -1 0 0 1 0 0 1 -1 0 -1 -1 0 0 0 1 0 -1 1 -1 -1 0 0 0 -1 0 1 0 0 0 1 1 0 0 0 0 0 0 0
0 0 1 0 0 -1 0 0 0 1 0 1 1 -1 0 0 -1 0 1 -1 2 1 0 0 0 1 0 -2 -1 0 0 -1 0 0 0 1 0 0 0 -1
0 0 0 0 0 0 0 1 0 0 -1 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
7 0 -6 -6 0 12 -3 -1 2 -3 -4 -7 -1 4 -6 3 3 -1 -3 0 -1 2 2 1 -3 -7 2 7 3 2 -3 2 0 0 0 -2 2 -1 1 1
9 0 -6 -7 0 14 -4 -2 1 -2 -4 -7 0 4 -8 4 2 -1 -3 -1 1 4 2 2 -4 -7 1 5 2 3 -4 1 1 0 -1 0 1 -1 1 0
21 0 -15 -18 2 34 -8 -6 5 -6 -9 -17 -2 11 -19 9 3 -4 -9 -4 2 11 7 3 -12 -21 3 14 6 5 -9 1 1 -1 -2 -2 3 -2 5 1
0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 -1
-1 0 1 1 -1 -1 0 0 0 1 1 1 0 -1 1 -1 0 1 0 0 0 -1 0 0 0 1 0 -1 -1 0 0 0 1 0 0 0 0 0 0 0
25 0 -19 -22 1 42 -11 -6 5 -7 -13 -21 -2 14 -23 12 5 -5 -9 -4 1 13 7 5 -13 -24 4 19 8 7 -12 2 0 -1 -2 -4 4 -3 5 3
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
15 0 -10 -14 1 26 -7 -4 3 -4 -8 -12 -1 8 -15 8 1 -3 -5 -3 3 9 5 3 -8 -15 2 11 4 5 -8 0 -1 -1 -1 -2 3 -2 4 1
-2 0 3 1 0 -3 -1 2 -1 1 -2 3 1 -1 0 1 -2 -2 4 -1 1 2 -1 1 2 3 1 -1 0 0 -1 -1 -3 0 0 0 0 0 0 0
2 0 -1 -2 -1 5 -2 1 0 -1 -3 -2 0 1 -3 2 1 -1 1 0 0 1 1 1 0 -1 1 3 1 2 -2 1 -1 0 0 -1 1 0 0 0
12 0 -9 -10 0 20 -5 -3 3 -4 -6 -11 -1 6 -11 5 4 -2 -5 -1 0 5 4 2 -6 -11 2 9 4 4 -5 2 1 0 -1 -2 2 -1 2 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
14 0 -9 -12 1 23 -7 -3 2 -3 -8 -10 0 7 -14 8 1 -4 -3 -3 2 10 3 4 -7 -12 2 9 4 4 -8 0 -1 0 -2 -1 2 -2 3 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 0 0 -1 0 0 0 0 1 0 0 0 0 0 0 0
-1 -1 1 3 -1 -3 1 1 1 0 0 1 0 -2 1 -2 1 1 1 0 0 -2 1 0 0 2 1 -2 -1 0 0 1 2 0 0 1 -1 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 -1 0 0 0 0 0 0 0 0 0 0 0 0
-16 0 12 14 0 -28 7 4 -4 5 8 14 1 -8 16 -8 -4 3 6 3 -1 -8 -6 -3 8 15 -3 -13 -5 -5 8 -2 0 1 1 2 -3 1 -4 0
9 0 -7 -7 0 15 -4 -2 2 -3 -4 -8 -1 5 -8 4 3 -1 -4 0 -1 3 2 2 -4 -8 1 7 3 3 -4 2 1 0 -1 -1 1 -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 1 0 0 0 0 0 0 0 0 0 0 0 0
19 -1 -15 -16 1 31 -8 -5 5 -6 -10 -17 -2 10 -17 7 5 -3 -8 -3 1 8 8 3 -11 -19 4 14 6 5 -8 2 1 -1 -1 -3 3 -2 4 2
27 0 -21 -23 1 45 -11 -7 6 -8 -12 -24 -2 14 -24 12 7 -4 -12 -3 0 12 8 5 -14 -26 4 20 8 7 -12 3 2 -1 -2 -3 4 -3 5 2
-9 -1 8 10 -1 -16 4 3 -1 3 4 9 1 -6 8 -5 -2 2 5 1 1 -5 -2 -2 4 10 -1 -9 -4 -2 4 -1 1 1 0 2 -2 1 -2 -2
-9 1 7 7 0 -14 3 3 -3 3 4 9 1 -4 7 -2 -3 0 5 1 0 -2 -5 -1 6 9 -1 -6 -2 -3 3 -1 -2 1 0 1 -1 1 -2 -1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 0 -7 -9 0 16 -4 -3 2 -2 -4 -8 -1 5 -9 5 2 -2 -4 -1 0 6 2 2 -4 -9 1 8 3 2 -5 1 0 -1 -1 -1 2 -1 2 1
22 0 -16 -20 2 38 -10 -6 4 -6 -11 -18 -2 12 -22 12 3 -5 -8 -4 2 14 6 5 -11 -22 3 17 7 6 -12 1 -1 -1 -3 -2 4 -3 5 2
14 0 -11 -13 0 26 -6 -4 4 -4 -6 -13 -2 8 -14 7 3 -2 -7 -2 1 7 5 2 -7 -15 2 12 4 4 -7 1 1 -1 -1 -2 3 -1 3 1
-5 0 3 5 -1 -8 3 1 0 2 4 3 0 -3 5 -4 0 2 0 1 -1 -4 0 -2 2 4 -1 -4 -2 -2 3 0 2 0 1 1 -1 1 -1 -1
14 1 -11 -14 0 26 -7 -3 3 -5 -8 -13 -1 8 -15 9 3 -4 -5 -2 0 9 4 3 -5 -14 3 14 6 4 -8 2 -2 -1 -1 -2 3 -1 3 1
2 0 -1 -2 -1 4 -1 -1 1 0 -1 -2 0 1 -2 1 1 0 -1 0 1 1 1 0 -1 -2 0 1 0 1 -1 0 0 0 0 -1 1 0 0 0
-3 1 3 2 0 -4 1 1 -1 1 2 3 0 -1 2 0 -2 0 1 1 1 0 -2 -1 3 3 -1 -2 -1 -1 1 -1 -1 0 0 1 0 1 -1 -1
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PROPERTIES
INTEGRAL = 1
MODULAR = 3
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REFERENCES
G. Nebe, Finite quaternionic matrix groups,
Representation Theory 2, 106-223 (April 1998)
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NOTES
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URL (links to other sites for this lattice)
All the quaternionic matrix groups
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe