The Lattice 2.M12.2GL2(3)
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 13:14:47 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.M12.2GL2(3)
-
DIMENSION
40
-
GRAM (floating point or integer Gram matrix)
40 0
6
0 6
2 0 6
1 1 1 6
1 2 1 3 6
1 1 2 1 1 6
1 1 1 1 0 2 6
3 0 2 1 0 2 3 6
-1 -1 0 1 1 -1 0 0 6
0 2 0 0 1 0 0 0 2 6
-1 1 0 -1 0 1 -1 -1 1 2 6
-1 1 -1 -1 1 0 1 -1 2 2 3 6
0 0 0 1 1 -1 -1 0 3 0 2 2 6
0 1 -1 0 0 -2 0 -2 1 0 2 2 2 6
-2 0 0 0 -1 0 1 0 2 1 1 1 1 1 6
2 -1 1 0 0 0 -2 1 1 0 0 0 2 1 -1 6
-1 0 0 1 0 1 2 1 1 2 0 1 0 -1 1 0 6
0 -1 3 2 2 0 0 -1 1 1 0 1 1 1 2 1 1 6
0 -1 0 -1 1 -1 -1 0 2 0 1 2 1 0 2 1 1 1 6
0 1 1 2 0 -1 -1 -1 1 0 1 1 3 3 1 1 1 2 0 6
0 3 0 1 2 -1 -1 0 1 3 0 2 1 1 0 2 1 1 1 2 6
0 0 -2 1 1 -1 -1 -1 2 2 1 2 0 1 1 1 1 1 3 0 2 6
-1 2 -1 0 1 2 1 -1 2 1 1 2 1 1 1 1 1 0 0 0 1 1 6
1 -1 1 1 1 1 0 0 2 1 1 1 -1 1 0 1 1 1 2 0 0 2 1 6
1 -2 1 1 0 0 0 2 1 0 1 0 1 0 1 2 1 1 2 0 -1 1 -1 3 6
-1 1 0 1 2 -1 0 -1 3 2 1 3 2 2 0 1 2 1 1 2 3 2 2 2 1 6
0 0 2 0 1 3 1 1 1 0 1 1 0 -1 1 1 0 1 2 -1 0 0 2 2 1 0 6
1 0 -1 3 1 0 -1 1 2 1 1 0 2 1 1 1 1 0 1 2 1 2 -1 2 2 1 -1 6
0 -1 0 -1 -1 1 0 0 0 -1 1 0 0 0 0 0 0 -1 0 0 -2 -1 0 0 0 -1 0 0 6
0 0 0 0 0 -1 -1 -1 0 1 1 0 0 1 -1 0 0 0 -1 1 0 0 -1 0 0 1 -1 0 3 6
0 -1 0 -1 -1 -2 -1 -1 0 0 0 0 0 1 1 0 0 1 1 1 0 1 -1 0 0 0 -1 0 3 3 6
0 0 0 0 0 1 1 1 0 -1 -1 0 0 -1 1 0 0 0 1 -1 0 0 1 0 0 -1 1 0 3 0 3 6
-1 1 0 0 0 1 0 0 -1 0 0 0 -1 -1 -1 -1 0 -1 -1 0 0 -1 0 0 0 0 0 -1 3 2 1 2 6
0 0 -1 0 1 0 -1 -1 1 1 1 1 1 0 0 0 -1 0 0 0 0 1 1 0 0 0 0 0 2 2 2 2 2 6
1 0 1 0 0 -1 0 0 0 1 0 0 0 1 -1 1 0 1 -1 1 1 0 0 0 0 1 0 -1 2 3 3 1 3 2 6
0 1 1 0 1 0 -1 0 0 1 0 -2 -1 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 6
0 1 -1 0 0 0 0 0 -1 1 0 0 -1 0 0 0 0 0 0 -1 1 1 0 0 0 -1 0 0 1 1 2 3 3 2 3 2 6
1 -1 1 0 0 0 0 0 0 0 -1 0 -1 0 -1 1 0 1 0 0 0 0 0 2 1 0 1 -1 1 2 3 2 2 2 3 1 3 6
-1 0 -1 2 -1 0 2 0 0 0 -1 0 -1 0 1 -1 2 0 -1 0 0 1 0 0 0 1 -1 1 2 2 2 2 2 1 2 1 2 1 6
0 1 -1 1 1 -1 -1 0 0 -1 0 -1 2 1 0 0 -1 -1 0 1 0 -1 0 -1 0 0 0 1 2 2 2 2 2 2 2 2 2 1 1 6
-
DIVISORS (elementary divisors)
1^20 2^20
-
MINIMAL_NORM
6
-
KISSING_NUMBER
84480
-
GROUP_ORDER
2^11 * 3^4 * 5 * 11
-
GROUP_GENERATORS
4
40
-23 -47 18 -87 109 -12 43 -18 -10 34 4 7 25 -51 16 32 -32 -65 -51 115 -9 54 -6 52 14 -73 -11 -42 -24 1 -21 21 -18 -41 -7 17 2 -7 67 22
-5 -8 3 -15 19 -2 7 -2 -3 6 0 1 6 -9 3 5 -6 -11 -9 20 -2 10 -1 10 2 -12 -2 -8 -3 0 -4 3 -4 -7 -1 3 1 -1 12 3
-6 -10 2 -20 24 -3 13 -4 -3 8 2 0 7 -14 3 9 -9 -13 -11 27 -2 12 -2 14 2 -16 -3 -10 -5 0 -4 4 -4 -9 -2 4 1 -2 15 5
-5 -13 3 -28 33 -4 14 -6 -1 8 3 1 7 -17 5 10 -9 -17 -17 35 -2 16 -3 16 4 -21 -3 -13 -7 0 -6 6 -5 -12 -3 5 1 -2 20 7
11 19 -12 27 -38 4 -12 5 7 -16 3 -6 -9 13 -5 -10 11 28 15 -39 6 -19 -1 -16 -5 27 4 13 10 -1 7 -8 6 14 1 -6 0 3 -23 -7
-1 0 -3 -1 1 0 4 0 -1 0 2 -2 1 -3 1 3 -2 1 0 2 0 0 -2 3 -2 1 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0
-19 -35 12 -68 85 -10 35 -13 -9 27 4 4 20 -41 13 27 -26 -49 -39 90 -9 42 -6 42 9 -55 -9 -33 -18 0 -17 16 -14 -31 -5 13 1 -5 52 17
-9 -15 3 -30 38 -4 18 -6 -4 12 3 1 9 -21 6 14 -13 -21 -17 42 -4 18 -4 21 3 -24 -5 -16 -8 0 -7 7 -7 -14 -2 6 1 -3 23 8
5 14 -9 23 -29 5 -8 4 3 -8 0 -3 -6 10 -4 -5 6 19 15 -28 1 -15 -1 -11 -5 20 1 9 6 0 5 -5 4 10 3 -4 -1 2 -18 -5
5 13 -9 20 -26 4 -7 4 2 -8 1 -4 -5 8 -3 -5 5 18 13 -25 1 -13 -1 -9 -5 19 1 8 6 0 4 -4 3 9 3 -4 -1 2 -16 -5
14 30 -15 54 -68 9 -23 10 7 -22 0 -6 -15 28 -9 -17 18 42 32 -70 6 -34 1 -29 -10 46 5 24 14 0 13 -12 11 25 5 -10 -2 4 -42 -13
0 -1 -2 -8 8 -1 4 -2 2 0 3 -1 0 -6 2 4 -2 -2 -5 9 -1 4 -3 4 1 -4 -1 -4 -2 0 -3 3 -1 -3 0 1 -1 0 5 2
-13 -23 8 -40 53 -4 22 -9 -6 19 1 4 13 -25 8 18 -17 -33 -22 57 -7 25 -4 26 6 -35 -7 -22 -13 1 -10 11 -9 -20 -2 9 1 -4 32 10
-14 -29 12 -56 69 -7 25 -11 -5 21 2 5 16 -31 10 19 -19 -41 -33 72 -6 35 -4 32 10 -47 -7 -27 -16 1 -14 14 -11 -26 -4 11 0 -4 43 14
-17 -30 10 -59 74 -7 30 -11 -7 24 3 4 17 -36 11 24 -23 -43 -33 79 -9 36 -6 37 8 -48 -9 -30 -17 1 -15 15 -13 -27 -3 11 1 -5 45 15
-5 -11 4 -20 25 -2 9 -4 -1 8 1 2 5 -11 3 7 -7 -15 -11 27 -2 12 -1 11 4 -18 -3 -10 -7 1 -5 6 -4 -10 -1 4 0 -2 16 5
-1 0 -2 -1 1 0 3 0 -1 1 1 -2 0 -2 0 2 -2 1 1 2 -1 0 0 1 -1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0
-2 -7 0 -21 22 -3 10 -4 1 4 4 -1 4 -13 3 7 -6 -9 -12 24 -1 11 -3 11 3 -14 -2 -9 -5 0 -5 5 -3 -8 -2 3 0 -1 14 5
5 7 -5 6 -11 2 -4 1 6 -7 2 -2 -5 3 -2 -3 4 10 3 -11 3 -6 -1 -5 0 7 1 3 2 0 2 -2 2 4 0 -2 0 0 -6 -1
-15 -30 14 -53 67 -7 25 -11 -7 22 0 6 16 -29 9 18 -19 -42 -31 70 -6 34 -2 30 10 -46 -7 -25 -15 1 -13 13 -11 -25 -4 11 1 -4 41 13
1 1 -2 -3 2 0 0 0 2 -1 1 -1 0 -2 0 0 0 1 -2 3 0 1 -1 1 1 -1 0 -2 0 0 -1 1 -1 -1 0 0 0 0 2 0
9 15 -8 21 -30 4 -12 4 7 -13 1 -3 -9 12 -4 -9 10 21 12 -31 4 -15 0 -14 -3 20 3 11 6 0 5 -5 5 11 2 -5 -1 2 -18 -5
5 14 -7 27 -33 4 -11 6 1 -9 -1 -3 -6 14 -4 -8 8 20 17 -34 2 -16 1 -14 -6 23 2 12 8 0 5 -6 5 12 3 -5 -1 3 -21 -7
9 15 -9 22 -31 3 -10 4 6 -13 2 -4 -8 11 -4 -8 9 22 12 -32 5 -15 0 -13 -4 21 3 11 7 0 6 -6 6 11 1 -5 -1 2 -19 -5
-10 -22 8 -41 51 -6 21 -9 -4 15 3 3 11 -25 8 16 -15 -30 -24 54 -4 25 -3 25 6 -34 -6 -20 -12 1 -10 10 -8 -19 -3 8 1 -4 31 11
1 4 -3 7 -9 1 -1 1 0 -2 0 -2 -1 2 -1 -1 1 6 5 -8 0 -4 0 -3 -2 7 0 3 3 0 1 -2 1 3 1 -1 0 1 -6 -2
20 39 -20 64 -84 10 -30 13 12 -30 1 -8 -20 35 -12 -23 24 55 37 -87 10 -42 1 -37 -11 56 8 30 19 -1 16 -16 14 31 5 -13 -2 5 -51 -16
-12 -24 7 -47 59 -5 24 -10 -4 18 3 3 13 -29 9 19 -18 -34 -27 63 -6 28 -5 29 7 -38 -7 -24 -14 1 -11 12 -10 -22 -3 9 1 -4 36 12
8 17 -8 30 -38 4 -11 5 4 -13 1 -4 -9 15 -5 -9 10 24 18 -40 4 -19 1 -17 -6 26 3 15 8 0 8 -8 7 14 2 -6 -1 3 -24 -7
25 49 -21 88 -112 12 -41 17 12 -37 -1 -9 -26 49 -16 -32 32 69 51 -117 11 -55 5 -52 -15 75 11 43 25 -1 22 -22 19 41 6 -17 -2 8 -69 -22
-1 -2 0 -8 8 -1 5 -2 1 1 2 -1 1 -6 1 3 -3 -3 -4 9 0 4 -1 4 1 -5 -1 -3 -2 0 -1 1 -1 -3 -1 1 0 0 5 2
-10 -18 3 -40 49 -5 23 -8 -3 14 5 0 11 -27 8 18 -16 -26 -22 53 -5 23 -6 26 4 -30 -6 -21 -11 0 -9 9 -8 -18 -3 7 1 -3 30 10
22 44 -18 81 -102 10 -37 16 9 -33 -2 -8 -23 45 -14 -29 29 62 47 -107 10 -50 5 -47 -14 69 10 39 24 -1 20 -21 17 38 5 -16 -1 7 -63 -20
11 25 -13 44 -55 7 -18 8 5 -17 0 -5 -12 22 -7 -13 14 34 27 -56 4 -28 0 -23 -9 38 4 19 12 0 10 -10 8 20 4 -8 -1 4 -34 -11
22 46 -20 84 -106 11 -38 17 9 -33 -2 -9 -23 46 -15 -30 29 65 50 -110 10 -52 5 -48 -15 71 10 40 25 -1 20 -21 17 39 6 -16 -2 8 -65 -21
21 45 -21 81 -103 12 -35 16 9 -32 -1 -10 -22 43 -15 -28 27 64 49 -106 10 -51 4 -45 -15 70 9 38 24 -1 20 -21 16 38 6 -16 -1 7 -63 -20
13 27 -15 44 -57 7 -20 10 7 -19 1 -7 -13 23 -8 -15 15 38 27 -58 5 -29 0 -24 -9 40 5 19 13 -1 11 -11 9 21 3 -9 -1 4 -34 -11
10 18 -9 29 -39 4 -14 6 6 -14 1 -4 -10 16 -6 -11 11 26 17 -40 5 -19 1 -18 -5 26 4 14 9 -1 8 -8 7 14 1 -6 -1 3 -23 -7
2 5 -3 7 -9 0 -2 2 1 -3 1 -2 -3 3 -1 -1 2 7 5 -9 -1 -5 0 -4 -3 8 1 4 2 0 2 -2 2 4 0 -2 0 1 -6 -2
-2 -3 -2 -8 10 0 7 -2 0 3 2 -1 3 -8 2 5 -5 -4 -4 12 -1 4 -3 7 0 -5 -2 -6 -2 0 -1 1 -2 -4 -1 2 1 -1 6 2
40
4 11 -5 23 -27 3 -7 4 0 -7 -1 -3 -4 11 -3 -6 6 15 14 -28 2 -13 1 -11 -5 19 2 10 7 0 6 -6 4 10 2 -4 0 2 -18 -6
-4 -6 4 -7 10 -1 5 -2 -3 5 -1 2 3 -4 1 3 -4 -8 -3 11 -1 5 1 5 1 -8 -2 -3 -3 1 -2 2 -2 -4 0 2 0 -1 6 2
8 16 -5 29 -37 3 -14 6 3 -12 -1 -3 -8 17 -5 -11 11 22 16 -39 4 -17 2 -17 -5 25 4 14 10 -1 7 -8 6 14 1 -6 0 3 -23 -7
28 54 -20 103 -130 14 -50 20 12 -42 -4 -8 -30 60 -19 -40 38 77 59 -137 15 -63 9 -62 -15 85 13 51 30 -1 25 -26 21 48 7 -20 -2 9 -80 -25
-8 -15 6 -25 32 -4 15 -6 -5 11 1 2 8 -16 5 10 -11 -20 -14 34 -2 16 -1 16 4 -21 -4 -12 -6 0 -6 5 -6 -12 -2 5 1 -2 19 7
-19 -37 15 -66 84 -9 34 -14 -9 27 2 6 20 -39 13 26 -25 -52 -39 89 -8 42 -5 41 10 -56 -9 -33 -19 1 -16 16 -14 -31 -5 13 2 -6 51 17
7 14 -8 21 -28 3 -8 4 4 -11 2 -4 -7 10 -3 -6 8 19 12 -29 3 -14 -1 -11 -5 20 2 10 6 0 5 -5 5 11 2 -5 -1 2 -18 -5
3 10 -5 23 -26 3 -7 5 -1 -5 -1 -3 -4 11 -3 -5 5 14 15 -26 0 -13 1 -10 -6 19 1 9 6 0 5 -5 4 10 2 -4 0 2 -17 -6
10 20 -10 34 -44 5 -16 7 5 -14 0 -4 -10 18 -6 -12 12 28 20 -45 4 -22 1 -19 -6 30 4 16 10 -1 8 -8 7 16 3 -7 -1 3 -27 -8
9 19 -11 30 -39 5 -13 6 6 -13 1 -4 -10 15 -5 -9 10 26 18 -39 3 -20 -1 -16 -6 27 3 13 8 0 7 -6 6 14 3 -6 -1 2 -24 -7
0 -4 2 -8 10 -2 2 -2 1 1 1 2 1 -4 2 2 -1 -6 -7 10 0 5 -1 4 2 -7 0 -4 -3 0 -2 3 -1 -4 -1 2 0 -1 6 2
-1 -4 -1 -12 14 -2 7 -3 1 2 3 0 2 -9 3 6 -4 -6 -8 15 -1 6 -3 8 1 -8 -1 -6 -4 0 -2 3 -1 -5 -1 2 0 -2 8 3
9 18 -7 36 -44 5 -17 7 3 -13 -2 -2 -9 20 -6 -13 12 25 21 -46 4 -22 3 -20 -6 29 4 17 10 -1 9 -9 7 16 3 -6 -1 3 -27 -9
-7 -16 7 -30 37 -4 13 -6 -3 11 1 3 8 -16 5 9 -10 -22 -18 38 -2 18 -1 16 6 -25 -3 -13 -8 0 -7 7 -6 -14 -2 6 0 -2 23 7
-1 -7 3 -16 18 -3 5 -3 1 3 2 1 2 -8 3 4 -3 -9 -11 18 0 9 -1 7 3 -12 -1 -6 -4 0 -4 4 -2 -6 -2 2 0 -1 11 4
-9 -14 7 -18 26 -2 10 -3 -7 13 -3 3 9 -10 3 7 -10 -19 -9 28 -4 13 1 13 3 -18 -3 -10 -5 0 -4 4 -5 -10 -1 5 1 -2 16 4
9 16 -6 29 -37 4 -16 6 5 -13 -1 -2 -10 18 -5 -12 12 22 16 -39 4 -18 2 -18 -4 24 4 14 8 0 6 -6 6 14 3 -6 -1 2 -23 -7
5 6 -3 5 -10 0 -4 1 4 -7 2 -2 -4 3 -1 -4 4 9 1 -11 4 -4 0 -5 0 7 2 4 4 -1 2 -3 2 4 -1 -2 0 1 -6 -1
-8 -19 9 -33 42 -6 15 -7 -4 13 1 3 9 -18 6 11 -11 -26 -20 43 -3 21 -1 18 6 -28 -3 -15 -9 0 -8 8 -6 -15 -3 6 1 -3 25 8
23 41 -12 79 -100 10 -43 16 10 -33 -5 -4 -24 50 -15 -34 32 58 44 -107 12 -48 9 -51 -10 64 12 41 23 -1 19 -20 17 37 5 -15 -2 7 -61 -20
0 3 -2 8 -9 2 -2 2 -1 0 -1 -1 -1 4 -2 -2 0 5 7 -8 0 -5 1 -3 -2 6 0 3 2 0 2 -2 1 3 1 -1 0 0 -5 -2
1 0 -2 -3 2 0 2 -1 2 -1 2 -1 -1 -3 0 1 -1 1 -2 3 1 1 -1 1 1 -1 0 -1 -1 0 0 1 0 -1 0 0 0 -1 1 1
-19 -36 14 -66 83 -9 33 -13 -9 27 2 6 20 -39 12 25 -25 -50 -38 88 -8 41 -4 41 10 -56 -9 -32 -19 1 -16 16 -14 -31 -4 13 1 -6 51 17
-6 -13 6 -24 30 -4 11 -5 -2 9 1 2 6 -13 4 8 -8 -18 -15 31 -2 15 -1 13 5 -20 -2 -11 -6 0 -6 6 -5 -11 -2 4 1 -2 18 6
15 29 -9 59 -72 7 -30 12 6 -22 -4 -3 -17 36 -11 -23 22 41 33 -77 7 -35 6 -36 -8 47 8 29 17 -1 14 -14 12 27 4 -11 -1 5 -45 -15
10 22 -9 42 -52 6 -20 9 4 -15 -2 -3 -12 24 -8 -15 14 31 25 -54 4 -26 3 -24 -7 35 5 20 12 -1 10 -10 8 19 4 -8 -1 3 -32 -10
-5 -12 4 -23 28 -4 12 -5 -2 8 2 1 6 -14 4 9 -8 -16 -14 30 -2 14 -2 14 3 -18 -2 -11 -6 0 -5 5 -4 -10 -3 4 1 -2 17 6
5 9 -1 23 -27 3 -12 4 1 -7 -3 0 -6 15 -4 -10 8 13 13 -29 3 -13 4 -15 -2 17 3 12 6 0 5 -5 4 10 2 -4 0 2 -17 -6
11 18 -3 40 -48 4 -22 7 3 -15 -4 0 -11 26 -6 -16 17 25 21 -53 5 -23 5 -25 -5 30 6 20 10 0 9 -9 9 18 3 -7 -1 3 -30 -10
26 50 -18 97 -120 12 -48 19 10 -37 -5 -6 -28 57 -17 -36 36 70 55 -127 11 -59 8 -58 -15 79 13 47 27 -1 23 -23 20 44 7 -18 -2 8 -74 -24
5 4 1 7 -10 -1 -7 1 2 -5 0 0 -4 7 -1 -5 6 6 2 -13 2 -4 2 -8 0 6 3 6 2 0 1 -1 3 4 0 -2 -1 1 -6 -2
-16 -33 16 -56 72 -9 27 -12 -9 24 1 6 17 -31 11 21 -20 -46 -33 74 -7 36 -2 33 9 -49 -7 -26 -17 1 -14 14 -11 -26 -4 11 1 -5 44 14
9 15 -2 33 -41 3 -18 6 3 -13 -3 0 -10 22 -6 -14 14 22 18 -45 5 -19 5 -22 -4 25 5 18 9 0 7 -8 8 15 2 -6 -1 3 -25 -8
21 40 -16 74 -94 9 -35 14 9 -31 -2 -6 -22 42 -13 -27 28 57 42 -99 10 -46 5 -44 -12 62 10 37 21 -1 18 -18 16 35 5 -14 -2 6 -58 -18
23 42 -16 76 -98 9 -38 15 10 -33 -2 -7 -23 45 -14 -30 30 60 43 -104 11 -47 6 -47 -12 65 11 39 23 -1 18 -19 17 36 5 -15 -2 7 -60 -19
-1 0 2 6 -6 0 -2 1 -3 1 -2 1 0 4 -1 -2 1 1 4 -6 0 -2 2 -3 -1 3 0 3 2 0 0 -1 0 2 1 0 0 1 -4 -1
-11 -23 10 -41 51 -7 21 -9 -6 16 2 3 12 -24 8 15 -15 -31 -24 53 -4 26 -2 24 6 -34 -5 -18 -11 1 -11 10 -8 -19 -3 8 1 -3 31 10
0 -4 3 -8 8 -3 3 -2 0 1 1 0 1 -3 1 1 -1 -4 -6 7 1 5 1 2 2 -6 1 -1 -1 0 -2 1 0 -3 -2 1 0 0 5 2
34 65 -25 121 -153 16 -60 24 15 -50 -4 -10 -36 71 -22 -46 46 92 69 -162 16 -75 9 -73 -19 101 16 60 34 -1 29 -29 26 57 9 -24 -3 10 -94 -30
5 9 0 26 -30 2 -12 4 -1 -7 -3 0 -6 16 -4 -10 9 14 15 -33 3 -14 5 -16 -4 19 3 14 7 0 5 -6 5 11 2 -4 -1 3 -19 -6
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
-11 -19 5 -36 46 -4 21 -8 -5 16 2 2 11 -24 7 17 -16 -27 -19 50 -6 21 -4 24 4 -29 -6 -19 -11 1 -8 9 -8 -17 -2 7 1 -4 28 9
9 17 -9 28 -37 3 -12 6 3 -13 1 -5 -8 14 -5 -10 10 25 16 -38 4 -18 1 -16 -6 27 4 14 10 -1 7 -8 6 14 1 -6 0 3 -23 -7
-4 -8 3 -13 17 -1 7 -3 -2 6 0 1 5 -7 2 5 -5 -11 -7 18 -1 8 -1 8 2 -12 -2 -7 -4 0 -3 3 -3 -6 -1 3 0 -1 11 3
-8 -14 1 -31 38 -2 17 -6 -2 12 3 0 9 -20 5 13 -13 -20 -16 42 -4 17 -5 20 4 -24 -5 -17 -9 0 -7 8 -7 -14 -1 6 0 -3 24 7
3 5 -3 7 -10 0 -2 1 1 -4 1 -2 -3 3 -1 -2 3 7 4 -10 1 -5 0 -5 -2 8 2 5 3 0 2 -2 2 4 0 -2 0 1 -7 -2
-14 -31 12 -58 73 -8 28 -13 -6 22 3 5 16 -34 12 22 -20 -44 -35 76 -7 36 -5 34 9 -48 -7 -28 -17 1 -14 15 -12 -27 -4 11 1 -5 44 15
-8 -16 6 -30 38 -4 15 -6 -4 12 1 3 9 -18 6 12 -11 -23 -18 40 -4 19 -3 19 4 -25 -4 -15 -8 0 -7 7 -7 -14 -2 6 1 -3 23 8
-14 -25 8 -47 59 -5 24 -9 -6 20 2 3 15 -28 8 18 -19 -35 -26 64 -6 29 -5 30 7 -39 -7 -25 -13 0 -12 12 -11 -22 -3 10 1 -4 37 12
4 8 -4 15 -18 2 -7 3 2 -5 0 -1 -5 8 -3 -4 5 11 9 -18 0 -10 0 -8 -3 13 2 6 3 0 4 -2 3 7 1 -3 0 0 -11 -4
2 7 -2 18 -21 2 -7 4 -1 -4 -2 -1 -4 10 -4 -6 4 11 12 -21 1 -11 3 -10 -3 14 2 9 5 0 5 -5 3 8 1 -3 1 1 -13 -5
-15 -31 12 -58 72 -7 26 -11 -6 23 2 5 16 -32 10 20 -21 -43 -33 76 -7 35 -4 33 10 -48 -7 -28 -17 1 -14 15 -12 -27 -4 11 1 -5 45 14
-8 -15 7 -26 32 -3 11 -4 -4 11 -1 3 9 -13 3 7 -10 -20 -14 34 -2 16 0 15 5 -23 -3 -12 -7 0 -6 5 -6 -12 -2 6 1 -2 21 6
3 6 -3 12 -15 3 -6 2 2 -4 -1 -1 -3 7 -3 -5 3 9 8 -15 2 -8 1 -7 -1 9 1 5 3 0 3 -3 2 5 1 -2 0 1 -8 -3
3 1 2 3 -5 -1 -4 0 2 -4 0 1 -3 4 -1 -4 4 3 0 -7 3 -2 2 -5 1 2 2 4 1 0 1 -1 2 2 -1 -1 0 0 -3 0
-10 -21 7 -45 53 -6 21 -8 -3 15 3 2 12 -26 7 15 -16 -29 -26 57 -4 27 -4 26 7 -35 -5 -21 -11 0 -11 10 -9 -20 -4 8 1 -3 34 11
-4 -10 2 -23 27 -3 11 -5 0 7 3 1 5 -14 4 9 -7 -14 -14 29 -3 13 -4 13 3 -17 -2 -11 -7 0 -5 6 -4 -10 -2 4 0 -2 17 6
15 25 -11 43 -57 6 -23 9 8 -21 0 -5 -14 26 -9 -19 18 37 24 -60 8 -28 3 -28 -6 38 7 22 13 -1 11 -11 10 21 2 -9 -1 4 -34 -11
-15 -29 9 -59 72 -7 29 -11 -5 22 4 3 16 -35 10 22 -22 -40 -33 77 -7 35 -6 35 9 -47 -8 -29 -16 0 -14 14 -12 -27 -4 11 1 -5 45 15
19 37 -15 68 -87 10 -34 14 9 -28 -3 -6 -19 40 -14 -27 25 53 40 -91 10 -43 5 -41 -10 57 9 33 20 -1 17 -18 14 32 4 -13 -1 6 -52 -17
-4 -6 -2 -18 21 -1 10 -3 0 6 3 -1 5 -13 3 9 -8 -9 -9 24 -3 9 -5 13 1 -12 -3 -11 -5 0 -4 5 -4 -8 -1 3 0 -2 14 4
-4 -7 0 -15 18 0 9 -3 0 6 2 0 4 -10 2 7 -7 -9 -7 21 -2 8 -3 10 2 -12 -3 -9 -5 0 -3 4 -3 -7 -1 3 0 -2 12 4
-15 -29 8 -59 72 -7 32 -13 -5 22 5 2 16 -37 11 24 -23 -41 -33 78 -7 35 -7 36 8 -46 -8 -29 -17 1 -14 15 -12 -27 -4 11 1 -5 44 15
-8 -13 2 -27 34 -2 16 -6 -3 12 3 0 8 -18 5 13 -12 -19 -14 38 -5 16 -5 18 3 -21 -5 -15 -8 0 -7 8 -6 -13 -1 5 0 -2 21 7
-12 -26 11 -51 62 -7 23 -10 -4 18 3 4 13 -28 8 17 -17 -36 -30 65 -5 31 -3 28 9 -42 -6 -23 -14 0 -12 12 -10 -23 -4 9 1 -4 39 13
-10 -17 2 -37 45 -3 20 -7 -3 15 4 0 11 -24 6 16 -16 -24 -19 50 -6 21 -6 24 4 -28 -6 -20 -11 0 -9 10 -8 -17 -2 7 0 -3 29 9
-7 -13 3 -29 35 -4 16 -6 -3 10 3 0 8 -19 6 12 -11 -19 -16 38 -4 17 -4 18 3 -21 -4 -14 -7 0 -7 7 -6 -13 -2 5 1 -2 21 7
-6 -8 5 -8 13 0 4 -1 -4 8 -3 3 5 -3 0 3 -5 -11 -3 14 -2 6 1 6 2 -11 -2 -5 -3 0 -2 2 -3 -5 0 3 0 -1 9 2
-11 -19 10 -28 38 -5 14 -5 -8 16 -2 4 10 -15 5 10 -12 -26 -15 40 -5 19 1 17 5 -26 -4 -13 -8 1 -8 7 -7 -14 -2 6 1 -2 23 7
-15 -26 10 -43 57 -6 23 -8 -9 22 0 4 15 -26 8 18 -19 -36 -23 61 -8 27 -2 28 6 -37 -7 -22 -13 1 -11 11 -10 -21 -3 9 2 -4 35 10
1 5 -3 13 -14 2 -4 3 -1 -2 -1 -1 -2 6 -2 -3 2 8 9 -14 0 -8 1 -5 -3 10 0 5 3 0 3 -3 2 5 1 -2 0 1 -9 -3
-21 -37 14 -67 86 -9 35 -13 -11 30 2 5 21 -40 13 27 -27 -52 -37 91 -10 42 -5 42 9 -56 -10 -33 -19 1 -17 17 -15 -32 -4 13 1 -5 52 17
8 18 -7 35 -43 4 -16 7 2 -12 -2 -3 -9 20 -6 -12 12 25 21 -45 3 -21 3 -20 -6 29 4 17 10 0 8 -8 7 16 3 -7 -1 3 -27 -9
9 19 -7 35 -45 5 -17 7 4 -14 -2 -3 -10 21 -7 -14 13 27 21 -47 5 -22 3 -21 -5 29 4 18 10 0 8 -8 7 17 3 -7 -1 3 -28 -9
25 51 -22 95 -119 13 -44 19 10 -37 -3 -9 -26 53 -17 -34 33 72 56 -124 11 -59 6 -54 -16 80 11 45 27 -1 23 -23 19 44 7 -18 -2 8 -73 -24
-7 -8 1 -14 19 -2 12 -3 -5 9 1 0 6 -12 3 9 -9 -11 -6 22 -4 9 -2 12 0 -11 -4 -8 -4 0 -4 4 -4 -7 0 3 0 -1 11 4
7 16 -7 31 -38 4 -13 6 2 -11 -1 -3 -8 17 -5 -10 10 23 19 -40 3 -19 2 -17 -6 26 3 15 9 0 7 -7 6 14 3 -6 -1 3 -24 -8
-2 -3 -1 -9 11 -1 6 -2 -1 3 2 -1 3 -7 3 5 -4 -5 -5 12 -2 5 -3 7 0 -5 -2 -5 -2 0 -3 3 -2 -4 0 1 0 0 6 2
-10 -19 10 -28 38 -5 14 -6 -7 15 -1 4 10 -15 6 11 -11 -26 -16 39 -5 19 0 17 4 -26 -4 -13 -9 1 -8 8 -6 -14 -2 6 0 -2 23 7
-2 0 0 3 -2 1 0 1 -2 2 -2 0 1 2 -1 0 -1 0 4 -2 -1 -2 1 0 -1 1 -1 1 0 0 1 -1 0 1 1 0 0 0 -1 -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
12 22 -7 41 -52 5 -23 9 6 -17 -2 -2 -13 26 -8 -17 17 31 23 -56 5 -25 4 -26 -6 33 6 21 11 0 9 -9 9 19 3 -8 -2 4 -31 -10
-4 -9 4 -15 19 -2 7 -3 -2 7 0 2 4 -8 2 5 -6 -12 -8 20 -2 9 0 8 3 -13 -2 -7 -5 0 -4 4 -3 -7 -1 3 0 -1 12 4
-22 -45 19 -85 105 -12 40 -17 -10 33 3 7 24 -48 15 30 -30 -63 -49 110 -10 53 -5 48 14 -70 -10 -39 -24 1 -21 21 -17 -39 -6 16 1 -6 65 21
-19 -44 21 -81 100 -13 35 -16 -8 30 3 8 21 -43 14 26 -26 -61 -49 103 -8 51 -3 43 15 -68 -8 -36 -23 1 -20 20 -15 -37 -7 15 1 -6 62 20
-4 -7 2 -13 16 -2 7 -2 -2 6 1 1 4 -8 1 5 -6 -9 -6 18 -2 7 0 8 2 -11 -2 -6 -4 0 -3 3 -3 -6 -1 3 0 -1 11 3
11 19 -6 39 -49 5 -21 8 4 -15 -3 -2 -11 25 -8 -17 15 28 23 -52 6 -24 5 -25 -5 31 6 20 11 0 9 -10 8 18 2 -7 -1 4 -29 -10
5 12 -6 24 -30 4 -9 5 1 -8 -1 -3 -5 12 -5 -8 6 18 16 -30 3 -15 2 -12 -5 20 2 11 7 0 6 -7 4 11 2 -4 0 2 -18 -6
-14 -25 10 -45 57 -6 23 -9 -7 20 1 3 14 -26 8 17 -18 -35 -25 61 -6 29 -3 27 7 -38 -6 -22 -12 0 -12 11 -10 -21 -3 9 1 -3 35 11
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 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-25 -45 20 -79 102 -11 38 -15 -12 36 0 9 24 -45 14 30 -31 -64 -45 108 -12 50 -4 48 13 -69 -11 -39 -23 1 -20 20 -18 -38 -5 16 2 -7 63 20
-19 -40 17 -76 95 -11 34 -15 -7 29 3 7 20 -42 14 27 -26 -57 -45 99 -9 47 -5 43 13 -64 -9 -36 -22 1 -19 19 -15 -35 -6 14 1 -6 59 19
-29 -56 25 -100 127 -14 48 -20 -14 42 1 10 30 -56 18 36 -37 -79 -58 133 -12 64 -5 59 17 -86 -13 -48 -28 1 -25 24 -21 -47 -7 20 2 -8 78 25
-23 -48 22 -87 110 -12 39 -18 -10 35 1 10 24 -47 16 30 -30 -68 -52 114 -10 55 -5 49 16 -75 -10 -41 -25 1 -22 22 -18 -41 -6 17 1 -7 68 22
-28 -52 19 -95 120 -12 49 -19 -13 41 3 7 29 -56 17 37 -38 -72 -53 128 -13 59 -7 58 14 -79 -13 -47 -27 1 -23 23 -20 -45 -7 19 2 -8 74 24
-9 -19 8 -39 47 -5 18 -8 -3 13 2 3 10 -22 7 13 -13 -27 -23 49 -3 24 -3 22 7 -32 -5 -18 -10 0 -10 9 -8 -17 -2 7 0 -3 29 10
22 42 -14 80 -102 11 -41 16 10 -33 -5 -5 -23 49 -16 -33 31 60 46 -108 12 -49 8 -50 -11 65 11 41 23 -1 20 -21 17 38 5 -15 -2 7 -62 -20
-32 -68 28 -128 159 -18 60 -26 -13 49 5 11 35 -72 23 45 -45 -95 -75 166 -14 79 -8 72 22 -106 -15 -60 -36 1 -31 31 -25 -59 -10 24 2 -10 98 32
-3 -5 1 -11 13 -1 6 -2 -1 5 1 0 3 -7 2 5 -5 -7 -6 15 -2 7 -2 7 1 -8 -2 -6 -3 0 -3 3 -2 -5 -1 2 0 -1 8 3
-10 -21 9 -42 51 -5 19 -9 -3 15 1 4 11 -23 7 14 -14 -30 -25 53 -4 26 -3 23 8 -35 -5 -19 -12 0 -10 10 -8 -19 -3 8 0 -3 32 11
8 11 -4 14 -21 1 -9 2 6 -11 2 -2 -7 9 -2 -7 9 15 6 -24 4 -9 0 -11 -2 13 3 9 4 0 3 -3 5 8 1 -4 -2 2 -13 -3
-7 -14 4 -31 37 -4 15 -6 -2 11 3 1 8 -19 6 12 -11 -20 -18 40 -4 19 -4 18 4 -24 -4 -15 -8 0 -8 8 -6 -14 -2 5 0 -2 23 8
11 20 -7 35 -46 4 -20 8 6 -16 -1 -3 -12 23 -8 -16 15 29 20 -49 6 -22 4 -24 -4 29 6 19 11 -1 8 -9 8 17 2 -7 -2 4 -27 -9
-8 -13 4 -25 32 -2 13 -5 -3 12 1 2 7 -15 4 11 -11 -19 -13 35 -5 15 -3 15 4 -21 -4 -13 -8 0 -6 7 -6 -12 -1 5 0 -2 20 6
-25 -45 18 -80 102 -9 41 -16 -12 36 1 7 25 -47 14 31 -33 -63 -44 109 -11 50 -5 49 13 -68 -12 -40 -23 1 -19 19 -18 -38 -5 16 2 -7 63 20
0 -5 6 -8 9 -2 -1 -2 1 1 -1 3 0 0 1 -1 1 -7 -7 7 1 6 2 0 4 -9 1 -1 -3 0 -2 2 0 -3 -1 1 -1 0 6 2
-7 -14 4 -28 34 -3 13 -5 -2 11 2 2 7 -16 4 10 -11 -19 -15 37 -3 16 -2 16 5 -23 -4 -14 -8 0 -7 7 -6 -13 -2 6 0 -2 22 7
-26 -46 18 -85 108 -11 44 -17 -13 37 2 7 27 -51 16 34 -34 -66 -48 115 -13 54 -7 53 12 -71 -12 -42 -24 1 -21 21 -19 -40 -5 17 2 -7 66 21
2 8 -7 13 -16 3 -3 3 1 -4 1 -3 -3 4 -2 -2 2 11 9 -14 0 -9 -2 -4 -4 13 0 4 4 -1 3 -3 1 6 2 -2 0 1 -10 -3
-10 -23 10 -44 54 -6 19 -9 -3 15 2 4 11 -24 8 14 -14 -32 -27 56 -4 27 -3 24 8 -36 -5 -20 -12 0 -11 11 -9 -20 -3 8 1 -3 33 11
8 17 -9 30 -38 5 -13 6 4 -12 0 -4 -9 16 -5 -10 10 24 18 -39 3 -19 0 -17 -6 27 3 14 9 -1 7 -7 6 14 3 -6 -1 3 -24 -7
13 30 -17 51 -65 8 -21 11 6 -20 1 -8 -14 26 -9 -16 16 42 32 -66 5 -33 0 -27 -11 46 5 23 15 -1 12 -12 10 24 5 -10 -2 5 -40 -13
24 49 -23 88 -111 13 -41 18 12 -36 -1 -9 -26 48 -16 -31 31 69 52 -115 10 -56 4 -50 -15 75 10 41 24 -1 22 -21 18 41 7 -17 -2 7 -68 -22
-15 -27 8 -53 66 -6 27 -10 -6 22 3 2 16 -32 9 20 -21 -38 -29 71 -7 32 -5 33 8 -43 -8 -27 -14 0 -13 13 -12 -25 -3 10 1 -4 41 13
20 36 -14 66 -84 9 -34 13 10 -29 -2 -5 -21 39 -12 -27 26 51 37 -89 10 -41 5 -41 -9 55 9 33 19 -1 16 -16 14 31 5 -13 -2 6 -52 -16
14 30 -12 59 -73 8 -28 13 5 -21 -3 -5 -16 34 -11 -22 20 43 35 -76 6 -36 5 -34 -10 49 7 28 17 -1 14 -14 11 27 5 -11 -1 5 -45 -15
7 16 -7 31 -38 4 -14 7 2 -11 -1 -3 -8 17 -5 -11 10 23 19 -40 3 -19 2 -17 -6 26 3 15 9 0 7 -7 6 14 3 -6 -1 3 -24 -8
4 8 -4 15 -19 3 -7 3 2 -6 0 -2 -5 9 -3 -6 5 12 10 -20 2 -10 1 -10 -2 13 1 8 4 0 3 -3 3 7 2 -3 -1 2 -12 -4
4 8 -3 15 -19 2 -8 3 1 -6 -1 -1 -4 9 -2 -6 6 11 9 -20 1 -9 1 -9 -3 13 2 8 4 0 3 -3 3 7 2 -3 -1 2 -12 -4
-4 -7 2 -12 15 -1 6 -2 -2 5 0 1 4 -7 2 4 -5 -9 -7 16 -1 8 -1 8 2 -10 -2 -6 -3 0 -3 3 -3 -6 0 3 0 -1 9 3
-
PROPERTIES
INTEGRAL = 1
MODULAR = 2
-
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