The Lattice 2.Alt7SS3
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 13:14:42 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
GRAM (floating point or integer Gram matrix)
MINIMAL_NORM
GROUP_ORDER
GROUP_GENERATORS
PROPERTIES
REFERENCES
NOTES
URL (links to other sites for this lattice)
LAST_LINE
-
NAME
2.Alt7SS3
-
DIMENSION
40
-
GRAM (floating point or integer Gram matrix)
40 0
16
4 16
3 3 16
3 4 2 16
7 4 5 3 16
-3 -3 0 -5 1 16
-3 -1 8 -1 -1 0 16
2 1 6 -1 1 -1 5 16
2 5 -2 3 3 -3 -2 3 16
-2 1 4 -1 -5 5 2 1 -1 16
-2 1 -2 -3 -4 5 2 -4 -2 7 16
0 0 3 0 1 3 4 5 -2 0 2 16
-3 -4 0 5 0 -3 3 -3 -4 -2 2 -1 16
2 -1 4 2 3 0 4 2 2 -3 -4 0 1 16
2 -2 1 1 -4 2 -4 0 -1 3 0 -2 -1 -2 16
0 3 1 7 2 -3 1 0 5 0 -4 0 3 3 4 16
1 -3 -3 -2 2 2 0 0 1 -1 3 4 1 2 -3 0 16
4 -2 5 0 2 5 0 4 0 0 -2 4 -5 6 5 -1 2 16
3 2 3 2 3 3 -3 0 -1 1 -1 5 -8 1 2 0 1 7 16
-1 1 4 -3 0 -1 6 7 1 1 -3 4 -3 3 1 2 -1 0 0 16
0 0 0 -4 -1 3 -1 3 -3 4 2 1 -3 2 4 1 6 2 0 4 16
2 -1 3 -1 2 3 1 2 3 2 -2 2 1 5 2 4 2 5 -2 0 3 16
-2 -2 -1 -4 -2 0 2 -1 -2 0 2 -3 3 -3 5 1 -3 -5 -6 1 2 3 16
0 4 -4 -3 -2 0 0 -1 0 -2 6 1 -5 -2 -1 -4 1 -3 -2 -2 3 -4 1 16
2 4 3 3 2 -3 -2 1 3 -2 -2 0 -2 2 0 -1 1 3 1 -1 2 1 -4 1 16
0 -1 -1 0 2 -1 0 0 2 -3 -4 -1 0 -2 -4 -2 3 -1 -3 -3 0 0 -1 -3 5 16
-1 -1 4 -2 -3 4 5 7 -3 5 1 4 1 2 4 -2 4 4 -2 4 7 6 4 1 0 -1 16
-3 -1 2 3 2 3 1 0 -4 4 -3 4 1 0 0 4 1 3 7 -1 0 2 -2 -7 -2 0 2 16
2 -2 2 4 -1 1 0 4 2 3 -3 1 -4 5 1 1 3 4 5 5 2 -1 -5 -2 1 -2 4 0 16
-1 2 0 1 2 -2 -1 -5 1 -2 -3 -3 1 3 -1 5 4 -3 -2 -2 2 -1 1 -1 2 7 -1 1 1 16
0 -1 -1 3 3 -4 -2 2 1 -3 -1 1 2 -3 0 0 5 -3 -1 3 4 -4 -2 1 3 4 1 0 2 3 16
-1 -4 -2 -3 4 2 -1 -2 -4 -3 2 2 5 0 -5 -3 5 0 -1 -2 2 1 2 -3 -2 -1 0 1 -4 -2 1 16
-1 -1 3 2 1 -3 3 3 -1 -4 -4 4 2 2 -5 1 4 1 -1 2 2 -1 -3 -2 4 4 2 1 4 5 7 2 16
0 0 0 -3 1 2 1 -2 1 1 4 1 -3 -2 -1 -5 4 0 0 0 2 1 1 3 4 3 3 -1 0 3 6 -1 3 16
-3 -3 -1 1 0 -1 1 -1 -1 -1 -3 5 1 2 -5 0 7 -1 1 0 1 -2 -2 0 -1 1 3 5 3 5 5 5 8 3 16
6 4 1 -2 2 -3 -4 4 1 -4 -2 2 -3 1 3 0 4 1 3 2 4 0 3 3 3 0 4 -3 3 3 4 1 1 0 1 16
-7 -1 -2 1 -4 -3 1 -2 -1 3 1 0 6 -3 4 5 0 -4 -3 -1 1 3 8 -1 -5 -2 5 5 -4 2 -1 1 -3 -4 2 0 16
-2 -3 2 -4 -2 3 7 1 -2 1 2 0 0 6 0 0 4 2 -3 2 5 4 3 3 0 -1 6 0 2 1 -2 1 1 3 1 0 0 16
0 -5 0 -2 2 1 2 -1 1 -2 1 1 5 3 -1 1 2 -1 -1 -1 -2 1 7 -4 -4 -2 0 2 -2 1 0 8 3 1 7 2 2 2 16
-2 3 0 0 -1 2 2 0 -1 1 4 4 1 1 0 0 4 -1 1 3 4 0 -1 4 0 -7 4 0 2 -3 0 1 2 2 2 0 1 8 0 16
-
MINIMAL_NORM
16
-
GROUP_ORDER
2^5 * 3^3 * 5 * 7
-
GROUP_GENERATORS
3
40
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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
-26 -61 -46 -31 40 -53 46 -12 112 65 28 -6 95 17 38 -24 -49 23 67 -18 -11 9 126 7 -30 -6 14 48 -47 33 -14 29 31 -47 88 54 -158 -24 -167 41
5 5 5 2 -5 7 -5 2 -8 -6 -3 0 -6 -1 -4 2 4 -2 -5 2 1 -2 -10 0 3 0 -3 -4 4 -3 1 -2 -2 5 -6 -5 16 3 12 -4
0 1 0 0 1 0 0 0 -3 -2 2 0 -4 1 1 1 0 -1 -3 -1 0 0 -3 -2 0 1 0 -1 1 -2 0 -1 0 1 0 0 3 0 2 0
-8 -25 -18 -15 14 -20 18 -4 48 28 10 -3 43 8 14 -9 -21 11 30 -7 -6 3 55 5 -12 -2 4 20 -19 14 -4 14 13 -19 37 21 -64 -10 -72 18
-17 -48 -35 -26 27 -39 34 -9 90 53 18 -5 81 12 25 -18 -39 21 57 -12 -9 6 102 9 -22 -5 10 37 -37 28 -9 24 23 -37 68 40 -123 -18 -132 32
27 65 49 35 -40 57 -48 13 -121 -72 -27 6 -107 -17 -37 25 53 -28 -76 18 13 -10 -139 -11 32 6 -16 -51 50 -38 12 -32 -31 52 -93 -55 172 26 179 -45
4 1 2 0 -3 5 -2 2 0 -1 -2 -1 3 -1 -2 0 0 0 1 2 1 -1 -2 2 1 0 -4 -1 1 -1 -1 0 1 3 0 -1 7 2 1 -2
-24 -62 -46 -33 38 -52 46 -11 115 67 27 -7 101 17 37 -24 -51 25 71 -17 -12 9 130 10 -30 -5 12 49 -47 34 -13 31 31 -47 90 54 -159 -24 -171 42
-8 -24 -17 -13 13 -19 17 -4 45 25 10 -3 40 6 13 -9 -20 10 28 -6 -4 3 50 4 -11 -2 5 19 -18 14 -5 12 11 -18 35 20 -61 -9 -66 16
-1 -10 -6 -6 2 -6 6 -1 20 11 2 -2 20 2 3 -3 -8 6 14 -1 -2 1 23 4 -4 -1 1 8 -8 7 -1 6 4 -7 14 7 -25 -4 -28 7
6 6 7 3 -7 9 -6 2 -11 -8 -4 0 -8 -2 -6 3 5 -2 -7 3 2 -2 -14 0 4 0 -4 -5 5 -4 1 -3 -3 7 -9 -6 21 3 17 -5
10 21 16 10 -14 19 -16 5 -38 -23 -8 1 -32 -5 -12 9 16 -8 -23 7 3 -3 -43 -2 10 3 -6 -16 16 -12 4 -9 -10 17 -28 -18 55 8 55 -14
2 9 6 7 -3 7 -6 1 -20 -12 -2 1 -21 -3 -4 3 8 -6 -14 2 2 -1 -24 -4 5 0 0 -8 7 -6 1 -6 -4 7 -15 -7 26 4 29 -7
3 9 6 4 -5 7 -7 1 -15 -9 -4 2 -13 -2 -5 3 7 -4 -9 2 2 -2 -17 -2 4 0 -1 -7 6 -5 2 -5 -4 6 -12 -8 21 5 23 -7
5 21 12 11 -8 15 -12 3 -38 -22 -6 3 -36 -4 -7 6 16 -11 -25 3 4 -2 -44 -7 9 1 -4 -16 15 -13 3 -11 -8 15 -27 -15 51 9 54 -15
-1 -12 -7 -8 3 -7 8 -1 24 14 2 -2 24 3 4 -4 -10 7 16 -2 -3 1 28 5 -5 -1 0 10 -9 8 -1 8 5 -8 17 9 -29 -5 -35 9
1 1 1 0 -1 1 -1 -1 -1 -1 -2 1 -1 -1 -2 0 1 0 -1 0 1 -1 -2 0 1 -1 1 -1 1 0 1 -1 -1 0 -3 -2 3 1 4 -1
-3 -9 -7 -4 5 -7 7 -2 16 10 2 0 14 2 4 -4 -7 4 10 -3 -1 1 18 1 -4 -2 2 6 -7 6 -1 4 4 -7 11 7 -22 -3 -23 6
2 3 2 3 -1 5 -2 2 -6 -5 0 0 -6 -1 -1 0 2 -3 -5 1 2 -1 -9 -3 2 -1 -3 -3 2 -3 -1 -3 0 4 -3 -1 12 3 8 -4
-11 -32 -23 -18 18 -25 23 -6 61 35 12 -3 54 9 17 -12 -26 13 38 -9 -6 3 69 5 -15 -4 7 25 -25 18 -6 16 16 -24 46 27 -82 -12 -90 21
-5 -13 -9 -7 8 -11 9 -3 25 13 6 -1 21 3 7 -5 -11 5 15 -4 -2 1 27 1 -6 -2 4 10 -10 7 -3 6 6 -10 19 11 -33 -4 -36 8
9 21 17 11 -14 19 -17 4 -38 -24 -8 2 -34 -5 -13 9 17 -9 -24 6 4 -4 -43 -4 10 2 -5 -16 16 -13 4 -10 -10 17 -29 -18 55 9 56 -15
-2 -2 -1 -1 1 -3 1 -1 3 3 0 0 2 1 1 0 0 1 2 -1 -1 0 5 1 -1 0 2 2 -2 1 0 1 1 -2 1 1 -7 -2 -4 2
-20 -56 -40 -30 32 -46 39 -10 104 61 22 -6 93 15 30 -21 -45 24 65 -14 -11 7 118 11 -27 -5 12 44 -43 32 -11 28 27 -42 79 47 -143 -22 -153 38
7 10 10 4 -9 11 -9 3 -18 -11 -5 0 -14 -1 -7 5 8 -4 -11 4 1 -2 -20 1 5 3 -5 -7 9 -7 2 -3 -5 10 -14 -9 29 3 26 -6
-5 -21 -13 -11 10 -14 13 -3 39 21 8 -3 35 5 9 -7 -17 9 24 -4 -3 1 43 4 -9 -2 3 16 -16 11 -5 10 10 -14 30 17 -49 -7 -57 13
16 42 30 22 -24 35 -29 7 -77 -46 -17 5 -69 -11 -23 15 33 -18 -49 10 9 -6 -89 -9 20 3 -9 -33 32 -24 8 -21 -20 32 -59 -35 108 17 114 -29
-2 -12 -8 -6 5 -7 8 -1 22 13 4 -2 21 3 5 -5 -10 6 14 -2 -2 1 25 3 -5 -1 0 9 -9 7 -2 6 6 -8 17 10 -27 -4 -33 8
3 9 7 5 -5 7 -6 1 -17 -10 -3 1 -17 -1 -4 3 8 -5 -12 2 1 -1 -19 -2 4 1 -2 -6 7 -6 2 -4 -4 7 -13 -7 23 3 24 -6
4 -1 0 -3 -3 3 0 2 5 3 -2 -1 9 1 -2 0 -2 3 5 1 -1 -1 7 3 0 0 -4 1 -1 1 1 2 1 1 4 0 -1 0 -8 1
-13 -41 -29 -23 22 -32 29 -7 77 44 16 -5 70 10 20 -14 -34 19 49 -10 -8 5 88 8 -19 -4 8 32 -31 24 -7 21 19 -31 59 34 -104 -16 -114 28
-3 -11 -9 -6 7 -8 9 -2 21 13 4 -1 19 3 6 -5 -9 5 13 -3 -2 1 24 1 -5 -2 1 8 -9 6 -2 5 6 -8 17 10 -27 -4 -32 7
-3 -16 -10 -10 6 -11 10 -2 32 18 4 -2 31 4 6 -6 -13 9 21 -3 -3 1 37 5 -7 -2 1 13 -12 10 -2 9 7 -11 23 12 -40 -6 -46 11
-9 -26 -18 -14 15 -21 19 -5 47 27 11 -3 41 7 14 -9 -21 11 28 -7 -5 3 54 4 -12 -2 5 21 -19 14 -5 13 12 -19 37 22 -65 -11 -71 18
-8 -30 -20 -16 14 -21 20 -4 57 33 10 -4 53 8 14 -11 -24 14 36 -6 -6 3 65 8 -14 -3 3 24 -23 17 -6 16 15 -21 43 25 -74 -11 -84 20
9 26 20 14 -15 21 -19 4 -49 -30 -9 3 -46 -6 -14 11 21 -12 -32 6 5 -4 -56 -6 12 3 -4 -20 20 -16 5 -13 -13 20 -37 -22 67 10 72 -18
16 42 30 23 -24 36 -30 8 -78 -46 -17 4 -69 -12 -24 15 34 -18 -48 11 9 -6 -89 -9 21 2 -9 -34 31 -24 8 -22 -20 32 -59 -35 109 18 115 -30
-5 -20 -14 -11 10 -14 14 -3 38 21 8 -3 35 5 10 -7 -17 9 24 -4 -4 2 43 4 -9 -2 2 16 -15 11 -4 11 10 -14 30 17 -49 -7 -57 13
-18 -42 -33 -21 28 -36 32 -8 77 46 18 -4 67 10 25 -17 -34 17 48 -12 -7 6 87 4 -20 -6 10 31 -34 24 -9 19 21 -33 61 37 -109 -15 -115 27
40
-7 -15 -11 -7 10 -13 11 -4 26 15 7 -1 21 3 8 -5 -12 6 15 -5 -2 2 29 1 -7 -2 5 11 -11 8 -3 6 7 -12 20 13 -38 -6 -38 10
7 14 11 7 -10 13 -10 3 -25 -15 -7 1 -21 -4 -9 5 11 -5 -15 4 3 -2 -29 -1 7 1 -4 -11 11 -7 3 -6 -7 11 -20 -13 37 5 38 -9
4 7 6 3 -5 7 -6 2 -14 -9 -2 0 -12 -2 -5 4 5 -3 -8 2 1 -1 -16 -1 4 1 -1 -6 6 -4 2 -3 -4 6 -10 -7 20 3 20 -5
-15 -40 -29 -23 23 -34 29 -8 75 44 16 -4 67 11 22 -14 -33 18 47 -11 -8 5 86 8 -19 -3 9 32 -30 23 -7 21 19 -31 57 33 -104 -17 -111 28
-8 -24 -17 -13 14 -19 17 -4 44 25 11 -3 39 6 13 -8 -20 10 28 -6 -5 3 50 4 -11 -2 5 18 -18 13 -5 12 12 -18 35 20 -60 -9 -66 16
9 13 10 5 -11 15 -10 4 -20 -12 -8 1 -14 -3 -9 4 10 -4 -11 5 2 -3 -23 0 7 0 -7 -10 9 -7 3 -5 -5 11 -16 -11 35 7 30 -10
10 33 23 19 -17 25 -23 5 -64 -37 -12 4 -59 -10 -18 12 27 -15 -40 8 7 -3 -73 -8 16 2 -4 -27 25 -18 7 -18 -17 24 -49 -28 84 13 95 -23
23 60 44 32 -36 50 -44 11 -113 -65 -25 6 -100 -16 -35 24 49 -24 -70 16 11 -8 -127 -10 29 6 -12 -48 46 -34 13 -30 -30 46 -87 -52 155 23 167 -40
-20 -50 -37 -26 31 -43 37 -10 92 53 22 -5 79 13 29 -19 -40 20 56 -14 -9 7 104 7 -24 -5 12 39 -38 28 -10 24 24 -39 71 42 -129 -20 -136 34
13 26 21 13 -19 25 -20 6 -47 -29 -12 2 -40 -7 -17 10 21 -10 -29 8 5 -4 -54 -3 13 2 -8 -20 20 -14 6 -12 -13 21 -37 -23 70 11 70 -18
6 15 11 8 -9 13 -10 2 -26 -16 -7 2 -23 -5 -9 4 12 -6 -17 4 4 -2 -31 -3 7 0 -4 -11 11 -8 3 -8 -7 11 -21 -12 38 7 40 -11
15 39 28 20 -23 32 -28 7 -72 -42 -15 4 -64 -10 -22 15 31 -16 -45 10 7 -5 -81 -7 19 4 -8 -30 30 -22 8 -19 -19 29 -55 -33 99 15 106 -26
-3 -4 -3 -2 3 -5 3 -2 7 5 1 0 6 0 2 -1 -3 2 5 -1 -1 1 8 1 -2 0 3 3 -3 3 0 2 1 -4 4 3 -12 -2 -9 3
-7 -14 -11 -7 11 -13 11 -3 24 14 8 -1 18 5 11 -5 -11 3 13 -5 -3 2 26 0 -7 -1 4 11 -10 6 -4 7 8 -10 19 13 -35 -6 -37 9
-12 -31 -23 -17 18 -26 22 -6 59 35 11 -3 53 8 17 -12 -25 14 37 -8 -6 4 67 7 -15 -3 7 25 -24 18 -6 16 15 -24 44 26 -81 -12 -86 21
-8 -19 -13 -10 11 -17 13 -4 34 20 8 -2 29 5 10 -6 -15 8 21 -5 -4 3 39 4 -9 -1 6 15 -14 11 -3 10 8 -15 25 15 -49 -9 -50 14
8 28 19 16 -14 21 -19 4 -53 -30 -10 4 -50 -7 -14 10 23 -13 -34 6 5 -3 -60 -7 13 2 -4 -22 21 -16 6 -15 -13 20 -41 -23 70 11 78 -19
-15 -39 -30 -22 24 -33 29 -7 74 44 16 -4 66 11 23 -15 -32 17 46 -11 -8 5 84 7 -19 -4 8 31 -30 22 -8 20 20 -30 57 34 -102 -15 -110 26
-6 -23 -16 -14 12 -17 16 -3 44 25 10 -3 40 8 13 -8 -20 10 27 -6 -5 2 50 5 -11 -1 2 19 -17 12 -5 13 12 -16 35 20 -57 -9 -67 16
4 17 11 10 -7 12 -11 3 -34 -19 -5 2 -33 -4 -7 6 14 -9 -22 3 3 -1 -38 -5 8 2 -2 -14 13 -10 3 -9 -8 12 -25 -14 43 6 49 -11
18 53 37 29 -29 43 -37 10 -99 -57 -21 6 -89 -14 -28 19 43 -23 -62 13 10 -6 -112 -11 25 4 -11 -42 40 -30 10 -27 -25 40 -75 -44 135 21 145 -36
1 2 2 1 -2 2 -2 1 -3 -2 -1 0 -2 -1 -1 1 2 -1 -2 1 0 0 -4 1 1 0 -1 -1 2 -1 0 0 -1 2 -3 -2 5 1 5 -2
13 35 25 20 -20 30 -25 7 -65 -39 -14 3 -57 -11 -20 12 28 -15 -40 10 8 -4 -75 -7 17 2 -8 -28 26 -20 6 -19 -17 27 -49 -29 91 15 97 -25
15 47 33 27 -25 37 -33 7 -88 -51 -19 6 -80 -13 -25 16 39 -21 -56 12 10 -6 -101 -10 22 3 -8 -37 35 -27 8 -25 -22 35 -68 -39 119 19 131 -33
-33 -91 -67 -50 53 -75 66 -16 171 100 37 -10 153 25 51 -34 -75 39 107 -24 -18 12 195 17 -44 -8 18 72 -69 52 -18 47 45 -69 132 77 -235 -36 -254 62
-10 -26 -21 -14 16 -22 20 -4 48 29 11 -3 44 6 14 -10 -22 12 32 -7 -5 5 56 4 -12 -3 5 19 -20 16 -4 12 12 -21 39 22 -68 -10 -72 18
28 80 56 43 -45 65 -56 14 -148 -85 -33 9 -132 -21 -43 29 65 -34 -92 20 15 -10 -168 -15 38 6 -16 -63 60 -45 16 -40 -38 60 -114 -67 203 32 219 -55
-4 -20 -13 -12 8 -14 13 -2 38 22 7 -3 36 6 9 -6 -17 10 25 -4 -5 2 44 6 -9 -1 2 16 -15 12 -3 12 9 -14 29 16 -49 -8 -57 14
6 17 12 8 -9 14 -12 3 -32 -18 -6 2 -30 -2 -8 7 14 -8 -21 3 2 -3 -35 -4 8 2 -4 -13 13 -11 4 -8 -7 13 -24 -14 44 6 45 -11
-1 0 -1 0 1 -1 1 0 -1 0 1 0 -2 1 1 0 0 -1 0 -1 -1 1 0 -1 0 0 1 0 0 0 1 0 0 -1 0 0 -1 -1 0 1
-15 -29 -23 -14 21 -28 23 -7 50 31 14 -2 40 8 18 -10 -23 11 30 -10 -6 5 59 2 -14 -2 10 22 -22 16 -5 13 13 -24 40 25 -77 -13 -76 21
7 23 15 13 -11 18 -15 4 -43 -25 -8 3 -39 -7 -12 8 18 -10 -27 5 5 -3 -49 -7 11 1 -4 -19 17 -13 4 -13 -11 17 -32 -18 58 10 63 -16
-1 5 2 2 0 1 -2 0 -11 -5 0 1 -12 0 -1 3 4 -3 -7 -1 0 0 -10 -3 2 1 2 -4 4 -3 2 -3 -3 2 -7 -4 9 0 14 -2
-15 -37 -27 -20 23 -32 28 -8 69 39 17 -3 58 11 22 -14 -30 14 41 -12 -7 5 79 4 -18 -4 9 30 -28 20 -7 18 18 -29 54 32 -97 -15 -103 25
1 12 7 8 -3 7 -7 1 -26 -15 -1 2 -28 -2 -4 5 10 -8 -18 1 2 -1 -29 -7 6 1 1 -10 9 -8 2 -8 -6 8 -18 -9 30 4 36 -8
16 46 32 26 -25 38 -32 8 -87 -50 -18 5 -79 -12 -25 17 37 -20 -55 11 9 -6 -99 -10 22 4 -9 -37 35 -27 9 -24 -22 35 -66 -38 119 18 128 -31
19 53 38 29 -31 43 -38 10 -98 -57 -22 5 -86 -15 -29 19 43 -22 -60 15 10 -6 -112 -8 25 5 -11 -41 40 -29 10 -26 -26 40 -76 -45 135 21 146 -36
15 44 31 24 -24 35 -31 7 -82 -48 -18 6 -75 -12 -24 16 36 -20 -52 10 9 -6 -94 -10 21 2 -7 -35 33 -25 9 -23 -21 33 -64 -37 112 18 122 -31
-10 -22 -17 -10 16 -19 17 -5 38 21 12 -2 30 5 13 -8 -18 7 22 -7 -3 3 42 -1 -10 -3 7 16 -17 11 -5 8 10 -17 31 20 -55 -8 -57 14
23 59 44 30 -36 49 -43 10 -107 -63 -26 7 -95 -15 -33 22 48 -25 -67 15 11 -9 -122 -9 28 5 -12 -45 45 -33 12 -28 -28 45 -85 -51 150 23 160 -40
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
-15 -36 -26 -17 22 -31 25 -7 63 38 15 -4 54 9 19 -12 -28 15 39 -9 -7 5 72 6 -17 -2 10 27 -27 20 -7 17 16 -27 48 30 -91 -15 -93 25
-2 -6 -3 -3 3 -5 3 -1 9 6 2 -1 8 2 3 -1 -4 2 6 -1 -2 1 11 2 -3 1 2 4 -4 3 -1 3 2 -4 7 4 -14 -3 -14 5
1 -3 0 -3 -1 -1 0 0 7 4 0 -1 7 3 1 0 -2 2 4 0 -2 -1 9 3 -2 1 -1 4 -2 1 0 4 2 -1 4 2 -7 -2 -11 3
-1 -10 -5 -7 2 -7 5 -1 20 12 2 -2 21 3 3 -2 -8 6 14 -1 -3 1 24 6 -5 1 1 9 -7 6 -1 7 4 -7 14 7 -26 -5 -29 8
2 2 1 0 -3 3 -1 1 -1 0 -3 0 2 -1 -2 0 1 1 1 1 0 0 0 2 1 0 -2 -1 1 0 1 0 -1 1 -1 -2 3 1 2 -1
1 4 3 2 -2 3 -3 1 -9 -4 -2 0 -8 -1 -2 2 4 -2 -5 1 0 0 -10 0 2 1 0 -4 3 -2 1 -2 -2 3 -7 -4 11 1 13 -2
-2 -6 -4 -3 4 -5 4 -1 10 6 3 -1 9 2 4 -2 -5 2 6 -1 -1 1 11 2 -3 1 1 5 -4 3 -2 3 3 -4 8 5 -14 -3 -15 5
-2 -3 -2 -1 2 -4 2 -2 4 3 1 0 2 0 0 0 -2 2 2 -1 0 0 5 0 -1 0 3 2 -2 2 0 1 0 -3 2 2 -8 -2 -5 3
-4 -6 -6 -3 6 -6 6 -2 11 7 3 0 8 2 5 -3 -5 2 6 -3 -1 1 13 -1 -3 -1 2 4 -5 3 -1 2 3 -6 10 6 -17 -2 -17 4
-3 -4 -6 -2 5 -4 6 -1 8 5 2 0 6 1 4 -3 -4 1 5 -3 0 1 9 -2 -2 -2 1 2 -4 2 -1 1 3 -4 8 5 -12 -1 -13 2
5 8 7 3 -7 8 -7 3 -15 -9 -4 0 -11 -2 -6 4 6 -2 -8 3 1 -1 -16 1 4 2 -3 -6 7 -4 2 -3 -5 7 -11 -8 22 2 22 -4
14 32 24 15 -21 28 -24 7 -57 -33 -15 3 -48 -7 -18 12 26 -13 -34 9 5 -5 -64 -3 15 3 -9 -24 24 -18 7 -14 -14 25 -45 -28 82 13 84 -22
-2 -11 -8 -7 4 -8 7 -1 22 15 1 -1 23 3 4 -4 -9 7 16 -2 -3 1 26 5 -5 -1 1 8 -9 8 -1 7 5 -8 15 8 -28 -4 -32 8
15 47 33 27 -25 37 -33 7 -88 -51 -19 6 -80 -13 -24 16 39 -21 -56 12 10 -6 -101 -10 22 3 -8 -37 35 -27 8 -25 -22 35 -68 -39 119 19 131 -33
7 15 12 7 -11 13 -13 3 -26 -14 -9 1 -20 -4 -10 6 13 -4 -15 6 2 -3 -29 1 7 2 -4 -11 11 -8 3 -6 -7 12 -22 -14 38 6 40 -10
10 22 16 10 -15 19 -15 5 -38 -22 -11 2 -31 -6 -13 8 17 -7 -23 6 4 -3 -43 -1 10 2 -7 -16 17 -11 5 -9 -11 17 -30 -19 55 8 57 -14
14 33 24 18 -21 29 -24 7 -61 -35 -15 3 -52 -9 -19 12 27 -13 -37 10 6 -4 -69 -4 16 3 -9 -26 25 -18 6 -16 -16 26 -47 -28 86 13 90 -22
5 18 13 10 -10 13 -13 2 -34 -19 -8 3 -31 -5 -10 7 15 -7 -22 4 3 -2 -38 -3 8 2 -2 -14 14 -10 4 -9 -10 13 -27 -15 44 6 51 -11
-3 -2 -1 0 3 -4 1 -1 1 1 2 0 -1 0 2 0 -1 0 0 -1 0 1 1 0 -1 1 3 1 -1 1 -1 0 0 -2 1 1 -5 -2 -1 2
3 7 4 3 -4 6 -4 2 -10 -6 -4 1 -7 -2 -3 1 5 -2 -6 2 2 -1 -12 0 3 0 -3 -5 5 -3 1 -3 -3 5 -8 -6 16 3 16 -5
13 26 20 12 -19 24 -20 6 -46 -26 -14 2 -36 -7 -17 10 21 -8 -26 9 4 -4 -51 0 13 3 -8 -20 20 -13 6 -11 -13 20 -37 -24 67 10 69 -17
-9 -16 -14 -8 13 -16 13 -4 29 18 8 -1 24 4 12 -7 -13 5 18 -5 -3 3 32 1 -8 -2 6 12 -13 9 -4 7 9 -14 23 14 -44 -6 -43 10
-21 -55 -41 -28 34 -45 41 -10 101 58 24 -6 88 14 31 -21 -45 22 62 -15 -9 7 113 7 -26 -6 12 42 -42 30 -12 26 27 -41 79 48 -139 -21 -150 36
3 4 4 3 -4 5 -4 1 -8 -6 -2 0 -7 -2 -5 2 3 -1 -5 2 2 -1 -10 -1 2 0 -1 -4 3 -2 1 -3 -3 4 -7 -4 13 2 13 -3
0 4 2 3 -1 2 -2 1 -9 -5 0 0 -9 -2 -2 1 3 -2 -6 1 1 1 -10 -2 2 0 0 -3 3 -1 1 -3 -3 2 -6 -3 9 1 13 -2
-11 -29 -21 -15 17 -24 21 -5 53 32 11 -3 47 8 17 -11 -23 12 33 -7 -6 4 60 7 -14 -2 6 23 -22 17 -6 15 14 -22 40 24 -74 -12 -78 20
17 40 31 20 -27 35 -31 8 -73 -42 -19 4 -62 -10 -24 16 33 -15 -45 12 6 -6 -82 -3 19 5 -10 -30 31 -22 9 -18 -20 31 -58 -35 103 15 109 -26
-23 -59 -43 -31 36 -50 43 -11 110 64 25 -6 96 16 35 -23 -48 24 67 -16 -11 8 124 10 -29 -5 12 47 -45 33 -13 30 29 -45 85 51 -152 -23 -163 40
-22 -56 -41 -29 33 -48 40 -10 103 61 23 -6 91 14 31 -21 -45 24 64 -14 -11 8 117 10 -27 -5 13 44 -43 33 -11 28 26 -43 79 47 -145 -22 -152 38
6 18 14 10 -10 14 -13 3 -34 -21 -6 2 -32 -4 -9 7 15 -9 -23 4 4 -3 -39 -4 8 2 -3 -13 14 -11 3 -9 -9 14 -26 -15 46 6 50 -12
1 -3 -2 -5 -1 -2 2 0 10 6 -1 0 12 2 1 -1 -3 3 8 -1 -2 0 13 4 -2 0 -1 4 -2 3 1 4 2 -3 6 1 -11 -2 -14 3
-8 -27 -18 -15 14 -21 18 -3 50 28 12 -4 45 8 15 -9 -22 11 31 -6 -6 3 57 6 -13 -1 4 22 -20 15 -6 15 13 -19 39 22 -67 -11 -75 19
-9 -21 -16 -10 13 -18 16 -4 38 22 9 -2 33 4 11 -8 -17 9 24 -6 -3 3 43 2 -10 -3 6 15 -17 13 -4 9 9 -17 30 18 -55 -8 -56 14
-10 -31 -21 -18 16 -25 21 -5 58 34 12 -3 52 9 16 -10 -25 14 36 -8 -7 3 67 7 -15 -2 6 25 -23 18 -5 17 14 -23 44 25 -79 -13 -86 22
-15 -30 -24 -14 22 -29 23 -7 53 32 14 -2 44 7 19 -12 -24 11 32 -9 -5 5 59 3 -15 -3 10 23 -23 17 -7 13 14 -24 41 26 -79 -12 -78 20
4 15 11 8 -8 11 -11 2 -29 -16 -6 2 -27 -3 -7 6 13 -7 -19 4 2 -2 -33 -2 7 2 -2 -11 12 -9 3 -7 -7 11 -23 -13 38 5 43 -10
-9 -27 -20 -15 15 -21 20 -4 52 31 9 -3 48 7 15 -11 -22 12 33 -7 -5 3 58 6 -13 -3 4 21 -21 16 -6 14 14 -20 39 23 -69 -10 -76 18
1 5 2 1 -2 2 -3 0 -8 -3 -3 2 -7 -1 -2 2 4 -2 -4 0 0 -1 -8 -1 2 0 1 -4 3 -2 2 -2 -2 2 -7 -5 9 2 12 -3
6 11 10 5 -9 11 -9 3 -19 -12 -6 1 -16 -2 -7 5 9 -4 -12 3 2 -3 -22 0 5 2 -4 -8 9 -7 2 -4 -5 10 -16 -10 30 4 29 -7
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PROPERTIES
INTEGRAL = 1
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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