The Lattice Uni64
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 Oct 6 11:04:40 CEST 2017
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIM
DET
MINIMUM
GROUP_ORDER
GROUP_NAME
GRAM
GROUP_GENERATORS
UNIMODULAR
REFERENCES
LAST_LINE
-
NAME
Uni64
-
DIM
64
-
DET
1
-
MINIMUM
6
-
GROUP_ORDER
119040
-
GROUP_NAME
2^2.L2(31).2
-
GRAM
64 0
924
889 1434
756 1086 1086
708 1080 907 1056
798 1074 924 990 1206
900 1218 984 1092 1135 1560
744 1074 858 972 1062 1110 1146
750 1122 894 756 762 936 721 1128
768 876 756 708 882 966 810 750 912
816 1260 936 930 900 1152 954 936 685 1374
720 1002 804 750 720 774 696 810 594 978 984
864 1314 1020 966 1062 1284 1092 1122 960 1218 895 1512
654 828 834 828 780 960 738 738 624 732 702 798 1008
888 1230 1002 996 1026 1164 1038 996 882 1032 768 1242 751 1326
726 876 840 822 720 918 732 726 666 822 708 816 696 816 1020
774 924 666 732 672 870 744 738 600 882 696 930 588 960 607 942
750 966 744 792 960 960 942 690 792 870 654 936 600 972 660 672 996
912 1212 1002 1092 1020 1230 954 954 780 1068 906 1104 954 1074 888 900 751 1338
744 1056 936 792 930 936 912 882 822 936 768 1182 660 1044 768 774 864 822 1206
816 1044 774 798 882 1182 828 798 822 1020 714 1086 624 882 690 738 720 1014 751 1128
816 996 750 804 918 924 840 744 828 756 762 894 612 906 654 744 804 924 810 828 1020
918 1140 1062 864 942 1116 870 1026 858 1038 804 1230 840 1092 750 882 714 1128 1002 1020 817 1362
858 1020 786 948 984 1116 960 780 828 978 858 972 822 858 912 696 876 1038 756 906 870 786 1218
738 984 822 774 804 1146 738 852 678 996 714 996 768 972 666 786 762 924 786 852 696 948 751 1116
726 1062 942 942 1044 1038 960 798 822 990 768 1068 654 1008 858 624 900 906 912 834 774 882 972 792 1194
738 864 678 678 636 882 666 756 648 900 672 972 630 858 642 786 624 840 738 786 588 906 744 732 685 882
762 996 828 888 1026 1050 1050 756 846 954 696 1104 714 978 732 714 924 870 924 834 768 912 984 750 1032 756 1122
876 1026 876 768 780 1014 702 912 744 936 840 1080 696 1002 732 882 618 1068 852 930 840 1110 756 900 756 816 685 1164
708 1014 918 846 882 846 888 744 660 858 720 888 726 972 660 702 804 876 864 630 750 882 708 726 798 594 798 708 936
900 1038 876 930 966 1266 924 864 852 1050 750 1212 750 1122 924 924 840 1080 984 1002 810 1068 984 1002 1008 930 978 1056 721 1338
450 738 672 684 672 804 564 618 540 660 618 786 648 636 594 522 480 744 750 600 594 696 624 666 654 522 588 666 522 762 786
600 762 570 624 624 840 606 702 612 648 438 858 450 816 636 648 558 738 702 678 588 732 630 630 630 624 624 702 474 882 505 720
18 32 9 16 6 34 6 34 6 34 6 34 6 34 6 34 6 34 6 34 6 34 6 34 6 34 6 34 6 34 6 34 6
108 192 54 96 36 204 36 204 36 204 36 204 36 204 36 204 36 204 36 204 36 204 36 204 36 204 36 204 36 204 36 204 35 210
30 30 27 13 34 6 19 26 19 26 31 24 6 34 2 23 32 18 27 13 30 30 13 27 33 12 24 31 32 18 5 5 0 0 6
180 180 162 78 204 36 114 156 114 156 186 144 36 204 12 138 192 108 162 78 180 180 78 162 198 72 144 186 192 108 30 30 0 0 35 210
15 15 2 23 30 30 29 1 14 21 14 21 26 19 1 29 32 18 27 13 22 8 25 25 8 22 28 7 19 26 27 13 0 0 0 0 6
90 90 12 138 180 180 174 6 84 126 84 126 156 114 6 174 192 108 162 78 132 48 150 150 48 132 168 42 114 156 162 78 0 0 0 0 35 210
4 11 14 21 8 22 3 17 2 23 22 8 22 8 34 6 9 16 5 5 0 0 30 30 33 12 16 9 1 29 27 13 0 0 0 0 0 0 6
24 66 84 126 48 132 18 102 12 138 132 48 132 48 204 36 54 96 30 30 0 0 180 180 198 72 96 54 6 174 162 78 0 0 0 0 0 0 35 210
28 7 26 19 8 22 16 9 11 4 10 10 30 30 30 30 7 28 17 3 13 27 8 22 3 17 6 34 24 31 9 16 0 0 0 0 0 0 0 0 6
168 42 156 114 48 132 96 54 66 24 60 60 180 180 180 180 42 168 102 18 78 162 48 132 18 102 36 204 144 186 54 96 0 0 0 0 0 0 0 0 35 210
1 29 30 30 26 19 34 6 7 28 2 23 1 29 21 14 21 14 33 12 8 22 4 11 34 6 29 1 32 18 15 15 0 0 0 0 0 0 0 0 0 0 6
6 174 180 180 156 114 204 36 42 168 12 138 6 174 126 84 126 84 198 72 48 132 24 66 204 36 174 6 192 108 90 90 0 0 0 0 0 0 0 0 0 0 35 210
26 19 25 25 20 20 11 4 19 26 27 13 22 8 21 14 6 34 6 34 18 32 28 7 24 31 19 26 14 21 17 3 0 0 0 0 0 0 0 0 0 0 0 0 6
156 114 150 150 120 120 66 24 114 156 162 78 132 48 126 84 36 204 36 204 108 192 168 42 144 186 114 156 84 126 102 18 0 0 0 0 0 0 0 0 0 0 0 0 35 210
10 10 17 3 18 32 3 17 29 1 2 23 10 10 5 5 4 11 24 31 24 31 1 29 11 4 7 28 2 23 32 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6
60 60 102 18 108 192 18 102 174 6 12 138 60 60 30 30 24 66 144 186 144 186 6 174 66 24 42 168 12 138 192 108 0 0 0 0 0 0 0 0 0 0 0 0 0 0 35 210
19 26 4 11 3 17 21 14 6 34 32 18 5 5 13 27 8 22 7 28 27 13 27 13 4 11 14 21 10 10 5 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6
114 156 24 66 18 102 126 84 36 204 192 108 30 30 78 162 48 132 42 168 162 78 162 78 24 66 84 126 60 60 30 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 35 210
4 11 14 21 30 30 33 12 16 9 1 29 27 13 0 0 8 22 3 17 2 23 22 8 22 8 34 6 9 16 5 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6
24 66 84 126 180 180 198 72 96 54 6 174 162 78 0 0 48 132 18 102 12 138 132 48 132 48 204 36 54 96 30 30 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 35 210
24 31 24 31 30 30 25 25 28 7 11 4 31 24 22 8 30 30 3 17 33 12 32 18 17 3 17 3 29 1 4 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6
144 186 144 186 180 180 150 150 168 42 66 24 186 144 132 48 180 180 18 102 198 72 192 108 102 18 102 18 174 6 24 66 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 35 210
12 33 18 32 31 24 26 19 21 14 24 31 7 28 27 13 18 32 26 19 34 6 29 1 28 7 13 27 13 27 25 25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6
72 198 108 192 186 144 156 114 126 84 144 186 42 168 162 78 108 192 156 114 204 36 174 6 168 42 78 162 78 162 150 150 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 35 210
7 28 33 12 10 10 6 34 1 29 31 24 34 6 17 3 2 23 28 7 1 29 9 16 4 11 3 17 23 2 23 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 6
42 168 198 72 60 60 36 204 6 174 186 144 204 36 102 18 12 138 168 42 6 174 54 96 24 66 18 102 138 12 138 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 35 210
8 22 16 9 12 33 22 8 18 32 13 27 8 22 11 4 29 1 14 21 5 5 13 27 21 14 16 9 15 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6
48 132 96 54 72 198 132 48 108 192 78 162 48 132 66 24 174 6 84 126 30 30 78 162 126 84 96 54 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 35 210
8 22 16 9 0 0 12 33 22 8 18 32 13 27 8 22 11 4 29 1 14 21 5 5 13 27 21 14 16 9 15 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6
48 132 96 54 0 0 72 198 132 48 108 192 78 162 48 132 66 24 174 6 84 126 30 30 78 162 126 84 96 54 90 90 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 35 210
33 12 11 4 20 20 20 20 32 18 7 28 3 17 33 12 28 7 31 24 14 21 34 6 25 25 33 12 6 34 1 29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6
198 72 66 24 120 120 120 120 192 108 42 168 18 102 198 72 168 42 186 144 84 126 204 36 150 150 198 72 36 204 6 174 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 35 210
-
GROUP_GENERATORS
7
64 64
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64 64
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UNIMODULAR
1
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REFERENCES
constructed by Ichiro Shimada
http://www.math.sci.hiroshima-u.ac.jp/~shimada/preprints/Extremal64/PaperGQR/GQR.pdf
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe