Groups of order 1440

Factorization and useful forms
The number 1440 has prime factors 2, 3, and 5, and prime factorization:

$$\! 1440 = 2^5 \cdot 3^2 \cdot 5^1 = 32 \cdot 9 \cdot 5$$

Other useful expressions for this number are:

$$1440 = 2(6!) = 2(9^3 - 9)$$

GAP implementation
gap> SmallGroupsInformation(1440);

There are 5958 groups of order 1440. They are sorted by their Frattini factors. 1 has Frattini factor [ 30, 1 ]. 2 has Frattini factor [ 30, 2 ]. 3 has Frattini factor [ 30, 3 ]. 4 has Frattini factor [ 30, 4 ]. 5 has Frattini factor [ 60, 6 ]. 6 has Frattini factor [ 60, 7 ]. 7 - 73 have Frattini factor [ 60, 8 ]. 74 has Frattini factor [ 60, 9 ]. 75 - 115 have Frattini factor [ 60, 10 ]. 116 - 156 have Frattini factor [ 60, 11 ]. 157 - 197 have Frattini factor [ 60, 12 ]. 198 - 216 have Frattini factor [ 60, 13 ]. 217 has Frattini factor [ 90, 5 ]. 218 has Frattini factor [ 90, 6 ]. 219 has Frattini factor [ 90, 7 ]. 220 has Frattini factor [ 90, 8 ]. 221 has Frattini factor [ 90, 9 ]. 222 has Frattini factor [ 90, 10 ]. 223 - 253 have Frattini factor [ 120, 36 ]. 254 - 257 have Frattini factor [ 120, 37 ]. 258 - 261 have Frattini factor [ 120, 38 ]. 262 - 268 have Frattini factor [ 120, 39 ]. 269 - 293 have Frattini factor [ 120, 40 ]. 294 - 318 have Frattini factor [ 120, 41 ]. 319 - 653 have Frattini factor [ 120, 42 ]. 654 - 660 have Frattini factor [ 120, 43 ]. 661 - 746 have Frattini factor [ 120, 44 ]. 747 - 832 have Frattini factor [ 120, 45 ]. 833 - 918 have Frattini factor [ 120, 46 ]. 919 - 942 have Frattini factor [ 120, 47 ]. 943 has Frattini factor [ 180, 20 ]. 944 has Frattini factor [ 180, 21 ]. 945 has Frattini factor [ 180, 22 ]. 946 has Frattini factor [ 180, 23 ]. 947 has Frattini factor [ 180, 24 ]. 948 has Frattini factor [ 180, 25 ]. 949 - 1015 have Frattini factor [ 180, 26 ]. 1016 - 1082 have Frattini factor [ 180, 27 ]. 1083 - 1123 have Frattini factor [ 180, 28 ]. 1124 - 1190 have Frattini factor [ 180, 29 ]. 1191 - 1231 have Frattini factor [ 180, 30 ]. 1232 has Frattini factor [ 180, 31 ]. 1233 - 1273 have Frattini factor [ 180, 32 ]. 1274 - 1314 have Frattini factor [ 180, 33 ]. 1315 - 1355 have Frattini factor [ 180, 34 ]. 1356 - 1396 have Frattini factor [ 180, 35 ]. 1397 - 1437 have Frattini factor [ 180, 36 ]. 1438 - 1456 have Frattini factor [ 180, 37 ]. 1457 - 1459 have Frattini factor [ 240, 192 ]. 1460 - 1462 have Frattini factor [ 240, 193 ]. 1463 - 1477 have Frattini factor [ 240, 194 ]. 1478 - 1508 have Frattini factor [ 240, 195 ]. 1509 - 1519 have Frattini factor [ 240, 196 ]. 1520 - 1530 have Frattini factor [ 240, 197 ]. 1531 - 1541 have Frattini factor [ 240, 198 ]. 1542 has Frattini factor [ 240, 199 ]. 1543 - 1555 have Frattini factor [ 240, 200 ]. 1556 - 1568 have Frattini factor [ 240, 201 ]. 1569 - 1621 have Frattini factor [ 240, 202 ]. 1622 - 1628 have Frattini factor [ 240, 203 ]. 1629 - 1630 have Frattini factor [ 240, 204 ]. 1631 - 1645 have Frattini factor [ 240, 205 ]. 1646 - 1660 have Frattini factor [ 240, 206 ]. 1661 - 1675 have Frattini factor [ 240, 207 ]. 1676 - 1681 have Frattini factor [ 240, 208 ]. 1682 - 1684 have Frattini factor [ 360, 119 ]. 1685 - 1687 have Frattini factor [ 360, 120 ]. 1688 - 1690 have Frattini factor [ 360, 121 ]. 1691 - 1693 have Frattini factor [ 360, 122 ]. 1694 has Frattini factor [ 360, 123 ]. 1695 has Frattini factor [ 360, 124 ]. 1696 has Frattini factor [ 360, 125 ]. 1697 - 1727 have Frattini factor [ 360, 126 ]. 1728 - 1758 have Frattini factor [ 360, 127 ]. 1759 - 1789 have Frattini factor [ 360, 128 ]. 1790 - 1814 have Frattini factor [ 360, 129 ]. 1815 - 1845 have Frattini factor [ 360, 130 ]. 1846 - 1870 have Frattini factor [ 360, 131 ]. 1871 - 1888 have Frattini factor [ 360, 132 ]. 1889 - 1917 have Frattini factor [ 360, 133 ]. 1918 - 1935 have Frattini factor [ 360, 134 ]. 1936 - 1940 have Frattini factor [ 360, 135 ]. 1941 - 1949 have Frattini factor [ 360, 136 ]. 1950 - 2520 have Frattini factor [ 360, 137 ]. 2521 - 2524 have Frattini factor [ 360, 138 ]. 2525 - 2528 have Frattini factor [ 360, 139 ]. 2529 - 2532 have Frattini factor [ 360, 140 ]. 2533 - 2536 have Frattini factor [ 360, 141 ]. 2537 - 2543 have Frattini factor [ 360, 142 ]. 2544 - 2550 have Frattini factor [ 360, 143 ]. 2551 - 2557 have Frattini factor [ 360, 144 ]. 2558 - 2582 have Frattini factor [ 360, 145 ]. 2583 - 2607 have Frattini factor [ 360, 146 ]. 2608 - 2632 have Frattini factor [ 360, 147 ]. 2633 - 2657 have Frattini factor [ 360, 148 ]. 2658 - 2682 have Frattini factor [ 360, 149 ]. 2683 - 2707 have Frattini factor [ 360, 150 ]. 2708 - 3042 have Frattini factor [ 360, 151 ]. 3043 - 3377 have Frattini factor [ 360, 152 ]. 3378 - 3572 have Frattini factor [ 360, 153 ]. 3573 - 3907 have Frattini factor [ 360, 154 ]. 3908 - 4102 have Frattini factor [ 360, 155 ]. 4103 - 4109 have Frattini factor [ 360, 156 ]. 4110 - 4195 have Frattini factor [ 360, 157 ]. 4196 - 4281 have Frattini factor [ 360, 158 ]. 4282 - 4367 have Frattini factor [ 360, 159 ]. 4368 - 4453 have Frattini factor [ 360, 160 ]. 4454 - 4539 have Frattini factor [ 360, 161 ]. 4540 - 4563 have Frattini factor [ 360, 162 ]. 4564 has Frattini factor [ 480, 1188 ]. 4565 has Frattini factor [ 480, 1189 ]. 4566 has Frattini factor [ 480, 1190 ]. 4567 has Frattini factor [ 480, 1191 ]. 4568 has Frattini factor [ 480, 1192 ]. 4569 has Frattini factor [ 480, 1193 ]. 4570 has Frattini factor [ 480, 1194 ]. 4571 has Frattini factor [ 480, 1195 ]. 4572 has Frattini factor [ 480, 1196 ]. 4573 has Frattini factor [ 480, 1197 ]. 4574 has Frattini factor [ 480, 1198 ]. 4575 has Frattini factor [ 480, 1199 ]. 4576 has Frattini factor [ 480, 1200 ]. 4577 has Frattini factor [ 480, 1201 ]. 4578 has Frattini factor [ 480, 1202 ]. 4579 has Frattini factor [ 480, 1203 ]. 4580 has Frattini factor [ 480, 1204 ]. 4581 has Frattini factor [ 480, 1205 ]. 4582 has Frattini factor [ 480, 1206 ]. 4583 has Frattini factor [ 480, 1207 ]. 4584 has Frattini factor [ 480, 1208 ]. 4585 has Frattini factor [ 480, 1209 ]. 4586 has Frattini factor [ 480, 1210 ]. 4587 has Frattini factor [ 480, 1211 ]. 4588 has Frattini factor [ 480, 1212 ]. 4589 has Frattini factor [ 480, 1213 ]. 4590 - 4591 have Frattini factor [ 720, 763 ]. 4592 - 4594 have Frattini factor [ 720, 764 ]. 4595 has Frattini factor [ 720, 765 ]. 4596 - 4598 have Frattini factor [ 720, 766 ]. 4599 - 4613 have Frattini factor [ 720, 767 ]. 4614 - 4616 have Frattini factor [ 720, 768 ]. 4617 - 4627 have Frattini factor [ 720, 769 ]. 4628 - 4638 have Frattini factor [ 720, 770 ]. 4639 - 4649 have Frattini factor [ 720, 771 ]. 4650 - 4656 have Frattini factor [ 720, 772 ]. 4657 - 4663 have Frattini factor [ 720, 773 ]. 4664 - 4678 have Frattini factor [ 720, 774 ]. 4679 - 4685 have Frattini factor [ 720, 775 ]. 4686 - 4692 have Frattini factor [ 720, 776 ]. 4693 - 4699 have Frattini factor [ 720, 777 ]. 4700 - 4706 have Frattini factor [ 720, 778 ]. 4707 - 4709 have Frattini factor [ 720, 779 ]. 4710 - 4712 have Frattini factor [ 720, 780 ]. 4713 - 4715 have Frattini factor [ 720, 781 ]. 4716 - 4718 have Frattini factor [ 720, 782 ]. 4719 - 4757 have Frattini factor [ 720, 783 ]. 4758 - 4796 have Frattini factor [ 720, 784 ]. 4797 - 4805 have Frattini factor [ 720, 785 ]. 4806 - 4808 have Frattini factor [ 720, 787 ]. 4809 - 4811 have Frattini factor [ 720, 788 ]. 4812 - 4814 have Frattini factor [ 720, 789 ]. 4815 - 4817 have Frattini factor [ 720, 790 ]. 4818 - 4832 have Frattini factor [ 720, 791 ]. 4833 - 4847 have Frattini factor [ 720, 792 ]. 4848 - 4862 have Frattini factor [ 720, 793 ]. 4863 - 4877 have Frattini factor [ 720, 794 ]. 4878 - 4892 have Frattini factor [ 720, 795 ]. 4893 - 4907 have Frattini factor [ 720, 796 ]. 4908 - 4922 have Frattini factor [ 720, 797 ]. 4923 - 4924 have Frattini factor [ 720, 798 ]. 4925 - 4931 have Frattini factor [ 720, 799 ]. 4932 - 4938 have Frattini factor [ 720, 800 ]. 4939 - 4945 have Frattini factor [ 720, 801 ]. 4946 - 4976 have Frattini factor [ 720, 802 ]. 4977 - 5007 have Frattini factor [ 720, 803 ]. 5008 - 5038 have Frattini factor [ 720, 804 ]. 5039 - 5063 have Frattini factor [ 720, 805 ]. 5064 - 5088 have Frattini factor [ 720, 806 ]. 5089 - 5119 have Frattini factor [ 720, 807 ]. 5120 - 5142 have Frattini factor [ 720, 808 ]. 5143 - 5177 have Frattini factor [ 720, 809 ]. 5178 - 5200 have Frattini factor [ 720, 810 ]. 5201 - 5205 have Frattini factor [ 720, 811 ]. 5206 - 5214 have Frattini factor [ 720, 812 ]. 5215 - 5361 have Frattini factor [ 720, 813 ]. 5362 - 5372 have Frattini factor [ 720, 814 ]. 5373 - 5383 have Frattini factor [ 720, 815 ]. 5384 - 5394 have Frattini factor [ 720, 816 ]. 5395 - 5405 have Frattini factor [ 720, 817 ]. 5406 - 5416 have Frattini factor [ 720, 818 ]. 5417 - 5427 have Frattini factor [ 720, 819 ]. 5428 - 5438 have Frattini factor [ 720, 820 ]. 5439 has Frattini factor [ 720, 821 ]. 5440 - 5452 have Frattini factor [ 720, 822 ]. 5453 - 5465 have Frattini factor [ 720, 823 ]. 5466 - 5478 have Frattini factor [ 720, 824 ]. 5479 - 5491 have Frattini factor [ 720, 825 ]. 5492 - 5504 have Frattini factor [ 720, 826 ]. 5505 - 5517 have Frattini factor [ 720, 827 ]. 5518 - 5570 have Frattini factor [ 720, 828 ]. 5571 - 5623 have Frattini factor [ 720, 829 ]. 5624 - 5660 have Frattini factor [ 720, 830 ]. 5661 - 5713 have Frattini factor [ 720, 831 ]. 5714 - 5750 have Frattini factor [ 720, 832 ]. 5751 - 5757 have Frattini factor [ 720, 833 ]. 5758 - 5759 have Frattini factor [ 720, 834 ]. 5760 - 5774 have Frattini factor [ 720, 835 ]. 5775 - 5789 have Frattini factor [ 720, 836 ]. 5790 - 5804 have Frattini factor [ 720, 837 ]. 5805 - 5819 have Frattini factor [ 720, 838 ]. 5820 - 5834 have Frattini factor [ 720, 839 ]. 5835 - 5840 have Frattini factor [ 720, 840 ]. 5841 - 5958 have trivial Frattini subgroup.

For the selection functions the values of the following attributes are precomputed and stored: IsAbelian, IsNilpotentGroup, IsSupersolvableGroup, IsSolvableGroup, LGLength, FrattinifactorSize and FrattinifactorId.

This size belongs to layer 5 of the SmallGroups library. IdSmallGroup is available for this size.