Groups of order 1200

Statistics at a glance
The number 1200 has prime factors 2, 3, and 5. The prime factorization is:

$$\! 1200 = 2^4 \cdot 3^1 \cdot 5^2 = 16 \cdot 3 \cdot 25$$

There are both solvable and non-solvable groups of this order.

GAP implementation
gap> SmallGroupsInformation(1200);

There are 1040 groups of order 1200. 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 - 31 have Frattini factor [ 60, 8 ]. 32 has Frattini factor [ 60, 9 ]. 33 - 48 have Frattini factor [ 60, 10 ]. 49 - 64 have Frattini factor [ 60, 11 ]. 65 - 80 have Frattini factor [ 60, 12 ]. 81 - 88 have Frattini factor [ 60, 13 ]. 89 - 95 have Frattini factor [ 120, 36 ]. 96 - 98 have Frattini factor [ 120, 37 ]. 99 - 101 have Frattini factor [ 120, 38 ]. 102 - 104 have Frattini factor [ 120, 39 ]. 105 - 111 have Frattini factor [ 120, 40 ]. 112 - 118 have Frattini factor [ 120, 41 ]. 119 - 145 have Frattini factor [ 120, 42 ]. 146 - 148 have Frattini factor [ 120, 43 ]. 149 - 158 have Frattini factor [ 120, 44 ]. 159 - 168 have Frattini factor [ 120, 45 ]. 169 - 178 have Frattini factor [ 120, 46 ]. 179 - 182 have Frattini factor [ 120, 47 ]. 183 has Frattini factor [ 150, 5 ]. 184 has Frattini factor [ 150, 6 ]. 185 has Frattini factor [ 150, 7 ]. 186 has Frattini factor [ 150, 8 ]. 187 has Frattini factor [ 150, 9 ]. 188 has Frattini factor [ 150, 10 ]. 189 has Frattini factor [ 150, 11 ]. 190 has Frattini factor [ 150, 12 ]. 191 has Frattini factor [ 150, 13 ]. 192 has Frattini factor [ 240, 191 ]. 193 has Frattini factor [ 240, 192 ]. 194 has Frattini factor [ 240, 193 ]. 195 has Frattini factor [ 240, 194 ]. 196 has Frattini factor [ 240, 195 ]. 197 has Frattini factor [ 240, 196 ]. 198 has Frattini factor [ 240, 197 ]. 199 has Frattini factor [ 240, 198 ]. 200 has Frattini factor [ 240, 199 ]. 201 has Frattini factor [ 240, 200 ]. 202 has Frattini factor [ 240, 201 ]. 203 has Frattini factor [ 240, 202 ]. 204 has Frattini factor [ 240, 203 ]. 205 has Frattini factor [ 240, 204 ]. 206 has Frattini factor [ 240, 205 ]. 207 has Frattini factor [ 240, 206 ]. 208 has Frattini factor [ 240, 207 ]. 209 has Frattini factor [ 240, 208 ]. 210 has Frattini factor [ 300, 23 ]. 211 has Frattini factor [ 300, 24 ]. 212 - 227 have Frattini factor [ 300, 25 ]. 228 - 243 have Frattini factor [ 300, 26 ]. 244 - 259 have Frattini factor [ 300, 27 ]. 260 has Frattini factor [ 300, 28 ]. 261 has Frattini factor [ 300, 29 ]. 262 has Frattini factor [ 300, 30 ]. 263 has Frattini factor [ 300, 31 ]. 264 has Frattini factor [ 300, 32 ]. 265 has Frattini factor [ 300, 33 ]. 266 has Frattini factor [ 300, 34 ]. 267 has Frattini factor [ 300, 35 ]. 268 - 283 have Frattini factor [ 300, 36 ]. 284 - 308 have Frattini factor [ 300, 37 ]. 309 - 333 have Frattini factor [ 300, 38 ]. 334 - 358 have Frattini factor [ 300, 39 ]. 359 - 374 have Frattini factor [ 300, 40 ]. 375 - 382 have Frattini factor [ 300, 41 ]. 383 has Frattini factor [ 300, 42 ]. 384 has Frattini factor [ 300, 43 ]. 385 - 400 have Frattini factor [ 300, 44 ]. 401 - 416 have Frattini factor [ 300, 45 ]. 417 - 432 have Frattini factor [ 300, 46 ]. 433 - 448 have Frattini factor [ 300, 47 ]. 449 - 464 have Frattini factor [ 300, 48 ]. 465 - 472 have Frattini factor [ 300, 49 ]. 473 - 475 have Frattini factor [ 600, 144 ]. 476 - 478 have Frattini factor [ 600, 145 ]. 479 - 481 have Frattini factor [ 600, 146 ]. 482 - 484 have Frattini factor [ 600, 147 ]. 485 has Frattini factor [ 600, 148 ]. 486 has Frattini factor [ 600, 149 ]. 487 - 491 have Frattini factor [ 600, 151 ]. 492 - 498 have Frattini factor [ 600, 152 ]. 499 - 505 have Frattini factor [ 600, 153 ]. 506 - 523 have Frattini factor [ 600, 154 ]. 524 has Frattini factor [ 600, 155 ]. 525 has Frattini factor [ 600, 156 ]. 526 - 530 have Frattini factor [ 600, 157 ]. 531 - 537 have Frattini factor [ 600, 158 ]. 538 - 544 have Frattini factor [ 600, 159 ]. 545 - 551 have Frattini factor [ 600, 160 ]. 552 - 558 have Frattini factor [ 600, 161 ]. 559 - 563 have Frattini factor [ 600, 162 ]. 564 - 568 have Frattini factor [ 600, 163 ]. 569 - 573 have Frattini factor [ 600, 164 ]. 574 - 580 have Frattini factor [ 600, 165 ]. 581 - 587 have Frattini factor [ 600, 166 ]. 588 - 594 have Frattini factor [ 600, 167 ]. 595 - 601 have Frattini factor [ 600, 168 ]. 602 - 606 have Frattini factor [ 600, 169 ]. 607 - 611 have Frattini factor [ 600, 170 ]. 612 - 618 have Frattini factor [ 600, 171 ]. 619 has Frattini factor [ 600, 172 ]. 620 - 621 have Frattini factor [ 600, 173 ]. 622 - 660 have Frattini factor [ 600, 174 ]. 661 - 670 have Frattini factor [ 600, 175 ]. 671 - 673 have Frattini factor [ 600, 176 ]. 674 - 676 have Frattini factor [ 600, 177 ]. 677 - 679 have Frattini factor [ 600, 178 ]. 680 - 682 have Frattini factor [ 600, 179 ]. 683 - 692 have Frattini factor [ 600, 180 ]. 693 - 695 have Frattini factor [ 600, 181 ]. 696 - 698 have Frattini factor [ 600, 182 ]. 699 - 701 have Frattini factor [ 600, 183 ]. 702 - 708 have Frattini factor [ 600, 184 ]. 709 - 715 have Frattini factor [ 600, 185 ]. 716 - 722 have Frattini factor [ 600, 186 ]. 723 - 729 have Frattini factor [ 600, 187 ]. 730 - 736 have Frattini factor [ 600, 188 ]. 737 - 743 have Frattini factor [ 600, 189 ]. 744 - 750 have Frattini factor [ 600, 190 ]. 751 - 757 have Frattini factor [ 600, 191 ]. 758 - 775 have Frattini factor [ 600, 192 ]. 776 - 802 have Frattini factor [ 600, 193 ]. 803 - 829 have Frattini factor [ 600, 194 ]. 830 - 856 have Frattini factor [ 600, 195 ]. 857 - 874 have Frattini factor [ 600, 196 ]. 875 - 878 have Frattini factor [ 600, 197 ]. 879 - 881 have Frattini factor [ 600, 198 ]. 882 - 884 have Frattini factor [ 600, 199 ]. 885 - 894 have Frattini factor [ 600, 200 ]. 895 - 904 have Frattini factor [ 600, 201 ]. 905 - 914 have Frattini factor [ 600, 202 ]. 915 - 924 have Frattini factor [ 600, 203 ]. 925 - 934 have Frattini factor [ 600, 204 ]. 935 - 938 have Frattini factor [ 600, 205 ]. 939 - 1040 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.