Groups of order 1008

Statistics at a glance
The number 1008 has the prime factors 2, 3, and 7. It has prime factorization:

$$\! 1008 = 2^4 \cdot 3^2 \cdot 7^1 = 16 \cdot 9 \cdot 7$$

GAP implementation
gap> SmallGroupsInformation(1008);

There are 954 groups of order 1008. They are sorted by their Frattini factors. 1 has Frattini factor [ 42, 1 ]. 2 has Frattini factor [ 42, 2 ]. 3 has Frattini factor [ 42, 3 ]. 4 has Frattini factor [ 42, 4 ]. 5 has Frattini factor [ 42, 5 ]. 6 has Frattini factor [ 42, 6 ]. 7 - 22 have Frattini factor [ 84, 7 ]. 23 - 47 have Frattini factor [ 84, 8 ]. 48 - 55 have Frattini factor [ 84, 9 ]. 56 has Frattini factor [ 84, 10 ]. 57 has Frattini factor [ 84, 11 ]. 58 - 73 have Frattini factor [ 84, 12 ]. 74 - 89 have Frattini factor [ 84, 13 ]. 90 - 105 have Frattini factor [ 84, 14 ]. 106 - 113 have Frattini factor [ 84, 15 ]. 114 has Frattini factor [ 126, 7 ]. 115 has Frattini factor [ 126, 8 ]. 116 has Frattini factor [ 126, 9 ]. 117 has Frattini factor [ 126, 10 ]. 118 has Frattini factor [ 126, 11 ]. 119 has Frattini factor [ 126, 12 ]. 120 has Frattini factor [ 126, 13 ]. 121 has Frattini factor [ 126, 14 ]. 122 has Frattini factor [ 126, 15 ]. 123 has Frattini factor [ 126, 16 ]. 124 - 126 have Frattini factor [ 168, 45 ]. 127 - 129 have Frattini factor [ 168, 46 ]. 130 - 139 have Frattini factor [ 168, 47 ]. 140 - 142 have Frattini factor [ 168, 48 ]. 143 - 145 have Frattini factor [ 168, 49 ]. 146 - 172 have Frattini factor [ 168, 50 ]. 173 - 176 have Frattini factor [ 168, 51 ]. 177 - 179 have Frattini factor [ 168, 52 ]. 180 - 182 have Frattini factor [ 168, 53 ]. 183 - 192 have Frattini factor [ 168, 54 ]. 193 - 202 have Frattini factor [ 168, 55 ]. 203 - 212 have Frattini factor [ 168, 56 ]. 213 - 216 have Frattini factor [ 168, 57 ]. 217 - 241 have Frattini factor [ 252, 26 ]. 242 has Frattini factor [ 252, 27 ]. 243 - 258 have Frattini factor [ 252, 28 ]. 259 - 274 have Frattini factor [ 252, 29 ]. 275 - 290 have Frattini factor [ 252, 30 ]. 291 has Frattini factor [ 252, 31 ]. 292 has Frattini factor [ 252, 32 ]. 293 - 317 have Frattini factor [ 252, 33 ]. 318 - 342 have Frattini factor [ 252, 34 ]. 343 - 358 have Frattini factor [ 252, 35 ]. 359 - 383 have Frattini factor [ 252, 36 ]. 384 - 399 have Frattini factor [ 252, 37 ]. 400 - 407 have Frattini factor [ 252, 38 ]. 408 has Frattini factor [ 252, 39 ]. 409 has Frattini factor [ 252, 40 ]. 410 - 425 have Frattini factor [ 252, 41 ]. 426 - 441 have Frattini factor [ 252, 42 ]. 442 - 457 have Frattini factor [ 252, 43 ]. 458 - 473 have Frattini factor [ 252, 44 ]. 474 - 489 have Frattini factor [ 252, 45 ]. 490 - 497 have Frattini factor [ 252, 46 ]. 498 has Frattini factor [ 336, 210 ]. 499 has Frattini factor [ 336, 211 ]. 500 has Frattini factor [ 336, 212 ]. 501 has Frattini factor [ 336, 213 ]. 502 has Frattini factor [ 336, 214 ]. 503 has Frattini factor [ 336, 215 ]. 504 has Frattini factor [ 336, 216 ]. 505 has Frattini factor [ 336, 217 ]. 506 has Frattini factor [ 336, 218 ]. 507 has Frattini factor [ 336, 219 ]. 508 has Frattini factor [ 336, 220 ]. 509 has Frattini factor [ 336, 221 ]. 510 has Frattini factor [ 336, 222 ]. 511 has Frattini factor [ 336, 223 ]. 512 has Frattini factor [ 336, 224 ]. 513 has Frattini factor [ 336, 225 ]. 514 has Frattini factor [ 336, 226 ]. 515 has Frattini factor [ 336, 227 ]. 516 has Frattini factor [ 336, 228 ]. 517 has Frattini factor [ 504, 157 ]. 518 - 520 have Frattini factor [ 504, 159 ]. 521 - 523 have Frattini factor [ 504, 160 ]. 524 - 526 have Frattini factor [ 504, 161 ]. 527 - 553 have Frattini factor [ 504, 162 ]. 554 - 556 have Frattini factor [ 504, 163 ]. 557 has Frattini factor [ 504, 164 ]. 558 has Frattini factor [ 504, 165 ]. 559 - 565 have Frattini factor [ 504, 166 ]. 566 - 570 have Frattini factor [ 504, 167 ]. 571 - 577 have Frattini factor [ 504, 168 ]. 578 - 582 have Frattini factor [ 504, 169 ]. 583 has Frattini factor [ 504, 170 ]. 584 - 585 have Frattini factor [ 504, 171 ]. 586 - 624 have Frattini factor [ 504, 172 ]. 625 - 627 have Frattini factor [ 504, 174 ]. 628 - 630 have Frattini factor [ 504, 175 ]. 631 - 633 have Frattini factor [ 504, 176 ]. 634 - 636 have Frattini factor [ 504, 177 ]. 637 - 646 have Frattini factor [ 504, 178 ]. 647 - 656 have Frattini factor [ 504, 179 ]. 657 - 666 have Frattini factor [ 504, 180 ]. 667 - 669 have Frattini factor [ 504, 181 ]. 670 - 672 have Frattini factor [ 504, 182 ]. 673 - 675 have Frattini factor [ 504, 183 ]. 676 - 678 have Frattini factor [ 504, 184 ]. 679 - 681 have Frattini factor [ 504, 185 ]. 682 - 684 have Frattini factor [ 504, 186 ]. 685 - 691 have Frattini factor [ 504, 187 ]. 692 - 698 have Frattini factor [ 504, 188 ]. 699 - 725 have Frattini factor [ 504, 189 ]. 726 - 752 have Frattini factor [ 504, 190 ]. 753 - 770 have Frattini factor [ 504, 191 ]. 771 - 797 have Frattini factor [ 504, 192 ]. 798 - 815 have Frattini factor [ 504, 193 ]. 816 - 819 have Frattini factor [ 504, 194 ]. 820 - 822 have Frattini factor [ 504, 195 ]. 823 - 825 have Frattini factor [ 504, 196 ]. 826 - 835 have Frattini factor [ 504, 197 ]. 836 - 845 have Frattini factor [ 504, 198 ]. 846 - 855 have Frattini factor [ 504, 199 ]. 856 - 865 have Frattini factor [ 504, 200 ]. 866 - 875 have Frattini factor [ 504, 201 ]. 876 - 879 have Frattini factor [ 504, 202 ]. 880 - 954 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.