Groups of order 1344

Statistics at a glance
The number 1344 has 2, 3, and 7 as its only prime factors. It has prime factorization:

$$\! 1344 = 2^6 \cdot 3 \dot 7 = 64 \cdot 3 \cdot 7$$

GAP implementation
gap> SmallGroupsInformation(1344);

There are 11720 groups of order 1344. 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 - 128 have Frattini factor [ 84, 7 ]. 129 - 337 have Frattini factor [ 84, 8 ]. 338 - 390 have Frattini factor [ 84, 9 ]. 391 - 392 have Frattini factor [ 84, 10 ]. 393 - 394 have Frattini factor [ 84, 11 ]. 395 - 516 have Frattini factor [ 84, 12 ]. 517 - 638 have Frattini factor [ 84, 13 ]. 639 - 760 have Frattini factor [ 84, 14 ]. 761 - 813 have Frattini factor [ 84, 15 ]. 814 has Frattini factor [ 168, 42 ]. 815 - 816 have Frattini factor [ 168, 43 ]. 817 - 818 have Frattini factor [ 168, 44 ]. 819 - 826 have Frattini factor [ 168, 45 ]. 827 - 834 have Frattini factor [ 168, 46 ]. 835 - 1436 have Frattini factor [ 168, 47 ]. 1437 - 1453 have Frattini factor [ 168, 48 ]. 1454 - 1473 have Frattini factor [ 168, 49 ]. 1474 - 4193 have Frattini factor [ 168, 50 ]. 4194 - 4330 have Frattini factor [ 168, 51 ]. 4331 - 4347 have Frattini factor [ 168, 52 ]. 4348 - 4367 have Frattini factor [ 168, 53 ]. 4368 - 4969 have Frattini factor [ 168, 54 ]. 4970 - 5571 have Frattini factor [ 168, 55 ]. 5572 - 6173 have Frattini factor [ 168, 56 ]. 6174 - 6310 have Frattini factor [ 168, 57 ]. 6311 - 6313 have Frattini factor [ 336, 208 ]. 6314 - 6316 have Frattini factor [ 336, 209 ]. 6317 has Frattini factor [ 336, 210 ]. 6318 has Frattini factor [ 336, 211 ]. 6319 - 6392 have Frattini factor [ 336, 212 ]. 6393 has Frattini factor [ 336, 213 ]. 6394 - 6441 have Frattini factor [ 336, 214 ]. 6442 - 6489 have Frattini factor [ 336, 215 ]. 6490 - 6863 have Frattini factor [ 336, 216 ]. 6864 - 6918 have Frattini factor [ 336, 217 ]. 6919 - 6976 have Frattini factor [ 336, 218 ]. 6977 - 9960 have Frattini factor [ 336, 219 ]. 9961 - 10028 have Frattini factor [ 336, 220 ]. 10029 - 10056 have Frattini factor [ 336, 221 ]. 10057 - 10085 have Frattini factor [ 336, 222 ]. 10086 - 10091 have Frattini factor [ 336, 223 ]. 10092 - 10097 have Frattini factor [ 336, 224 ]. 10098 - 10471 have Frattini factor [ 336, 225 ]. 10472 - 10845 have Frattini factor [ 336, 226 ]. 10846 - 11219 have Frattini factor [ 336, 227 ]. 11220 - 11287 have Frattini factor [ 336, 228 ]. 11288 - 11298 have Frattini factor [ 672, 1254 ]. 11299 - 11305 have Frattini factor [ 672, 1255 ]. 11306 - 11308 have Frattini factor [ 672, 1256 ]. 11309 has Frattini factor [ 672, 1257 ]. 11310 has Frattini factor [ 672, 1258 ]. 11311 - 11315 have Frattini factor [ 672, 1259 ]. 11316 - 11370 have Frattini factor [ 672, 1260 ]. 11371 - 11373 have Frattini factor [ 672, 1261 ]. 11374 - 11394 have Frattini factor [ 672, 1262 ]. 11395 - 11415 have Frattini factor [ 672, 1263 ]. 11416 - 11422 have Frattini factor [ 672, 1264 ]. 11423 - 11429 have Frattini factor [ 672, 1265 ]. 11430 - 11449 have Frattini factor [ 672, 1266 ]. 11450 - 11470 have Frattini factor [ 672, 1267 ]. 11471 - 11491 have Frattini factor [ 672, 1268 ]. 11492 - 11496 have Frattini factor [ 672, 1269 ]. 11497 - 11501 have Frattini factor [ 672, 1270 ]. 11502 - 11581 have Frattini factor [ 672, 1271 ]. 11582 - 11588 have Frattini factor [ 672, 1272 ]. 11589 - 11597 have Frattini factor [ 672, 1273 ]. 11598 - 11606 have Frattini factor [ 672, 1274 ]. 11607 - 11611 have Frattini factor [ 672, 1275 ]. 11612 - 11616 have Frattini factor [ 672, 1276 ]. 11617 - 11636 have Frattini factor [ 672, 1277 ]. 11637 - 11656 have Frattini factor [ 672, 1278 ]. 11657 - 11676 have Frattini factor [ 672, 1279 ]. 11677 - 11683 have Frattini factor [ 672, 1280 ]. 11684 - 11720 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.