Groups of order 1344

This article gives information about, and links to more details on, groups of order 1344
See pages on algebraic structures of order 1344 | See pages on groups of a particular order

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

The order 1344 is part of GAP's SmallGroup library. Hence, any group of order 1344 can be constructed using the SmallGroup function by specifying its group ID. Also, IdGroup is available, so the group ID of any group of this order can be queried.

Further, the collection of all groups of order 1344 can be accessed as a list using GAP's AllSmallGroups function.

Here is GAP's summary information about how it stores groups of this order, accessed using GAP's SmallGroupsInformation function:

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.