Groups of order 576

Statistics at a glance
The number 576 has the following prime factorization:

$$\! 576 = 2^6 \cdot 3^2 = 64 \cdot 9$$

GAP implementation
gap> SmallGroupsInformation(576);

There are 8681 groups of order 576. They are sorted by their Frattini factors. 1 has Frattini factor [ 6, 1 ]. 2 has Frattini factor [ 6, 2 ]. 3 - 4 have Frattini factor [ 12, 3 ]. 5 - 126 have Frattini factor [ 12, 4 ]. 127 - 179 have Frattini factor [ 12, 5 ]. 180 has Frattini factor [ 18, 3 ]. 181 has Frattini factor [ 18, 4 ]. 182 has Frattini factor [ 18, 5 ]. 183 - 190 have Frattini factor [ 24, 12 ]. 191 - 207 have Frattini factor [ 24, 13 ]. 208 - 809 have Frattini factor [ 24, 14 ]. 810 - 946 have Frattini factor [ 24, 15 ]. 947 has Frattini factor [ 36, 9 ]. 948 - 1069 have Frattini factor [ 36, 10 ]. 1070 - 1071 have Frattini factor [ 36, 11 ]. 1072 - 1193 have Frattini factor [ 36, 12 ]. 1194 - 1315 have Frattini factor [ 36, 13 ]. 1316 - 1368 have Frattini factor [ 36, 14 ]. 1369 - 1416 have Frattini factor [ 48, 48 ]. 1417 - 1444 have Frattini factor [ 48, 49 ]. 1445 - 1450 have Frattini factor [ 48, 50 ]. 1451 - 1824 have Frattini factor [ 48, 51 ]. 1825 - 1892 have Frattini factor [ 48, 52 ]. 1893 has Frattini factor [ 72, 39 ]. 1894 - 1963 have Frattini factor [ 72, 40 ]. 1964 - 1980 have Frattini factor [ 72, 41 ]. 1981 - 1988 have Frattini factor [ 72, 42 ]. 1989 - 1996 have Frattini factor [ 72, 43 ]. 1997 - 2013 have Frattini factor [ 72, 44 ]. 2014 - 2105 have Frattini factor [ 72, 45 ]. 2106 - 3607 have Frattini factor [ 72, 46 ]. 3608 - 3624 have Frattini factor [ 72, 47 ]. 3625 - 4226 have Frattini factor [ 72, 48 ]. 4227 - 4828 have Frattini factor [ 72, 49 ]. 4829 - 4965 have Frattini factor [ 72, 50 ]. 4966 - 4986 have Frattini factor [ 96, 226 ]. 4987 - 4993 have Frattini factor [ 96, 227 ]. 4994 - 5002 have Frattini factor [ 96, 228 ]. 5003 - 5007 have Frattini factor [ 96, 229 ]. 5008 - 5027 have Frattini factor [ 96, 230 ]. 5028 - 5034 have Frattini factor [ 96, 231 ]. 5035 - 5052 have Frattini factor [ 144, 182 ]. 5053 - 5126 have Frattini factor [ 144, 183 ]. 5127 - 5129 have Frattini factor [ 144, 184 ]. 5130 - 5156 have Frattini factor [ 144, 185 ]. 5157 - 5412 have Frattini factor [ 144, 186 ]. 5413 - 5452 have Frattini factor [ 144, 187 ]. 5453 - 5500 have Frattini factor [ 144, 188 ]. 5501 - 5548 have Frattini factor [ 144, 189 ]. 5549 - 5603 have Frattini factor [ 144, 190 ]. 5604 - 5729 have Frattini factor [ 144, 191 ]. 5730 - 7411 have Frattini factor [ 144, 192 ]. 7412 - 7439 have Frattini factor [ 144, 193 ]. 7440 - 7445 have Frattini factor [ 144, 194 ]. 7446 - 7819 have Frattini factor [ 144, 195 ]. 7820 - 8193 have Frattini factor [ 144, 196 ]. 8194 - 8261 have Frattini factor [ 144, 197 ]. 8262 has Frattini factor [ 192, 1537 ]. 8263 has Frattini factor [ 192, 1538 ]. 8264 has Frattini factor [ 192, 1539 ]. 8265 has Frattini factor [ 192, 1540 ]. 8266 has Frattini factor [ 192, 1541 ]. 8267 has Frattini factor [ 192, 1542 ]. 8268 has Frattini factor [ 192, 1543 ]. 8269 - 8275 have Frattini factor [ 288, 1024 ]. 8276 - 8278 have Frattini factor [ 288, 1025 ]. 8279 - 8283 have Frattini factor [ 288, 1026 ]. 8284 - 8300 have Frattini factor [ 288, 1027 ]. 8301 - 8355 have Frattini factor [ 288, 1028 ]. 8356 - 8360 have Frattini factor [ 288, 1029 ]. 8361 - 8373 have Frattini factor [ 288, 1030 ]. 8374 - 8420 have Frattini factor [ 288, 1031 ]. 8421 - 8432 have Frattini factor [ 288, 1032 ]. 8433 - 8453 have Frattini factor [ 288, 1033 ]. 8454 - 8474 have Frattini factor [ 288, 1034 ]. 8475 - 8481 have Frattini factor [ 288, 1035 ]. 8482 - 8488 have Frattini factor [ 288, 1036 ]. 8489 - 8509 have Frattini factor [ 288, 1037 ]. 8510 - 8514 have Frattini factor [ 288, 1038 ]. 8515 - 8535 have Frattini factor [ 288, 1039 ]. 8536 - 8590 have Frattini factor [ 288, 1040 ]. 8591 - 8599 have Frattini factor [ 288, 1041 ]. 8600 - 8604 have Frattini factor [ 288, 1042 ]. 8605 - 8624 have Frattini factor [ 288, 1043 ]. 8625 - 8644 have Frattini factor [ 288, 1044 ]. 8645 - 8651 have Frattini factor [ 288, 1045 ]. 8652 - 8681 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 2 of the SmallGroups library. IdSmallGroup is available for this size.