Groups of order 1600

Statistics at a glance
The number 1600 has prime factors 2 and 5. The prime factorization is as follows:

$$\! 1600 = 2^6 \cdot 5^2 = 64 \cdot 25$$

GAP implementation
gap> SmallGroupsInformation(1600);

There are 10281 groups of order 1600. They are sorted by their Frattini factors. 1 has Frattini factor [ 10, 1 ]. 2 has Frattini factor [ 10, 2 ]. 3 has Frattini factor [ 20, 3 ]. 4 - 125 have Frattini factor [ 20, 4 ]. 126 - 178 have Frattini factor [ 20, 5 ]. 179 - 272 have Frattini factor [ 40, 12 ]. 273 - 874 have Frattini factor [ 40, 13 ]. 875 - 1011 have Frattini factor [ 40, 14 ]. 1012 has Frattini factor [ 50, 3 ]. 1013 has Frattini factor [ 50, 4 ]. 1014 has Frattini factor [ 50, 5 ]. 1015 has Frattini factor [ 80, 49 ]. 1016 - 1141 have Frattini factor [ 80, 50 ]. 1142 - 1515 have Frattini factor [ 80, 51 ]. 1516 - 1583 have Frattini factor [ 80, 52 ]. 1584 has Frattini factor [ 100, 9 ]. 1585 has Frattini factor [ 100, 10 ]. 1586 has Frattini factor [ 100, 11 ]. 1587 has Frattini factor [ 100, 12 ]. 1588 - 1709 have Frattini factor [ 100, 13 ]. 1710 - 1831 have Frattini factor [ 100, 14 ]. 1832 - 1953 have Frattini factor [ 100, 15 ]. 1954 - 2006 have Frattini factor [ 100, 16 ]. 2007 - 2009 have Frattini factor [ 160, 234 ]. 2010 - 2012 have Frattini factor [ 160, 235 ]. 2013 - 2033 have Frattini factor [ 160, 236 ]. 2034 - 2053 have Frattini factor [ 160, 237 ]. 2054 - 2060 have Frattini factor [ 160, 238 ]. 2061 has Frattini factor [ 200, 40 ]. 2062 - 2198 have Frattini factor [ 200, 41 ]. 2199 - 2295 have Frattini factor [ 200, 42 ]. 2296 - 2365 have Frattini factor [ 200, 43 ]. 2366 - 2382 have Frattini factor [ 200, 44 ]. 2383 - 2476 have Frattini factor [ 200, 45 ]. 2477 - 2570 have Frattini factor [ 200, 46 ]. 2571 - 2664 have Frattini factor [ 200, 47 ]. 2665 - 2756 have Frattini factor [ 200, 48 ]. 2757 - 4258 have Frattini factor [ 200, 49 ]. 4259 - 4860 have Frattini factor [ 200, 50 ]. 4861 - 5462 have Frattini factor [ 200, 51 ]. 5463 - 5599 have Frattini factor [ 200, 52 ]. 5600 has Frattini factor [ 320, 1635 ]. 5601 has Frattini factor [ 320, 1636 ]. 5602 has Frattini factor [ 320, 1637 ]. 5603 has Frattini factor [ 320, 1638 ]. 5604 has Frattini factor [ 320, 1639 ]. 5605 has Frattini factor [ 320, 1640 ]. 5606 - 5642 have Frattini factor [ 400, 205 ]. 5643 - 5657 have Frattini factor [ 400, 206 ]. 5658 - 5745 have Frattini factor [ 400, 207 ]. 5746 - 5772 have Frattini factor [ 400, 208 ]. 5773 - 6187 have Frattini factor [ 400, 209 ]. 6188 - 6489 have Frattini factor [ 400, 210 ]. 6490 - 6745 have Frattini factor [ 400, 211 ]. 6746 - 6785 have Frattini factor [ 400, 212 ]. 6786 has Frattini factor [ 400, 213 ]. 6787 - 6912 have Frattini factor [ 400, 214 ]. 6913 - 7038 have Frattini factor [ 400, 215 ]. 7039 - 7164 have Frattini factor [ 400, 216 ]. 7165 - 7290 have Frattini factor [ 400, 217 ]. 7291 - 8972 have Frattini factor [ 400, 218 ]. 8973 - 9346 have Frattini factor [ 400, 219 ]. 9347 - 9720 have Frattini factor [ 400, 220 ]. 9721 - 9788 have Frattini factor [ 400, 221 ]. 9789 - 9795 have Frattini factor [ 800, 1191 ]. 9796 - 9820 have Frattini factor [ 800, 1192 ]. 9821 - 9832 have Frattini factor [ 800, 1193 ]. 9833 - 9868 have Frattini factor [ 800, 1194 ]. 9869 - 9871 have Frattini factor [ 800, 1195 ]. 9872 - 9874 have Frattini factor [ 800, 1196 ]. 9875 - 9877 have Frattini factor [ 800, 1197 ]. 9878 - 9890 have Frattini factor [ 800, 1198 ]. 9891 - 9942 have Frattini factor [ 800, 1199 ]. 9943 - 10005 have Frattini factor [ 800, 1200 ]. 10006 - 10052 have Frattini factor [ 800, 1201 ]. 10053 - 10064 have Frattini factor [ 800, 1202 ]. 10065 - 10067 have Frattini factor [ 800, 1203 ]. 10068 - 10088 have Frattini factor [ 800, 1204 ]. 10089 - 10109 have Frattini factor [ 800, 1205 ]. 10110 - 10130 have Frattini factor [ 800, 1206 ]. 10131 - 10151 have Frattini factor [ 800, 1207 ]. 10152 - 10206 have Frattini factor [ 800, 1208 ]. 10207 - 10226 have Frattini factor [ 800, 1209 ]. 10227 - 10246 have Frattini factor [ 800, 1210 ]. 10247 - 10253 have Frattini factor [ 800, 1211 ]. 10254 - 10281 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.