Groups of order 800

Statistics at a glance
The number 800 has prime factors 2 and 5. The prime factorization is:

$$\! 800 = 2^5 \cdot 5^2 = 32 \cdot 25$$

GAP implementation
gap> SmallGroupsInformation(800);

There are 1211 groups of order 800. 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 - 44 have Frattini factor [ 20, 4 ]. 45 - 63 have Frattini factor [ 20, 5 ]. 64 - 88 have Frattini factor [ 40, 12 ]. 89 - 174 have Frattini factor [ 40, 13 ]. 175 - 198 have Frattini factor [ 40, 14 ]. 199 has Frattini factor [ 50, 3 ]. 200 has Frattini factor [ 50, 4 ]. 201 has Frattini factor [ 50, 5 ]. 202 has Frattini factor [ 80, 49 ]. 203 - 215 have Frattini factor [ 80, 50 ]. 216 - 230 have Frattini factor [ 80, 51 ]. 231 - 236 have Frattini factor [ 80, 52 ]. 237 has Frattini factor [ 100, 9 ]. 238 has Frattini factor [ 100, 10 ]. 239 has Frattini factor [ 100, 11 ]. 240 has Frattini factor [ 100, 12 ]. 241 - 281 have Frattini factor [ 100, 13 ]. 282 - 322 have Frattini factor [ 100, 14 ]. 323 - 363 have Frattini factor [ 100, 15 ]. 364 - 382 have Frattini factor [ 100, 16 ]. 383 has Frattini factor [ 160, 234 ]. 384 has Frattini factor [ 160, 235 ]. 385 has Frattini factor [ 160, 236 ]. 386 has Frattini factor [ 160, 237 ]. 387 has Frattini factor [ 160, 238 ]. 388 has Frattini factor [ 200, 40 ]. 389 - 419 have Frattini factor [ 200, 41 ]. 420 - 442 have Frattini factor [ 200, 42 ]. 443 - 460 have Frattini factor [ 200, 43 ]. 461 - 465 have Frattini factor [ 200, 44 ]. 466 - 490 have Frattini factor [ 200, 45 ]. 491 - 515 have Frattini factor [ 200, 46 ]. 516 - 540 have Frattini factor [ 200, 47 ]. 541 - 565 have Frattini factor [ 200, 48 ]. 566 - 760 have Frattini factor [ 200, 49 ]. 761 - 846 have Frattini factor [ 200, 50 ]. 847 - 932 have Frattini factor [ 200, 51 ]. 933 - 956 have Frattini factor [ 200, 52 ]. 957 - 961 have Frattini factor [ 400, 205 ]. 962 - 964 have Frattini factor [ 400, 206 ]. 965 - 973 have Frattini factor [ 400, 207 ]. 974 - 980 have Frattini factor [ 400, 208 ]. 981 - 1011 have Frattini factor [ 400, 209 ]. 1012 - 1036 have Frattini factor [ 400, 210 ]. 1037 - 1059 have Frattini factor [ 400, 211 ]. 1060 - 1064 have Frattini factor [ 400, 212 ]. 1065 has Frattini factor [ 400, 213 ]. 1066 - 1078 have Frattini factor [ 400, 214 ]. 1079 - 1091 have Frattini factor [ 400, 215 ]. 1092 - 1104 have Frattini factor [ 400, 216 ]. 1105 - 1117 have Frattini factor [ 400, 217 ]. 1118 - 1154 have Frattini factor [ 400, 218 ]. 1155 - 1169 have Frattini factor [ 400, 219 ]. 1170 - 1184 have Frattini factor [ 400, 220 ]. 1185 - 1190 have Frattini factor [ 400, 221 ]. 1191 - 1211 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.