Groups of order 1120

Statistics at a glance
The number 1120 has prime factors 2, 5, and 7. The prime factorization is as follows:

$$\! 1120 = 2^5 \cdot 5^1 \cdot 7^1 = 32 \cdot 5 \cdot 7$$

All groups of this order are solvable groups, and in particular, finite solvable groups.

GAP implementation
gap> SmallGroupsInformation(1120);

There are 1092 groups of order 1120. They are sorted by their Frattini factors. 1 has Frattini factor [ 70, 1 ]. 2 has Frattini factor [ 70, 2 ]. 3 has Frattini factor [ 70, 3 ]. 4 has Frattini factor [ 70, 4 ]. 5 has Frattini factor [ 140, 5 ]. 6 has Frattini factor [ 140, 6 ]. 7 - 73 have Frattini factor [ 140, 7 ]. 74 - 114 have Frattini factor [ 140, 8 ]. 115 - 155 have Frattini factor [ 140, 9 ]. 156 - 196 have Frattini factor [ 140, 10 ]. 197 - 215 have Frattini factor [ 140, 11 ]. 216 - 246 have Frattini factor [ 280, 32 ]. 247 - 271 have Frattini factor [ 280, 34 ]. 272 - 296 have Frattini factor [ 280, 35 ]. 297 - 631 have Frattini factor [ 280, 36 ]. 632 - 717 have Frattini factor [ 280, 37 ]. 718 - 803 have Frattini factor [ 280, 38 ]. 804 - 889 have Frattini factor [ 280, 39 ]. 890 - 913 have Frattini factor [ 280, 40 ]. 914 has Frattini factor [ 560, 170 ]. 915 - 945 have Frattini factor [ 560, 171 ]. 946 has Frattini factor [ 560, 172 ]. 947 has Frattini factor [ 560, 173 ]. 948 - 960 have Frattini factor [ 560, 174 ]. 961 - 973 have Frattini factor [ 560, 175 ]. 974 - 1026 have Frattini factor [ 560, 176 ]. 1027 - 1041 have Frattini factor [ 560, 177 ]. 1042 - 1056 have Frattini factor [ 560, 178 ]. 1057 - 1071 have Frattini factor [ 560, 179 ]. 1072 - 1077 have Frattini factor [ 560, 180 ]. 1078 - 1092 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.