Groups of order 280

Statistics at a glance
The number 280 has prime factors 2, 5, and 7. The prime factorization is:

$$\! 280 = 2^3 \cdot 5^1 \cdot 7^1 = 8 \cdot 5 \cdot 7$$

All groups of this order are solvable groups, and hence finite solvable groups.

GAP implementation
gap> SmallGroupsInformation(280);

There are 40 groups of order 280. 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 - 13 have Frattini factor [ 140, 7 ]. 14 - 18 have Frattini factor [ 140, 8 ]. 19 - 23 have Frattini factor [ 140, 9 ]. 24 - 28 have Frattini factor [ 140, 10 ]. 29 - 31 have Frattini factor [ 140, 11 ]. 32 - 40 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.