Groups of order 140

Statistics at a glance
The number 140 has prime factors 2, 5, and 7. The prime factorization is:

$$\! 140 = 2^2 \cdot 5^1 \cdot 7^1 = 4 \cdot 5 \cdot 7$$

All groups of this order are solvable groups, and in particular, finite solvable groups, so 140 is a solvability-forcing number.

GAP implementation
gap> SmallGroupsInformation(140);

There are 11 groups of order 140. 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 - 11 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.