Groups of order 560

Statistics at a glance
The number 560 has prime factors 2, 5, and 7. The prime factorization is:

$$\! 560 = 2^4 \cdot 5^1 \cdot 7^1 = 16 \cdot 5 \cdot 7$$

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

GAP implementation
gap> SmallGroupsInformation(560);

There are 180 groups of order 560. 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 - 31 have Frattini factor [ 140, 7 ]. 32 - 47 have Frattini factor [ 140, 8 ]. 48 - 63 have Frattini factor [ 140, 9 ]. 64 - 79 have Frattini factor [ 140, 10 ]. 80 - 87 have Frattini factor [ 140, 11 ]. 88 - 94 have Frattini factor [ 280, 32 ]. 95 - 101 have Frattini factor [ 280, 34 ]. 102 - 108 have Frattini factor [ 280, 35 ]. 109 - 135 have Frattini factor [ 280, 36 ]. 136 - 145 have Frattini factor [ 280, 37 ]. 146 - 155 have Frattini factor [ 280, 38 ]. 156 - 165 have Frattini factor [ 280, 39 ]. 166 - 169 have Frattini factor [ 280, 40 ]. 170 - 180 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.