Groups of order 252

Statistics at a glance
The number 252 has prime factors 2, 3, and 7. The prime factorization is:

$$\! 252 = 2^2 \cdot 3^2 \cdot 7^1 = 4 \cdot 9 \cdot 7$$

All groups of this order are finite solvable groups. In particular, there is no simple non-abelian group of this order.

GAP implementation
gap> SmallGroupsInformation(252);

There are 46 groups of order 252. They are sorted by their Frattini factors. 1 has Frattini factor [ 42, 1 ]. 2 has Frattini factor [ 42, 2 ]. 3 has Frattini factor [ 42, 3 ]. 4 has Frattini factor [ 42, 4 ]. 5 has Frattini factor [ 42, 5 ]. 6 has Frattini factor [ 42, 6 ]. 7 has Frattini factor [ 84, 7 ]. 8 has Frattini factor [ 84, 8 ]. 9 has Frattini factor [ 84, 9 ]. 10 has Frattini factor [ 84, 10 ]. 11 has Frattini factor [ 84, 11 ]. 12 has Frattini factor [ 84, 12 ]. 13 has Frattini factor [ 84, 13 ]. 14 has Frattini factor [ 84, 14 ]. 15 has Frattini factor [ 84, 15 ]. 16 has Frattini factor [ 126, 7 ]. 17 has Frattini factor [ 126, 8 ]. 18 has Frattini factor [ 126, 9 ]. 19 has Frattini factor [ 126, 10 ]. 20 has Frattini factor [ 126, 11 ]. 21 has Frattini factor [ 126, 12 ]. 22 has Frattini factor [ 126, 13 ]. 23 has Frattini factor [ 126, 14 ]. 24 has Frattini factor [ 126, 15 ]. 25 has Frattini factor [ 126, 16 ]. 26 - 46 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.