Groups of order 528

Statistics at a glance
The order 528 has prime factorization:

$$\! 528 = 2^4 \cdot 3^1 \cdot 11^1 = 16 \cdot 3\cdot 11$$

GAP implementation
gap> SmallGroupsInformation(528);

There are 170 groups of order 528. They are sorted by their Frattini factors. 1 has Frattini factor [ 66, 1 ]. 2 has Frattini factor [ 66, 2 ]. 3 has Frattini factor [ 66, 3 ]. 4 has Frattini factor [ 66, 4 ]. 5 - 29 have Frattini factor [ 132, 5 ]. 30 has Frattini factor [ 132, 6 ]. 31 - 46 have Frattini factor [ 132, 7 ]. 47 - 62 have Frattini factor [ 132, 8 ]. 63 - 78 have Frattini factor [ 132, 9 ]. 79 - 86 have Frattini factor [ 132, 10 ]. 87 - 89 have Frattini factor [ 264, 31 ]. 90 - 92 have Frattini factor [ 264, 32 ]. 93 - 95 have Frattini factor [ 264, 33 ]. 96 - 122 have Frattini factor [ 264, 34 ]. 123 - 125 have Frattini factor [ 264, 35 ]. 126 - 135 have Frattini factor [ 264, 36 ]. 136 - 145 have Frattini factor [ 264, 37 ]. 146 - 155 have Frattini factor [ 264, 38 ]. 156 - 159 have Frattini factor [ 264, 39 ]. 160 - 170 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.