Groups of order 216

Statistics at a glance
The number 216 has prime factorization $$216 = 2^3 \cdot 3^3$$.

GAP implementation
gap> SmallGroupsInformation(216);

There are 177 groups of order 216. They are sorted by their Frattini factors. 1 has Frattini factor [ 6, 1 ]. 2 has Frattini factor [ 6, 2 ]. 3 has Frattini factor [ 12, 3 ]. 4 - 8 have Frattini factor [ 12, 4 ]. 9 - 11 have Frattini factor [ 12, 5 ]. 12 - 15 have Frattini factor [ 18, 3 ]. 16 - 17 have Frattini factor [ 18, 4 ]. 18 - 20 have Frattini factor [ 18, 5 ]. 21 has Frattini factor [ 24, 12 ]. 22 has Frattini factor [ 24, 13 ]. 23 has Frattini factor [ 24, 14 ]. 24 has Frattini factor [ 24, 15 ]. 25 has Frattini factor [ 36, 9 ]. 26 - 37 have Frattini factor [ 36, 10 ]. 38 - 42 have Frattini factor [ 36, 11 ]. 43 - 62 have Frattini factor [ 36, 12 ]. 63 - 72 have Frattini factor [ 36, 13 ]. 73 - 81 have Frattini factor [ 36, 14 ]. 82 has Frattini factor [ 54, 12 ]. 83 has Frattini factor [ 54, 13 ]. 84 has Frattini factor [ 54, 14 ]. 85 has Frattini factor [ 54, 15 ]. 86 has Frattini factor [ 72, 39 ]. 87 has Frattini factor [ 72, 40 ]. 88 has Frattini factor [ 72, 41 ]. 89 - 92 have Frattini factor [ 72, 42 ]. 93 - 95 have Frattini factor [ 72, 43 ]. 96 - 99 have Frattini factor [ 72, 44 ]. 100 has Frattini factor [ 72, 45 ]. 101 - 102 have Frattini factor [ 72, 46 ]. 103 - 107 have Frattini factor [ 72, 47 ]. 108 - 111 have Frattini factor [ 72, 48 ]. 112 - 113 have Frattini factor [ 72, 49 ]. 114 - 116 have Frattini factor [ 72, 50 ]. 117 has Frattini factor [ 108, 36 ]. 118 has Frattini factor [ 108, 37 ]. 119 - 123 have Frattini factor [ 108, 38 ]. 124 - 130 have Frattini factor [ 108, 39 ]. 131 - 133 have Frattini factor [ 108, 40 ]. 134 has Frattini factor [ 108, 41 ]. 135 - 139 have Frattini factor [ 108, 42 ]. 140 - 144 have Frattini factor [ 108, 43 ]. 145 - 149 have Frattini factor [ 108, 44 ]. 150 - 152 have Frattini factor [ 108, 45 ]. 153 - 177 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.