Groups of order 756

Statistics at a glance
The number 756 has prime factors 2, 3, and 7. It has the prime factorization:

$$\! 756 = 2^2 \cdot 3^3 \cdot 7$$

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

GAP implementation
gap> SmallGroupsInformation(756);

There are 189 groups of order 756. 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 - 21 have Frattini factor [ 126, 7 ]. 22 - 26 have Frattini factor [ 126, 8 ]. 27 - 31 have Frattini factor [ 126, 9 ]. 32 - 37 have Frattini factor [ 126, 10 ]. 38 - 40 have Frattini factor [ 126, 11 ]. 41 - 44 have Frattini factor [ 126, 12 ]. 45 - 48 have Frattini factor [ 126, 13 ]. 49 - 50 have Frattini factor [ 126, 14 ]. 51 - 52 have Frattini factor [ 126, 15 ]. 53 - 55 have Frattini factor [ 126, 16 ]. 56 - 60 have Frattini factor [ 252, 26 ]. 61 - 69 have Frattini factor [ 252, 27 ]. 70 - 75 have Frattini factor [ 252, 28 ]. 76 - 80 have Frattini factor [ 252, 29 ]. 81 - 85 have Frattini factor [ 252, 30 ]. 86 has Frattini factor [ 252, 31 ]. 87 has Frattini factor [ 252, 32 ]. 88 - 91 have Frattini factor [ 252, 33 ]. 92 - 93 have Frattini factor [ 252, 34 ]. 94 - 95 have Frattini factor [ 252, 35 ]. 96 - 98 have Frattini factor [ 252, 36 ]. 99 - 100 have Frattini factor [ 252, 37 ]. 101 - 106 have Frattini factor [ 252, 38 ]. 107 - 111 have Frattini factor [ 252, 39 ]. 112 - 117 have Frattini factor [ 252, 40 ]. 118 - 120 have Frattini factor [ 252, 41 ]. 121 - 124 have Frattini factor [ 252, 42 ]. 125 - 128 have Frattini factor [ 252, 43 ]. 129 - 130 have Frattini factor [ 252, 44 ]. 131 - 132 have Frattini factor [ 252, 45 ]. 133 - 135 have Frattini factor [ 252, 46 ]. 136 has Frattini factor [ 378, 47 ]. 137 has Frattini factor [ 378, 48 ]. 138 has Frattini factor [ 378, 49 ]. 139 has Frattini factor [ 378, 50 ]. 140 has Frattini factor [ 378, 51 ]. 141 has Frattini factor [ 378, 52 ]. 142 has Frattini factor [ 378, 53 ]. 143 has Frattini factor [ 378, 54 ]. 144 has Frattini factor [ 378, 55 ]. 145 has Frattini factor [ 378, 56 ]. 146 has Frattini factor [ 378, 57 ]. 147 has Frattini factor [ 378, 58 ]. 148 has Frattini factor [ 378, 59 ]. 149 has Frattini factor [ 378, 60 ]. 150 - 189 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.