Groups of order 784

Statistics at a glance
The number 784 has prime factors 2 and 7. The prime factorization is:

$$\! 784 = 2^4 \cdot 7^2 = 16 \cdot 49$$

GAP implementation
gap> SmallGroupsInformation(784);

There are 172 groups of order 784. They are sorted by their Frattini factors. 1 has Frattini factor [ 14, 1 ]. 2 has Frattini factor [ 14, 2 ]. 3 - 18 have Frattini factor [ 28, 3 ]. 19 - 26 have Frattini factor [ 28, 4 ]. 27 - 36 have Frattini factor [ 56, 12 ]. 37 - 40 have Frattini factor [ 56, 13 ]. 41 has Frattini factor [ 98, 3 ]. 42 has Frattini factor [ 98, 4 ]. 43 has Frattini factor [ 98, 5 ]. 44 has Frattini factor [ 112, 41 ]. 45 has Frattini factor [ 112, 42 ]. 46 has Frattini factor [ 112, 43 ]. 47 has Frattini factor [ 196, 8 ]. 48 - 63 have Frattini factor [ 196, 9 ]. 64 - 79 have Frattini factor [ 196, 10 ]. 80 - 95 have Frattini factor [ 196, 11 ]. 96 - 103 have Frattini factor [ 196, 12 ]. 104 has Frattini factor [ 392, 36 ]. 105 - 109 have Frattini factor [ 392, 37 ]. 110 has Frattini factor [ 392, 38 ]. 111 - 117 have Frattini factor [ 392, 40 ]. 118 - 135 have Frattini factor [ 392, 41 ]. 136 - 145 have Frattini factor [ 392, 42 ]. 146 - 155 have Frattini factor [ 392, 43 ]. 156 - 159 have Frattini factor [ 392, 44 ]. 160 - 172 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.