Groups of order 360

Factorization and useful forms
The number 360 has prime factorization:

$$360 = 2^3 \cdot 3^2 \cdot 5^1 = 8 \cdot 9 \cdot 5$$

Other expressions for this number are:

$$360 = 6!/2 = (9^3 - 9)/2 = 2^4(2^2 - 1)(2^4 - 1)/2$$

GAP implementation
gap> SmallGroupsInformation(360);

There are 162 groups of order 360. They are sorted by their Frattini factors. 1 has Frattini factor [ 30, 1 ]. 2 has Frattini factor [ 30, 2 ]. 3 has Frattini factor [ 30, 3 ]. 4 has Frattini factor [ 30, 4 ]. 5 has Frattini factor [ 60, 6 ]. 6 has Frattini factor [ 60, 7 ]. 7 - 13 have Frattini factor [ 60, 8 ]. 14 has Frattini factor [ 60, 9 ]. 15 - 19 have Frattini factor [ 60, 10 ]. 20 - 24 have Frattini factor [ 60, 11 ]. 25 - 29 have Frattini factor [ 60, 12 ]. 30 - 32 have Frattini factor [ 60, 13 ]. 33 has Frattini factor [ 90, 5 ]. 34 has Frattini factor [ 90, 6 ]. 35 has Frattini factor [ 90, 7 ]. 36 has Frattini factor [ 90, 8 ]. 37 has Frattini factor [ 90, 9 ]. 38 has Frattini factor [ 90, 10 ]. 39 has Frattini factor [ 120, 36 ]. 40 has Frattini factor [ 120, 37 ]. 41 has Frattini factor [ 120, 38 ]. 42 has Frattini factor [ 120, 39 ]. 43 has Frattini factor [ 120, 40 ]. 44 has Frattini factor [ 120, 41 ]. 45 has Frattini factor [ 120, 42 ]. 46 has Frattini factor [ 120, 43 ]. 47 has Frattini factor [ 120, 44 ]. 48 has Frattini factor [ 120, 45 ]. 49 has Frattini factor [ 120, 46 ]. 50 has Frattini factor [ 120, 47 ]. 51 has Frattini factor [ 180, 19 ]. 52 has Frattini factor [ 180, 20 ]. 53 has Frattini factor [ 180, 21 ]. 54 has Frattini factor [ 180, 22 ]. 55 has Frattini factor [ 180, 23 ]. 56 has Frattini factor [ 180, 24 ]. 57 has Frattini factor [ 180, 25 ]. 58 - 64 have Frattini factor [ 180, 26 ]. 65 - 71 have Frattini factor [ 180, 27 ]. 72 - 76 have Frattini factor [ 180, 28 ]. 77 - 83 have Frattini factor [ 180, 29 ]. 84 - 88 have Frattini factor [ 180, 30 ]. 89 has Frattini factor [ 180, 31 ]. 90 - 94 have Frattini factor [ 180, 32 ]. 95 - 99 have Frattini factor [ 180, 33 ]. 100 - 104 have Frattini factor [ 180, 34 ]. 105 - 109 have Frattini factor [ 180, 35 ]. 110 - 114 have Frattini factor [ 180, 36 ]. 115 - 117 have Frattini factor [ 180, 37 ]. 118 - 162 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.