Groups of order 540

Statistics at a glance
The order 540 has prime factorization:

$$\! 540 = 2^2 \cdot 3^3 \cdot 5^1 = 4 \cdot 27 \cdot 5$$

GAP implementation
gap> SmallGroupsInformation(540);

There are 119 groups of order 540. 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 has Frattini factor [ 60, 8 ]. 8 has Frattini factor [ 60, 9 ]. 9 has Frattini factor [ 60, 10 ]. 10 has Frattini factor [ 60, 11 ]. 11 has Frattini factor [ 60, 12 ]. 12 has Frattini factor [ 60, 13 ]. 13 - 15 have Frattini factor [ 90, 5 ]. 16 - 19 have Frattini factor [ 90, 6 ]. 20 - 23 have Frattini factor [ 90, 7 ]. 24 - 25 have Frattini factor [ 90, 8 ]. 26 - 27 have Frattini factor [ 90, 9 ]. 28 - 30 have Frattini factor [ 90, 10 ]. 31 has Frattini factor [ 180, 19 ]. 32 - 34 have Frattini factor [ 180, 20 ]. 35 - 38 have Frattini factor [ 180, 21 ]. 39 - 40 have Frattini factor [ 180, 22 ]. 41 has Frattini factor [ 180, 23 ]. 42 has Frattini factor [ 180, 24 ]. 43 has Frattini factor [ 180, 25 ]. 44 - 47 have Frattini factor [ 180, 26 ]. 48 - 49 have Frattini factor [ 180, 27 ]. 50 - 51 have Frattini factor [ 180, 28 ]. 52 - 54 have Frattini factor [ 180, 29 ]. 55 - 56 have Frattini factor [ 180, 30 ]. 57 - 61 have Frattini factor [ 180, 31 ]. 62 - 64 have Frattini factor [ 180, 32 ]. 65 - 68 have Frattini factor [ 180, 33 ]. 69 - 72 have Frattini factor [ 180, 34 ]. 73 - 74 have Frattini factor [ 180, 35 ]. 75 - 76 have Frattini factor [ 180, 36 ]. 77 - 79 have Frattini factor [ 180, 37 ]. 80 has Frattini factor [ 270, 23 ]. 81 has Frattini factor [ 270, 24 ]. 82 has Frattini factor [ 270, 25 ]. 83 has Frattini factor [ 270, 26 ]. 84 has Frattini factor [ 270, 27 ]. 85 has Frattini factor [ 270, 28 ]. 86 has Frattini factor [ 270, 29 ]. 87 has Frattini factor [ 270, 30 ]. 88 - 119 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.