Groups of order 1500

Statistics at a glance
The order 1500 has the following prime factorization:

$$\! 1500 = 2^2 \cdot 3^1 \cdot 5^3 = 4 \cdot 3 \cdot 125$$

GAP implementation
gap> SmallGroupsInformation(1500);

There are 174 groups of order 1500. 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 has Frattini factor [ 150, 5 ]. 14 has Frattini factor [ 150, 6 ]. 15 has Frattini factor [ 150, 7 ]. 16 - 19 have Frattini factor [ 150, 8 ]. 20 - 21 have Frattini factor [ 150, 9 ]. 22 - 24 have Frattini factor [ 150, 10 ]. 25 - 28 have Frattini factor [ 150, 11 ]. 29 - 30 have Frattini factor [ 150, 12 ]. 31 - 33 have Frattini factor [ 150, 13 ]. 34 has Frattini factor [ 300, 22 ]. 35 has Frattini factor [ 300, 23 ]. 36 has Frattini factor [ 300, 24 ]. 37 has Frattini factor [ 300, 25 ]. 38 has Frattini factor [ 300, 26 ]. 39 has Frattini factor [ 300, 27 ]. 40 - 43 have Frattini factor [ 300, 28 ]. 44 - 46 have Frattini factor [ 300, 29 ]. 47 - 48 have Frattini factor [ 300, 30 ]. 49 - 50 have Frattini factor [ 300, 31 ]. 51 - 54 have Frattini factor [ 300, 32 ]. 55 - 57 have Frattini factor [ 300, 33 ]. 58 - 59 have Frattini factor [ 300, 34 ]. 60 - 61 have Frattini factor [ 300, 35 ]. 62 - 63 have Frattini factor [ 300, 36 ]. 64 - 67 have Frattini factor [ 300, 37 ]. 68 - 69 have Frattini factor [ 300, 38 ]. 70 - 72 have Frattini factor [ 300, 39 ]. 73 - 74 have Frattini factor [ 300, 40 ]. 75 has Frattini factor [ 300, 41 ]. 76 - 78 have Frattini factor [ 300, 42 ]. 79 has Frattini factor [ 300, 43 ]. 80 - 83 have Frattini factor [ 300, 44 ]. 84 - 85 have Frattini factor [ 300, 45 ]. 86 - 88 have Frattini factor [ 300, 46 ]. 89 - 92 have Frattini factor [ 300, 47 ]. 93 - 94 have Frattini factor [ 300, 48 ]. 95 - 97 have Frattini factor [ 300, 49 ]. 98 has Frattini factor [ 750, 26 ]. 99 has Frattini factor [ 750, 27 ]. 100 has Frattini factor [ 750, 28 ]. 101 has Frattini factor [ 750, 29 ]. 102 has Frattini factor [ 750, 30 ]. 103 has Frattini factor [ 750, 31 ]. 104 has Frattini factor [ 750, 32 ]. 105 has Frattini factor [ 750, 33 ]. 106 has Frattini factor [ 750, 34 ]. 107 has Frattini factor [ 750, 35 ]. 108 has Frattini factor [ 750, 36 ]. 109 has Frattini factor [ 750, 37 ]. 110 has Frattini factor [ 750, 38 ]. 111 has Frattini factor [ 750, 39 ]. 112 - 174 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 5 of the SmallGroups library. IdSmallGroup is available for this size.