Groups of order 600

Statistics at a glance
The number 600 has prime factors 2, 3, and 5. The prime factorization is:

$$\! 600 = 2^3 \cdot 3 \cdot 5^2 = 8 \cdot 3 \cdot 25$$

There are both solvable and non-solvable groups of this order. For all the non-solvable groups, the unique non-abelian composition factor is alternating group:A5 (order 60), and the abelian composition factors are thus cyclic group:Z2 and cyclic group:Z5.

GAP implementation
gap> SmallGroupsInformation(600);

There are 205 groups of order 600. 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 [ 120, 36 ]. 34 has Frattini factor [ 120, 37 ]. 35 has Frattini factor [ 120, 38 ]. 36 has Frattini factor [ 120, 39 ]. 37 has Frattini factor [ 120, 40 ]. 38 has Frattini factor [ 120, 41 ]. 39 has Frattini factor [ 120, 42 ]. 40 has Frattini factor [ 120, 43 ]. 41 has Frattini factor [ 120, 44 ]. 42 has Frattini factor [ 120, 45 ]. 43 has Frattini factor [ 120, 46 ]. 44 has Frattini factor [ 120, 47 ]. 45 has Frattini factor [ 150, 5 ]. 46 has Frattini factor [ 150, 6 ]. 47 has Frattini factor [ 150, 7 ]. 48 has Frattini factor [ 150, 8 ]. 49 has Frattini factor [ 150, 9 ]. 50 has Frattini factor [ 150, 10 ]. 51 has Frattini factor [ 150, 11 ]. 52 has Frattini factor [ 150, 12 ]. 53 has Frattini factor [ 150, 13 ]. 54 has Frattini factor [ 300, 22 ]. 55 has Frattini factor [ 300, 23 ]. 56 has Frattini factor [ 300, 24 ]. 57 - 61 have Frattini factor [ 300, 25 ]. 62 - 66 have Frattini factor [ 300, 26 ]. 67 - 71 have Frattini factor [ 300, 27 ]. 72 has Frattini factor [ 300, 28 ]. 73 has Frattini factor [ 300, 29 ]. 74 has Frattini factor [ 300, 30 ]. 75 has Frattini factor [ 300, 31 ]. 76 has Frattini factor [ 300, 32 ]. 77 has Frattini factor [ 300, 33 ]. 78 has Frattini factor [ 300, 34 ]. 79 has Frattini factor [ 300, 35 ]. 80 - 84 have Frattini factor [ 300, 36 ]. 85 - 91 have Frattini factor [ 300, 37 ]. 92 - 98 have Frattini factor [ 300, 38 ]. 99 - 105 have Frattini factor [ 300, 39 ]. 106 - 110 have Frattini factor [ 300, 40 ]. 111 - 113 have Frattini factor [ 300, 41 ]. 114 has Frattini factor [ 300, 42 ]. 115 has Frattini factor [ 300, 43 ]. 116 - 120 have Frattini factor [ 300, 44 ]. 121 - 125 have Frattini factor [ 300, 45 ]. 126 - 130 have Frattini factor [ 300, 46 ]. 131 - 135 have Frattini factor [ 300, 47 ]. 136 - 140 have Frattini factor [ 300, 48 ]. 141 - 143 have Frattini factor [ 300, 49 ]. 144 - 205 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.