Groups of order 486

Statistics at a glance
The number 486 has prime factors 2 and 3. The prime factorization is:

$$\! 486 = 2^1 \cdot 3^5= 2 \cdot 243$$

The 3-Sylow subgroup is a group of order $$3^5 = 243$$ and is a normal Sylow subgroup. The 2-Sylow subgroup is isomorphic to cyclic group:Z2 and the whole group is an internal semidirect product of the 3-Sylow subgroup and the 2-Sylow subgroup. There are two possibilities:


 * The group is a finite nilpotent group: In this case, it is a direct product of its 3-Sylow subgroup and its 2-Sylow subgroup.
 * The group is the semidirect product of its 3-Sylow subgroup by a subgroup of orer two generated by a non-identity automorphism.

GAP implementation
gap> SmallGroupsInformation(486);

There are 261 groups of order 486. They are sorted by their Frattini factors. 1 has Frattini factor [ 6, 1 ]. 2 has Frattini factor [ 6, 2 ]. 3 - 41 have Frattini factor [ 18, 3 ]. 42 - 61 have Frattini factor [ 18, 4 ]. 62 - 90 have Frattini factor [ 18, 5 ]. 91 - 132 have Frattini factor [ 54, 12 ]. 133 - 179 have Frattini factor [ 54, 13 ]. 180 - 189 have Frattini factor [ 54, 14 ]. 190 - 219 have Frattini factor [ 54, 15 ]. 220 - 226 have Frattini factor [ 162, 51 ]. 227 - 239 have Frattini factor [ 162, 52 ]. 240 - 246 have Frattini factor [ 162, 53 ]. 247 - 249 have Frattini factor [ 162, 54 ]. 250 - 255 have Frattini factor [ 162, 55 ]. 256 - 261 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.