Groups of order 660
This article gives information about, and links to more details on, groups of order 660
See pages on algebraic structures of order 660| See pages on groups of a particular order
Statistics at a glance
The number 660 has the prime factorization:
There are both solvable and non-solvable groups of this order (see the table below).
The order 660 is part of GAP's SmallGroup library. Hence, any group of order 660 can be constructed using the SmallGroup function by specifying its group ID. Also, IdGroup is available, so the group ID of any group of this order can be queried.
Further, the collection of all groups of order 660 can be accessed as a list using GAP's AllSmallGroups function.
Here is GAP's summary information about how it stores groups of this order, accessed using GAP's SmallGroupsInformation function:
gap> SmallGroupsInformation(660); There are 40 groups of order 660. They are sorted by their Frattini factors. 1 has Frattini factor [ 330, 1 ]. 2 has Frattini factor [ 330, 2 ]. 3 has Frattini factor [ 330, 3 ]. 4 has Frattini factor [ 330, 4 ]. 5 has Frattini factor [ 330, 5 ]. 6 has Frattini factor [ 330, 6 ]. 7 has Frattini factor [ 330, 7 ]. 8 has Frattini factor [ 330, 8 ]. 9 has Frattini factor [ 330, 9 ]. 10 has Frattini factor [ 330, 10 ]. 11 has Frattini factor [ 330, 11 ]. 12 has Frattini factor [ 330, 12 ]. 13 - 40 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.