Groups of order 1100

Statistics at a glance
The number 1100 has prime factors 2, 5, and 11. The prime factorization is:

$$\! 1100 = 2^2 \cdot 5^2 \cdot 11^1 = 4 \cdot 25 \cdot 11$$

{| class="sortable" border="1" ! Quantity !! Value !! Explanation
 * Total number of groups up to isomorphism || count::51 ||
 * Number of abelian groups up to isomorphism || abelian count::4 || (number of abelian groups of order $$2^2$$) $$\times$$ (number of abelian groups of order $$5^2$$) $$\times$$ (number of abelian groups of order $$11^1$$) = (number of unordered integer partitions of 2) $$\times$$ (number of unordered integer partitions of 2)$$\times$$ (number of unordered integer partitions of 1) = $$2 \times 2 \times 1 = 4$$.
 * Number of nilpotent groups up to isomorphism || nilpotent count::4 || (number of groups of order 4) $$\times$$ (number of groups of order 25) $$\times$$ (number of groups of order 11) = $$2 \times 2 \times 1 = 4$$. Note that, in this case, the nilpotent groups are the same as the abelian groups, which follows from the fact that abelian implies nilpotent and nilpotent of cube-free order implies abelian.
 * Number of supersolvable groups up to isomorphism || supersolvable count::51 || All groups of the order are supersolvable.
 * Number of solvable groups up to isomorphism || solvable count::51 || All groups of the order are solvable.
 * Number of simple non-abelian groups up to isomorphism || 0 || Follows from all groups of the order being solvable.
 * Number of supersolvable groups up to isomorphism || supersolvable count::51 || All groups of the order are supersolvable.
 * Number of solvable groups up to isomorphism || solvable count::51 || All groups of the order are solvable.
 * Number of simple non-abelian groups up to isomorphism || 0 || Follows from all groups of the order being solvable.
 * Number of solvable groups up to isomorphism || solvable count::51 || All groups of the order are solvable.
 * Number of simple non-abelian groups up to isomorphism || 0 || Follows from all groups of the order being solvable.
 * Number of simple non-abelian groups up to isomorphism || 0 || Follows from all groups of the order being solvable.

GAP implementation
gap> SmallGroupsInformation(1100);

There are 51 groups of order 1100. They are sorted by their Frattini factors. 1 has Frattini factor [ 110, 1 ]. 2 has Frattini factor [ 110, 2 ]. 3 has Frattini factor [ 110, 3 ]. 4 has Frattini factor [ 110, 4 ]. 5 has Frattini factor [ 110, 5 ]. 6 has Frattini factor [ 110, 6 ]. 7 has Frattini factor [ 220, 7 ]. 8 has Frattini factor [ 220, 8 ]. 9 has Frattini factor [ 220, 9 ]. 10 has Frattini factor [ 220, 10 ]. 11 has Frattini factor [ 220, 11 ]. 12 has Frattini factor [ 220, 12 ]. 13 has Frattini factor [ 220, 13 ]. 14 has Frattini factor [ 220, 14 ]. 15 has Frattini factor [ 220, 15 ]. 16 has Frattini factor [ 550, 7 ]. 17 has Frattini factor [ 550, 8 ]. 18 has Frattini factor [ 550, 9 ]. 19 has Frattini factor [ 550, 10 ]. 20 has Frattini factor [ 550, 11 ]. 21 has Frattini factor [ 550, 12 ]. 22 has Frattini factor [ 550, 13 ]. 23 has Frattini factor [ 550, 14 ]. 24 has Frattini factor [ 550, 15 ]. 25 has Frattini factor [ 550, 16 ]. 26 - 51 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.