Groups of order 110

This article gives information about, and links to more details on, groups of order 110
See pages on algebraic structures of order 110 | See pages on groups of a particular order

Statistics at a glance

The number 110 has the prime factorization:

$\!110=2\cdot 5\cdot 11$

Quantity	Value	Explanation
Total number of groups up to isomorphism	6
Number of abelian groups (i.e., finite abelian groups) up to isomorphism	1	(number of abelian groups of order $2^{1}$) times (number of abelian groups of order $5^{1}$) times (number of abelian groups of order $11^{1}$) = (number of unordered integer partitions of 1) times (number of unordered integer partitions of 1) times (number of unordered integer partitions of 1) = $1\times 1\times 1=1$. See classification of finite abelian groups and structure theorem for finitely generated abelian groups.

The list

Group	Second part of GAP ID (GAP ID is (110,second part))	abelian?
general affine group:GA(1,11)	1	No
direct product of Z2 and semidirect product of Z11 and Z5	2	No
direct product of Z11 and D10	3	No
direct product of Z5 and D22	4	No
dihedral group:D110	5	No
cyclic group:Z110	6	Yes