Groups of order 58

This article gives information about, and links to more details on, groups of order 58
See pages on algebraic structures of order 58 | See pages on groups of a particular order

There are, up to isomorphism, two groups of order 58, indicated in the table below:

Group	GAP ID (second part)	Abelian?
dihedral group:D58	1	No
cyclic group:Z58	2	Yes

That these are the only two possibilities can be shown via the classification of groups of an order two times a prime, or more generally the classification of groups of order a product of two distinct primes. Since $58=29\cdot 2$ and $2\mid (29-1)$, the number $58$ falls in the two isomorphism classes case in that classification.