Groups of order 10

This article gives information about, and links to more details on, groups of order 10
See pages on algebraic structures of order 10 | See pages on groups of a particular order

This article gives basic information comparing and contrasting groups of order 10. See also more detailed information on specific subtopics through the links:

Information type	Page summarizing information for groups of order 10
element structure (element orders, conjugacy classes, etc.)	element structure of groups of order 10
subgroup structure	subgroup structure of groups of order 10
linear representation theory	linear representation theory of groups of order 10 projective representation theory of groups of order 10 modular representation theory of groups of order 10
endomorphism structure, automorphism structure	endomorphism structure of groups of order 10
group cohomology	group cohomology of groups of order 10

There are, up to isomorphism, two groups of order 10, indicated in the table below:

Group	GAP ID (second part)	Abelian?
dihedral group:D10	1	No
cyclic group:Z10	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 $10=5\cdot 2$ and $2\mid (5-1)$, the number $10$ falls in the two isomorphism classes case in that classification.