Groups of order 10

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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

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 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.