# Groups of order 10

From Groupprops

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 and , the number falls in the *two isomorphism classes* case in that classification.