For more information about cyclic groups see this page.

## Cayley Table

The Cayley table is symmetric about its leading diagonal. For a cyclic group the table can be drawn with same terms on the bottom-left to top-right diagonals:

1 | a | b | c | ... | n | |

1 | 1 | a | b | c | ... | n |

a | a | b | c | ... | n | n-1 |

b | b | c | ... | n | n-1 | |

c | c | ... | n | n-1 | ||

... | ... | n | n-1 | |||

n | n | n-1 |

For more information about Cayley table see this page.

## Cayley Graph

For more information about Cayley graph see this page.

## Cyclic Notation

The group is shown as a single cycle:

(1,2,3..n)

For more information about cyclic notation see this page.

## Group Presentation

There is only one generator which when applied n times cycles back to the identity.

<a | a^{n}=1>

For more information about group presentation see this page.

## Group Representation

This is the n^{th} root of the identity matix (such that lesser roots are not identity). See this page for information about taking roots of a matrix. One a matrix which will do this is an n×n matrix of this form:

0 | 0 | … | 0 | 0 | 1 |

1 | 0 | … | 0 | 0 | 0 |

0 | 1 | … | 0 | 0 | 0 |

0 | 0 | … | 1 | 0 | 0 |

0 | 0 | … | 0 | 1 | 0 |

For more information about group representation see this page.