# General linear group:GL(2,Z9)

From Groupprops

This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this groupView a complete list of particular groups (this is a very huge list!)[SHOW MORE]

## Contents

## Definition

This group can be defined in the following equivalent ways:

- It is the group or , i.e., the general linear group of degree two over the ring of integers modulo .
- It is the group , i.e., the general linear group of degree two over the ring .

Note that although the rings in question are different, the corresponding general linear groups are isomorphic.

## Arithmetic functions

Want to compare and contrast arithmetic function values with other groups of the same order? Check out groups of order 3888#Arithmetic functions

### Basic arithmetic functions

Function | Value | Similar groups | Explanation |
---|---|---|---|

order (number of elements, equivalently, cardinality or size of underlying set) | 3888 | groups with same order | As , a discrete valuation ring of length with residue field of size : |

exponent of a group | 72 | groups with same order and exponent of a group | groups with same exponent of a group | |

nilpotency class | -- | not a nilpotent group | |

derived length | 4 | groups with same order and derived length | groups with same derived length |

## GAP implementation

### Other descriptions

Description | Functions used |
---|---|

GL(2,ZmodnZ(9)) |
GL and ZmodnZ |