# Conway group:Co1

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## Contents

## Definition

The group, denoted , is defined as the inner automorphism group of (see Conway group:Co0), which in turn is defined as the automorphism group of the Leech lattice.

Note that has a center which is isomorphic to cyclic group:Z2, with the non-identity element corresponding to the automorphism given by sending every vector to its negative. Thus, is the quotient group of by a subgroup of order two.

The group is a finite simple non-abelian group, and in fact, it is one of the 26 sporadic simple groups. It is also one of the three Conway groups.

## Arithmetic functions

### Basic arithmetic functions

Function | Value | Similar groups | Explanation for function value |
---|---|---|---|

order (number of elements, equivalently, cardinality or size of underlying set) | 4157776806543360000 | groups with same order |

### Arithmetic functions of a counting nature

Function | Value | Similar groups | Explanation for function value |
---|---|---|---|

number of conjugacy classes | 101 | groups with same order and number of conjugacy classes | groups with same number of conjugacy classes | equals number of irreducible representations, see also linear representation theory of Conway group:Co1. |

## Linear representation theory

`Further information: linear representation theory of Conway group:Co1`