# Conway group:Co0

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, denoted or , is defined in the following equivalent ways:

- It is the automorphism group of the Leech lattice.
- It is the Schur covering group (specifically, it is a double cover) of Conway group:Co1.

Its center is cyclic group:Z2 and the inner automorphism group is Conway group:Co1.

## Arithmetic functions

### Basic arithmetic functions

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

order (number of elements, equivalently, cardinality or size of underlying set) | 8315553613086720000 | groups with same order | The order has factorization: . |

### Arithmetic functions of a counting nature

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## Group properties

Property | Satisfied? | Explanation |
---|---|---|

simple group | No | the center is nontrivial |

perfect group | Yes | |

quasisimple group | Yes | |

solvable group | No |

## Linear representation theory

`Further information: linear representation theory of Conway group:Co0`

Item | Value |
---|---|

degrees of irreducible representations over a splitting field (such as or ) | too long to list, see Linear representation theory of Conway group:Co0#GAP implementation number: 167, sum of squares: 8315553613086720000, maximum: 1021620600, quasirandom degree: 24 |

## GAP implementation

The group itself is too large to be constructed, stored and manipulated in GAP. However, information about its linear representation theory and character table is stored under the symbol "2.Co1" -- for more on this, see Linear representation theory of Conway group:Co0#GAP implementation.