# Double coset index of a subgroup

## Contents

## Definition

### Symbol-free definition

The **double coset index** of a subgroup in a group is the cardinality of its double coset space, or equivalently, the number of double cosets the subgroup has.

The **double coset index** of a subgroup in a group is the cardinality of its double coset space, or equivalently, the number of double cosets the subgroup has.