Examples for

Finite Groups

A finite group is a finite set of elements with an associated group operation. The set is a group if it is closed and associative with respect to the operation on the set, and the set contains the identity and the inverse of every element in the set. Finite groups can be classified using a variety of properties, such as simple, complex, cyclic and Abelian. The study of groups is called group theory.
Finite Groups

Find information about a finite group of a given order or type.

Get information about a finite group:

quaternion group
alternating group A_5
symmetric group S3

Ask about a property of a group:

order of the monster group

Find groups of a specified order:

groups of order 12

Find the number of groups of a given order:

number of groups of order 120
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Permutations

Find information and perform operations on permutations.

Compute properties of a permutation:

permutation (1 3 5)(2 4)(6 7 8)

Do algebra with permutations:

perm (1 2 3 4)^3(1 2 3)^-1

Generate a random permutation:

random permutation on 15 elements
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