# Endomorphism structure of alternating group:A4

From Groupprops

This article gives specific information, namely, endomorphism structure, about a particular group, namely: alternating group:A4.

View endomorphism structure of particular groups | View other specific information about alternating group:A4

## Summary of information

Construct | Value | Order | Second part of GAP ID (if group) |
---|---|---|---|

endomorphism monoid | ? | 33 | -- |

automorphism group | symmetric group:S4 | 24 | 12 |

inner automorphism group | alternating group:A4 | 12 | 3 |

outer automorphism group | cyclic group:Z2 | 2 | 1 |

extended automorphism group | direct product of S4 and Z2 | 48 | 48 |

## Family contexts

Family name | Parameter value | General discussion of endomorphism structure of family |
---|---|---|

alternating group | degree , i.e., the group | endomorphism structure of alternating groups |

projective special linear group of degree two | field:F3, i.e., the group | endomorphism structure of projective special linear group of degree two over a finite field |