# Direct product of SL(2,5) and SL(2,7)

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## Definition

This group is defined as the external direct product of the following two groups:

- The group special linear group:SL(2,5) (order 120), which is also the double cover of alternating group:A5 (and also its Schur covering group).
- The group special linear group:SL(2,7) (order 336), which is also the double cover of PSL(3,2) (and also its Schur covering group).

## Arithmetic functions

Want to compare and contrast arithmetic function values with other groups of the same order? Check out groups of order 40320#Arithmetic functions

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

order (number of elements, equivalently, cardinality or size of underlying set) | 40320 | groups with same order | order of direct product is product of orders, so the order is |

## Group properties

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

abelian group | No | |

nilpotent group | No | |

solvable group | No | |

simple group, simple non-abelian group | No | |

quasisimple group | No | |

directly indecomposable group | No | |

perfect group | Yes |

## GAP implementation

Description | Functions used |
---|---|

DirectProduct(SL(2,5),SL(2,7)) |
DirectProduct, SL |

PerfectGroup(40320,1) |
PerfectGroup |