# Difference between revisions of "Direct product of SL(2,5) and PSL(3,2)"

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! Function !! Value !! Similar groups !! Explanation | ! Function !! Value !! Similar groups !! Explanation | ||

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− | | {{arithmetic function value order| | + | | {{arithmetic function value order|20160}} || [[order of direct product is product of orders]], so the order is <math>120 \times 168 = 20160</math> |

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## Revision as of 21:15, 21 May 2012

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]

## Definition

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

- The group , i.e., special linear group:SL(2,5) (order 120), which is also the double cover of alternating group:A5.
- The group , i.e., projective special linear group:PSL(3,2) (order 168), which is also the projective special linear group of degree two over field:F7, i.e., the group .

## Arithmetic functions

Want to compare and contrast arithmetic function values with other groups of the same order? Check out groups of order 20160#Arithmetic functions

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

order (number of elements, equivalently, cardinality or size of underlying set) | 20160 | 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 | |

perfect group | Yes |

## GAP implementation

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

DirectProduct(SL(2,5),PSL(3,2)) |
DirectProduct, SL, PSL |

PerfectGroup(20160,2) |
PerfectGroup |