Direct product of SL(2,5) and PSL(3,2)

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VIEW FACTS ABOUT THIS GROUP: All factsGroup property satisfactionsSubgroup property satisfactionsGroup property dissatisfactionsSubgroup property satisfactions
VIEW DEFINITIONS USING THIS AS EXAMPLE: All terms |Group properties |Subgroup properties|
VIEW FACTS USING THIS AS EXAMPLE: All facts |Group property non-implications |Subgroup property non-implications |Group metaproperty dissatisfactionsSubgroup metaproperty dissatisfactions

Definition

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

1. The group $SL(2,5)$, i.e., special linear group:SL(2,5) (order 120), which is also the double cover of alternating group:A5.
2. The group $PSL(3,2)$, 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 $PSL(2,7)$.

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 $120\times 168=20160$

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),PSL(3,2))	DirectProduct, SL, PSL
PerfectGroup(20160,2)	PerfectGroup