Central product of SL(2,5) and SL(2,7)

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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 central product of special linear group:SL(2,5) (order 120) and special linear group:SL(2,7) (order 336) where we perform the unique identification of the centers of these two groups with each other.

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	Using the product formula, we get $|SL(2,5)||SL(2,7)|/2$ where the "2" comes because that's the order of the subgroup identified. This gives $120 * 336/2 = 20160$.

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	Yes
perfect group	Yes

GAP implementation

Description	Functions used
PerfectGroup(20160,3)	PerfectGroup