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

From Groupprops
Jump to: navigation, search
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 group
View a complete list of particular groups (this is a very huge list!)[SHOW MORE]


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