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 |