Double cover of alternating group:A7

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Definition

This group is defined as the double cover of alternating group where the alternating group is alternating group:A7, i.e., has degree 7. More explicitly, it is the unique stem extension with base normal subgroup cyclic group:Z2 and quotient group alternating group:A7.

Arithmetic functions

Want to compare and contrast arithmetic function values with other groups of the same order? Check out groups of order 5040#Arithmetic functions

Function	Value	Similar groups	Explanation
order (number of elements, equivalently, cardinality or size of underlying set)	5040	groups with same order	As $2\cdot A_{n},n=7$: The order is $2(n!/2)=n!$, which is $7!=5040$.

GAP implementation

Description	Functions used
PerfectGroup(5040,1)	PerfectGroup