Double cover of alternating group:A8

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Definition

The double cover of alternating group:A8, denoted $2 \cdot A_8$, is defined as the double cover of alternating group for alternating group:A8. It is the unique Schur covering group for alternating group:A8, whose Schur multiplier is cyclic group:Z2.

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 for function value
order (number of elements, equivalently, cardinality or size of underlying set)	40320	groups with same order	As $2 \cdot A_n, n = 8$: $2(n!)/2 = n! = 8! = 40320$

GAP implementation

Description	Functions used
PerfectGroup(40320,3)	PerfectGroup
SchurCover(AlternatingGroup(8))	SchurCover, AlternatingGroup