Double cover of alternating group:A8

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]

VIEW FACTS ABOUT THIS GROUP: All factsGroup property satisfactionsSubgroup property satisfactionsGroup property dissatisfactionsSubgroup property satisfactions
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

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