Schur cover of alternating group:A6
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This group, termed the Schur cover of alternating group:A6 and sometimes denoted , is defined in the following equivalent ways:
- It is the unique quasisimple group with center cyclic group:Z6 and quotient group alternating group:A6.
- It is the Schur covering group of alternating group:A6.
- It is the Schur covering group of special linear group:SL(2,9).
Want to compare and contrast arithmetic function values with other groups of the same order? Check out groups of order 2160#Arithmetic functions
|order (number of elements, equivalently, cardinality or size of underlying set)||2160||groups with same order||As the Schur covering group of : order of Schur multiplier of (which is 6) times order of (which is )|
|simple group, simple non-abelian group||No||nontrivial center of order six|
|almost simple group||No|
|almost quasisimple group||Yes|
|PerfectGroup(2160) or equivalently PerfectGroup(2160,1)||PerfectGroup|