Schur cover of alternating group:A7

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Definition

This group, termed the Schur cover of alternating group:A7 and sometimes denoted $6\cdot A_{7}$, is defined in the following equivalent ways:

1. It is the unique quasisimple group with center cyclic group:Z6 and quotient group alternating group:A7.
2. It is the Schur covering group of 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 15120#Arithmetic functions

Function	Value	Similar groups	Explanation
order (number of elements, equivalently, cardinality or size of underlying set)	15120	groups with same order	As the Schur covering group of $A_{6}$: order of Schur multiplier of $A_{7}$ (which is 6) times order of $A_{7}$ (which is $7!/2=2520$)

GAP implementation

Description	Functions used
SchurCover(AlternatingGroup(7))	SchurCover, AlternatingGroup
PerfectGroup(15120,1)	PerfectGroup