# 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