# Triple cover of alternating group:A7

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## Definition

This group, termed the triple cover of alternating group:A7, and denoted $3 \cdot A_7$, is defined in the following equivalent ways:

1. It is the unique quasisimple group whose center is isomorphic to cyclic group:Z3 and inner automorphism group is alternating group:A7.
2. It is the quotient of the Schur cover of alternating group:A7 by a subgroup of order two inside its center (which is isomorphic to cyclic group:Z6).

## Arithmetic functions

Want to compare and contrast arithmetic function values with other groups of the same order? Check out groups of order 7560#Arithmetic functions

### Basic arithmetic functions

Function Value Similar groups Explanation for function value
order (number of elements, equivalently, cardinality or size of underlying set) 7560 groups with same order As $3 \cdot A_7$: $3|A_7| = 3(7!)/2 = 3(2520) = 7560$

## GAP implementation

Description Functions used
PerfectGroup(7560,1) or simply PerfectGroup(7560) PerfectGroup