# Triple cover of alternating group:A7

From Groupprops

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## Definition

This group, termed the **triple cover of alternating group:A7**, and denoted , is defined in the following equivalent ways:

- It is the unique quasisimple group whose center is isomorphic to cyclic group:Z3 and inner automorphism group is alternating group:A7.
- 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 : |

## GAP implementation

Description | Functions used |
---|---|

PerfectGroup(7560,1) or simply PerfectGroup(7560) |
PerfectGroup |