# Schur cover of alternating group:A7

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## Definition

This group, termed the **Schur cover of alternating group:A7** 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:A7.
- 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 : order of Schur multiplier of (which is 6) times order of (which is ) |

## GAP implementation

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

SchurCover(AlternatingGroup(7)) |
SchurCover, AlternatingGroup |

PerfectGroup(15120,1) |
PerfectGroup |