Editing Alternating group (section)

=== ''H''<sub>2</sub>: Schur multipliers ===
{{main|Covering groups of the alternating and symmetric groups}}
The [[Schur multiplier]]s of the alternating groups A<sub>''n''</sub> (in the case where ''n'' is at least 5) are the cyclic groups of order 2, except in the case where ''n'' is either 6 or 7, in which case there is also a triple cover. In these cases, then, the Schur multiplier is (the cyclic group) of order 6.<ref name="raw">{{citation|first=Robert |last=Wilson |author-link=Robert Arnott Wilson |date=October 31, 2006 |url=http://www.maths.qmul.ac.uk/~raw/fsgs.html |title=The finite simple groups, 2006 versions |chapter=Chapter 2: Alternating groups |chapter-url=http://www.maths.qmul.ac.uk/~raw/fsgs_files/alt.ps |postscript=, 2.7: Covering groups |url-status=dead |archive-url=https://web.archive.org/web/20110522121819/http://www.maths.qmul.ac.uk/~raw/fsgs.html |archive-date=May 22, 2011 }}</ref> These were first computed in {{Harv|Schur|1911}}.

:''H''<sub>2</sub>(A<sub>''n''</sub>, Z) = Z<sub>1</sub> for ''n'' = 1, 2, 3;
:''H''<sub>2</sub>(A<sub>''n''</sub>, Z) = Z<sub>2</sub> for ''n'' = 4, 5;
:''H''<sub>2</sub>(A<sub>''n''</sub>, Z) = Z<sub>6</sub> for ''n'' = 6, 7;
:''H''<sub>2</sub>(A<sub>''n''</sub>, Z) = Z<sub>2</sub> for ''n'' ≥ 8.