Automorphism group of alternating group:A6
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This group is defined in the following equivalent ways:
- It is the automorphism group of alternating group:A6.
- It is the automorphism group of symmetric group:S6.
This finite group has order 1440 and has ID 5841 among the groups of order 1440 in GAP's SmallGroup library. For context, there are 5,958 groups of order 1440. It can thus be defined using GAP's SmallGroup function as:
For instance, we can use the following assignment in GAP to create the group and name it :
gap> G := SmallGroup(1440,5841);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [1440,5841]
or just do:
to have GAP output the group ID, that we can then compare to what we want.