Direct product of A4 and A4
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This group is defined as the external direct product of alternating group:A4 and alternating group:A4 (i.e., two copies of the same group). Equivalently, it is the square (in the direct power sense) of alternating group:A4.
This finite group has order 144 and has ID 184 among the groups of order 144 in GAP's SmallGroup library. For context, there are 197 groups of order 144. 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(144,184);
Conversely, to check whether a given group is in fact the group we want, we can use GAP's IdGroup function:
IdGroup(G) = [144,184]
or just do:
to have GAP output the group ID, that we can then compare to what we want.