Inner automorphism group of wreath product of Z2 and A4

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This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation theory, subgroup structure) about this group
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This group is defined in the following equivalent ways:

  1. It is the inner automorphism group of the wreath product of Z2 and A4.

GAP implementation

Group ID

This finite group has order 96 and has ID 70 among the groups of order 96 in GAP's SmallGroup library. For context, there are 231 groups of order 96. 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 G:

gap> G := SmallGroup(96,70);

Conversely, to check whether a given group G is in fact the group we want, we can use GAP's IdGroup function:

IdGroup(G) = [96,70]

or just do:


to have GAP output the group ID, that we can then compare to what we want.

Other descriptions

Description Functions used
InnerAutomorphismsAutomorphismGroup(AutomorphismGroup(WreathProduct(CyclicGroup(2),AlternatingGroup(4)))) InnerAutomorphismsAutomorphismGroup, GAP:AutomorphismGroup, WreathProduct, CyclicGroup, AlternatingGroup