Direct product of A4 and Z2

Definition
This group is defined in the following equivalent ways:


 * 1) it is the external direct product of the alternating group of degree four and the cyclic group of order two.
 * 2) It is the wreath product of the cyclic group of order two and the cyclic group of order three, acting regularly. In other words, it is the group $$\Z_2 \wr Z_3$$, or equivalently, the group $$(\Z_2 \times \Z_2 \times \Z_2) \rtimes \Z_3$$, where the latter acts on the former by cylic permutations of coordinates.

Other descriptions
The group can be defined using GAP's WreathProduct and CyclicGroup functions:

WreathProduct(CyclicGroup(2),CyclicGroup(3))

The group can be defined using GAP's DirectProduct, AlternatingGroup and CyclicGroup functions:

DirectProduct(AlternatingGroup(4),CyclicGroup(2))