Consider two permutation groups. The first is the subgroup of S7 generated by (1,2,3) and (4,5,6,7). The second is a subgroup of S12 generated by (1,2,3)(4,5,6)(7,8,9)(10,11,12) and (1,10,7,4)(2,11,8,5)(3,12,9,6). Build these two groups and use the proper Sage command to see that they are isomorphic. Then construct a homomorphism between these two groups that is an isomorphism and include enough details to verify that the mapping is really an isomorphism.