Summary In this project, we show the wreath product of groups containing the Linear group . Also, we give permutational generating sets of and . We show that and can be generated using . We also show that and can be generated using the wreath product . In addition, we give symmetric permutational generating sets of and . We show how to generate and symmetrically using . Moreover, we show how to generate . We also show that and can be generated using . We show how to generate . We also show that and can be generated using . Finally, we show how to generate . We also show that and can be generated using .