[GAP Forum] normal subgroup semidirect product

[Bill Chin]

I need to know the normal subgroups of the following group G'.

G' is defined as follows.

G=symmetric group on 7 elements.

S=symmetric group on 5 elements, embedded in G as the subgroup stabilizing 6
and 7.

R = integers mod 3.

K=the free R-module with R-basis the set of right cosets of S in G.

Finally G' is the semidirect product of K by G.

Can anyone help?


Esther