Is S7 x {0} a Maximal Normal Subgroup of S7 x Z7?

[CreekGroup]

1. Is the group S₇ X {0} a maximal normal subgroup of the product group S₇ X Z₇ ?



2. No relevant equations



3. That kinda is my answer, original question was asking about S7 X Z7

 

[jbunniii]

How far have you got so far? What are your answers to the following questions?

1) Is S_7 \times \{0\} a normal subgroup of S_7 \times Z_7?

2) Are there any subgroups G such that S_7 \times \{0\} < G < S_7 \times Z_7?

3) If yes to 2), are any of the subgroups G normal?