Algebraic Structures Question I am having problems understanding what this question is asking. any help would be appreciated. Thanks.
The dihedral group D8 is an 8 -element subgroup of the 24 -element symmetric group S4 .
Write down all left and right cosets of D8 in S4 and draw conclusions regarding normality of D8 in S4 .
According to your result determine NS4 (D8) .

HINT:
Represent $D_8$ with your preferred notation. Perhaps it is the group generated by $(1234)$ and $(13)$. That's ok. Then write down the 8 elements. Then multiply each on the right and on the left by elements of $S_4$, i.e. write down the right and left cosets. You can just sort of do it, and I recommend it in order to get a feel for the group. Patterns will quickly emerge, and it's not that much work.
By the way, I want to note that you should pay attention to what elements you multiply by each time. To see if it's normal, you're going to want to see if ever left coset is a right coset.
