I know if G is a group, H is a subgroup of G, and g is an element of G

gH= {gh: h an element of H} is a left coset of H in G

But just cant apply to the Questions Help me !

Thanks

1) consider the element X=(1423) ∈ S₄

ⅰ) Write down the elements of <X>

ⅱ)Write down the elements of the left coset<12><X>

ⅲ)Write down the elements of the left coset<123><X>

ⅳ)Determine the index [S₄: (X)]