# Thread: Factor groups question

1. ## Factor groups question

Basically I know how to do the first part, it's just the multiplication table giving me problems. I know the headings for the table should be H, (1,2)H, (1,3)H, (2,3)H, (1,2,3)H, (1,3,2)H but I don't know anymore.

2. Multiplication in factor groups is easy. It is defined as
$(aH)(bH) = abH$.

For example Let $G=\mathbb{Z}, H = Z\mathbb{Z}$. Since G is abelian, H is normal in G.

Consider two cosets of $4\mathbb{Z}$, $(1+ 4\mathbb{Z}) +(2+4\mathbb{Z}) = (3 + 4\mathbb{Z})$.

Now in your example, we take $[(12)H][(24)H] = (14)H$. since $(12)(24) = (14)$