I was reading about $A_4$ and $S_4$ groups and I got curious about some of the subgroups. And if we have $H:= \{(),(12)(34),(13)(24),(14)(23)\}$, how would I determine and how would the structure look like of the quotient group $A_4/H$ and is $A_4$ a simple group?
2026-03-26 17:30:24.1774546224
Structure of $A_4/H$
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$H$ is normal and the corresponding factor group is cyclic of order three.