Exercise · ZW-INDEX-OF-A-SUBGROUP-003 · ★☆☆ Basic
The alternating group \(A_4\) has \(12\) elements and sits in \(S_4\), which has \(24\). What is \([S_4:A_4]\)?
Choose one option.
Show answer
- A. \(2\)
Explanation
There are \(24/12=2\) cosets: the even permutations and the odd ones.
Review the concept: Index of a subgroup
The index of a subgroup \(H\) of a group \(G\) is the number of distinct left cosets of \(H\) in \(G\).
\[[G:H]\]
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