Exercise · ZW-INDEX-OF-A-SUBGROUP-008 · ★★☆ Intermediate
Let \(H=\langle(1\ 2\ 3)\rangle\), of order \(3\), in \(S_4\). How many distinct left cosets does \(H\) have?
Choose one option.
Show answer
- A. \(8\)
Explanation
Since \(|S_4|=24\) and \(|H|=3\), the number of cosets is \(24/3=8\). It is not \(3\), which is the size of each coset.
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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