Exercise · ZW-INDEX-OF-A-SUBGROUP-004 · ★☆☆ Basic
A group \(G\) of order \(60\) has a subgroup \(H\) of order \(12\). The index \([G:H]\) is:
Choose one option.
Show answer
- D. \(5\)
Explanation
All cosets have \(12\) elements and split the \(60\) elements of \(G\), so their number is \(60/12=5\).
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 \(G\).
\[[G:H]\]
More practice problems: index of a subgroup
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