Find a subgroup of $D_{42}$ that is isomorphic to $S_3$.
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$begingroup$
Note that $D_{42}$ is generated by $rho, r$ where $ord(rho) = 21$ , $ord(r)= 2$ . To locate a copy of $S_3$ , there must be a subgroup of order $3$ , which can be $e, rho^{7}, rho^{14}$ . What about order $2$ elements? Inevitably, I have to introduce some reflections which will enlarge the group.
abstract-algebra
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asked Dec 14 '18 at 17:47
koch koch
184 1 8
$endgroup$