How can we show that the subgroup of $A_7$ generated by the permutations $x= (1234567)$ and $b=(26)(34)$ has order $168$?
$PSL(2,7)$ as a subgroup of $A_7$
5
$\begingroup$
abstract-algebra
group-theory
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0Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. – 2012-12-02
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0For some basic information about writing math at this site see e.g. [here](http://meta.math.stackexchange.com/questions/5020/), [here](http://meta.stackexchange.com/a/70559/155238), [here](http://meta.math.stackexchange.com/questions/1773/) and [here](http://math.stackexchange.com/editing-help#latex). – 2012-12-02
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0related: http://math.stackexchange.com/q/1401/152 – 2012-12-03
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0related: http://math.stackexchange.com/questions/250024/element-of-order-4-in-psl2-7#comment549856_250024 – 2012-12-04