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Please, I can't find an element of the subgroup of $A_7$ generated by $a=(1234567)$ and $b=(26)(34)$ with order 4.

If anybody could give me the combination of $a$ and $b$ I need, it would be fantastic. I have tried everything I swear. I have tried to find a matrix of $SL(3,2)$ with order $4$, generated by $[0 1 1, 0 0 1, 1 1 1]$ and $[1 0 1, 0 1 0, 0 0 1]$ and use an isomorphism (other matrices don't work with my isomorphism).

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    Since Maria asked a question about this group 21 hours earlier, he/she/they are unlikely to be actually sitting an exam. It's more likely to be a take home assignment.2012-12-03

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Hint: Try $(26)(34)\circ(37)(45)$. And figure out why it belongs to the group.