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- Jan 26, 2012

- 995

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**Problem**: Let $\mathbb{F}_q$ be a field with $q$ elements. How many conjugacy classes are there in $\mathrm{GL}_2(F_q)$? Use rational canonical form, considering the two cases of a cyclic $\mathbb{F}_q$-module and a non-cyclic $\mathbb{F}_q$-module separately.

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