The projective general special linear group $PSL(n)$ (in some dimension $n$ and over some coefficients) is the quotient group of the special linear group $SL(n)$ by its center.
there is an exceptional isomorphism between the rotational icosahedral group $I$ and the projectiver special linear group in dimension 2 with coefficients in a prime field: $I \simeq PSL_2(\mathbb{F}_5)$ (this Prop.)
the automorphism group of the Fano plane is $\simeq PSL(2,\mathbb{F}_7)$ (…)
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