= Ree group of type G2
{c}
{title2=$ {}^{2}G_2(q),\quad q=3^{2a+1}\ge27$}
For $q=3^{2a+1}\geq27$, the small Ree group ${}^2G_2(q)$ is a twisted <finite group of Lie type>. In <characteristic three>, the <algebraic group> of <G2 root system>[type G2] has an exceptional <endomorphism> $\sigma$ with $\sigma^2=F_3$, the <Frobenius endomorphism of an algebraic group>. The fixed points of $\sigma^{2a+1}$ form ${}^2G_2(q)$. This explains both the twist and the odd exponent restriction.<On the simple groups of Suzuki and Ree by Robert A. Wilson>[Introduction, exceptional Chevalley-group automorphisms; sections 3-5]{ref}
It is simple, has order $q^3(q^3+1)(q-1)$, and acts two-transitively on $q^3+1$ points. At $q=27$ the degree is $19684$ and the order is $10073444472$. The excluded parameter $q=3$ gives a nonsimple group. The characteristic-two family ${}^2F_4(q)$ is a different Ree family.
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