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Green showed that there exist constants $C_1,C_2>0$ such that the cliquenumber $\omega$ of the random Cayley graph on $\mathbb{F}_2^n$ satisfies$\lim_{n\to\infty}\mathbb{P}(C_1n\log n < \omega < C_2n\log n)=1$. In thispaper we find the best possible $C_1$ and $C_2$. Moreover, we prove that for$n$ in a set of density $1$, clique number is actually concentrated on a singlevalue. As a simple consequence of these results, we also prove the one-pointconcentration result for the chromatic number, thus proving the$\mathbb{F}_2^n$ analogue of the famous conjecture by Bollob\'{a}s and givingalmost the complete answer to the question by Green.

One-point concentration of the clique and chromatic numbers of the random Cayley graph on F_2^n