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If $\\mathcal{C}$ is a conjugation-stable subset of a finite group $G$, the Killing form on $\\mathbb{C}\\mathcal{C}$ is given by $K_\\mathcal{C}(a,b) = |C_G(ab) \\cap \\mathcal{C}|$ for $a,b \\in \\mathcal{C}$. 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