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The symmetric group $\\Sigma_s$ acts on $H_*(\\Gamma_{k,s})$ by permuting leaves, and for trivial rational coefficients we compute the $\\Sigma_s$-module structure on $H_*(\\Gamma_{k,s})$ completely for $k \\leq 2$. 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The symmetric group $\\Sigma_s$ acts on $H_*(\\Gamma_{k,s})$ by permuting leaves, and for trivial rational coefficients we compute the $\\Sigma_s$-module structure on $H_*(\\Gamma_{k,s})$ completely for $k \\leq 2$. 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