The magnetic properties of a β-Mn-type alloy Co7Zn8Mn5, which is a chiral magnet hosting skyrmion phase, are comprehensively investigated, exhibiting a ferromagnetic transition around 184 K and a spin freezing near 20 K. The generated Rhodes-Wolfarth ratio (RWR) equals 1.10, which indicates a weak itinerant character of the ferromagnetism in Co7Zn8Mn5. The spin dynamics of the spin freezing agrees with the universal scaling law of critical slowing down with τ0
= 1.7 × 10−5 s, Tg
= 20.2 K, and zν = 3.92. Critical exponents β = 0.423(1) and γ = 1.366(4) are deduced by the modified Arrott plot, whereas δ = 4.22(2) is obtained by a critical isotherm analysis. The validity of the deduced critical exponents is verified by the Widom scaling relation and the scaling hypothesis. The boundary between the first-order and the second-order phase transition is evaluated by a scaling analysis. The magnetic interaction, obtained by a renormalization group theory, decays with distance r as J(r) ≈ r−4.9
, lying between the mean-field model and the 3D Heisenberg model. The analyses on critical behavior could shed new light on the origin of ferromagnetism and topological Hall effect. Moreover, the magnetic entropy change −∆SM
exhibits a maximal value around TC
, and the peak position gradually raises with an increasing fields, eliminating the mean-field model. The −∆SM
max
features a power-law behavior with n > 2/3, excluding any universal standard models of ferromagnetism. The −∆SM(T,H) plots can be scaled into a universal curve, further verifying the reliability and accuracy of the yielded critical exponents.