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We first describe the Sekine quantum groups ${𝒜}_k$ (the finite-dimensional Kac algebra of Kac-Paljutkin type) by generators and relations explicitly, which maybe convenient for further study. Then we classify all irreducible representations of ${𝒜}_k$ and describe their representation rings $r\left({𝒜}_k\right)$. Finally, we compute the the Frobenius-Perron dimension of the Casimir element and the Casimir number of $r\left({𝒜}_k\right)$.