How do I prove that $\sum^t_i S_{N_i} \wr D_{m_i}$ is a non-Abelian group?
Here, $i, N_i, m_i$ are positive integers, $S_{N_i}$ is the symmetric group over $N_i$ symbols, $D_{m_i}$ is the dihedral group of order $2 m_i$.
How do I prove that $\sum^t_i S_{N_i} \wr D_{m_i}$ is a non-Abelian group?
Here, $i, N_i, m_i$ are positive integers, $S_{N_i}$ is the symmetric group over $N_i$ symbols, $D_{m_i}$ is the dihedral group of order $2 m_i$.
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