# (Non-)Morita invariance of the isomorphism type of a defect group

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The smallest pair of examples is SmallGroup(512,453) and SmallGroup(512,456). These groups have cyclic derived subgroup of order four and nilpotency class three. They have presentations $\langle x,y,z \mid z=[y,x],x^{16}=y^8=z^4=1, z^x=z^y=z^{-1} \rangle$ and $\langle x,y,z \mid z=[y,x],x^{16}=y^8=z^4=1, z^x=z^{-1}, z^y=z \rangle$ respectively.