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Label	Subgroup									Ambient			Quotient
	Name	Order	Sylow	norm	char	max	cent	cyc		ab	nilp		sup solv	solv	perf	simp	Agp	Zgp	metab	metacyc	Name	Order	Name	Size	max	cyc	ab	nilp	sup solv	solv	simp	Agp	metab
768.1088320.768.a1	$C_1$	$1$		✓	✓		✓	✓	✓	✓	✓	✓	✓		✓	✓	✓	✓		$D_4.\GL(2,\mathbb{Z}/4)$	$2^{8} \cdot 3$		$D_4.\GL(2,\mathbb{Z}/4)$	$2^{8} \cdot 3$						✓

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