Extensions 1→N→G→Q→1 with N=C₄ and Q=Dic₂₀

Direct product G=N×Q with N=C₄ and Q=Dic₂₀

		d	ρ	Label	ID
C₄×Dic₂₀		320		C4xDic20	320,325

Semidirect products G=N:Q with N=C₄ and Q=Dic₂₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊₁Dic₂₀ = C₂₀⋊₄Q₁₆	φ: Dic₂₀/C₄₀ → C₂ ⊆ Aut C₄	320		C4:1Dic20	320,326
C₄⋊₂Dic₂₀ = C₄⋊Dic₂₀	φ: Dic₂₀/Dic₁₀ → C₂ ⊆ Aut C₄	320		C4:2Dic20	320,476

Non-split extensions G=N.Q with N=C₄ and Q=Dic₂₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁Dic₂₀ = C₈₀⋊₁₃C₄	φ: Dic₂₀/C₄₀ → C₂ ⊆ Aut C₄	320		C4.1Dic20	320,62
C₄.₂Dic₂₀ = C₈₀⋊₁₄C₄	φ: Dic₂₀/C₄₀ → C₂ ⊆ Aut C₄	320		C4.2Dic20	320,63
C₄.₃Dic₂₀ = C₂₀.₁₄Q₁₆	φ: Dic₂₀/C₄₀ → C₂ ⊆ Aut C₄	320		C4.3Dic20	320,308
C₄.₄Dic₂₀ = C₄₀⋊₈Q₈	φ: Dic₂₀/C₄₀ → C₂ ⊆ Aut C₄	320		C4.4Dic20	320,309
C₄.₅Dic₂₀ = C₄.Dic₂₀	φ: Dic₂₀/Dic₁₀ → C₂ ⊆ Aut C₄	320		C4.5Dic20	320,39
C₄.₆Dic₂₀ = C₂₀.₄₇D₈	φ: Dic₂₀/Dic₁₀ → C₂ ⊆ Aut C₄	320		C4.6Dic20	320,40
C₄.₇Dic₂₀ = C₂₀.₇Q₁₆	φ: Dic₂₀/Dic₁₀ → C₂ ⊆ Aut C₄	320		C4.7Dic20	320,477
C₄.₈Dic₂₀ = Dic₁₀⋊₃C₈	central extension (φ=1)	320		C4.8Dic20	320,14
C₄.₉Dic₂₀ = C₄₀⋊₅C₈	central extension (φ=1)	320		C4.9Dic20	320,16

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