Extensions 1→N→G→Q→1 with N=C₄₂ and Q=D₅

Direct product G=NxQ with N=C₄₂ and Q=D₅

		d	ρ	Label	ID
D₅xC₄₂		210	2	D5xC42	420,35

Semidirect products G=N:Q with N=C₄₂ and Q=D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄₂:₁D₅ = D₂₁₀	φ: D₅/C₅ → C₂ ⊆ Aut C₄₂	210	2+	C42:1D5	420,40
C₄₂:₂D₅ = C₆xD₃₅	φ: D₅/C₅ → C₂ ⊆ Aut C₄₂	210	2	C42:2D5	420,36
C₄₂:₃D₅ = C₁₄xD₁₅	φ: D₅/C₅ → C₂ ⊆ Aut C₄₂	210	2	C42:3D5	420,39

Non-split extensions G=N.Q with N=C₄₂ and Q=D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄₂.₁D₅ = Dic₁₀₅	φ: D₅/C₅ → C₂ ⊆ Aut C₄₂	420	2-	C42.1D5	420,11
C₄₂.₂D₅ = C₃xDic₃₅	φ: D₅/C₅ → C₂ ⊆ Aut C₄₂	420	2	C42.2D5	420,7
C₄₂.₃D₅ = C₇xDic₁₅	φ: D₅/C₅ → C₂ ⊆ Aut C₄₂	420	2	C42.3D5	420,10
C₄₂.₄D₅ = Dic₅xC₂₁	central extension (φ=1)	420	2	C42.4D5	420,6

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