Extensions 1→N→G→Q→1 with N=C₃₀ and Q=D₇

Direct product G=NxQ with N=C₃₀ and Q=D₇

		d	ρ	Label	ID
D₇xC₃₀		210	2	D7xC30	420,34

Semidirect products G=N:Q with N=C₃₀ and Q=D₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃₀:₁D₇ = D₂₁₀	φ: D₇/C₇ → C₂ ⊆ Aut C₃₀	210	2+	C30:1D7	420,40
C₃₀:₂D₇ = C₆xD₃₅	φ: D₇/C₇ → C₂ ⊆ Aut C₃₀	210	2	C30:2D7	420,36
C₃₀:₃D₇ = C₁₀xD₂₁	φ: D₇/C₇ → C₂ ⊆ Aut C₃₀	210	2	C30:3D7	420,38

Non-split extensions G=N.Q with N=C₃₀ and Q=D₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃₀.₁D₇ = Dic₁₀₅	φ: D₇/C₇ → C₂ ⊆ Aut C₃₀	420	2-	C30.1D7	420,11
C₃₀.₂D₇ = C₃xDic₃₅	φ: D₇/C₇ → C₂ ⊆ Aut C₃₀	420	2	C30.2D7	420,7
C₃₀.₃D₇ = C₅xDic₂₁	φ: D₇/C₇ → C₂ ⊆ Aut C₃₀	420	2	C30.3D7	420,9
C₃₀.₄D₇ = C₁₅xDic₇	central extension (φ=1)	420	2	C30.4D7	420,5

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