Extensions 1→N→G→Q→1 with N=C₃₀ and Q=S₃

Direct product G=N×Q with N=C₃₀ and Q=S₃

		d	ρ	Label	ID
S₃×C₃₀		60	2	S3xC30	180,33

Semidirect products G=N:Q with N=C₃₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃₀⋊₁S₃ = C₂×C₃⋊D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₃₀	90		C30:1S3	180,36
C₃₀⋊₂S₃ = C₆×D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₃₀	60	2	C30:2S3	180,34
C₃₀⋊₃S₃ = C₁₀×C₃⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃₀	90		C30:3S3	180,35

Non-split extensions G=N.Q with N=C₃₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃₀.₁S₃ = Dic₄₅	φ: S₃/C₃ → C₂ ⊆ Aut C₃₀	180	2-	C30.1S3	180,3
C₃₀.₂S₃ = D₉₀	φ: S₃/C₃ → C₂ ⊆ Aut C₃₀	90	2+	C30.2S3	180,11
C₃₀.₃S₃ = C₃⋊Dic₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₃₀	180		C30.3S3	180,17
C₃₀.₄S₃ = C₃×Dic₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₃₀	60	2	C30.4S3	180,15
C₃₀.₅S₃ = C₅×Dic₉	φ: S₃/C₃ → C₂ ⊆ Aut C₃₀	180	2	C30.5S3	180,1
C₃₀.₆S₃ = C₁₀×D₉	φ: S₃/C₃ → C₂ ⊆ Aut C₃₀	90	2	C30.6S3	180,10
C₃₀.₇S₃ = C₅×C₃⋊Dic₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃₀	180		C30.7S3	180,16
C₃₀.₈S₃ = Dic₃×C₁₅	central extension (φ=1)	60	2	C30.8S3	180,14

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