Extensions 1→N→G→Q→1 with N=C₄⋊F₅ and Q=S₃

Direct product G=N×Q with N=C₄⋊F₅ and Q=S₃

		d	ρ	Label	ID
S₃×C₄⋊F₅		60	8	S3xC4:F5	480,996

Semidirect products G=N:Q with N=C₄⋊F₅ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
C₄⋊F₅⋊₁S₃ = D₆₀⋊C₄	φ: S₃/C₃ → C₂ ⊆ Out C₄⋊F₅	120	8+	C4:F5:1S3	480,227
C₄⋊F₅⋊₂S₃ = D₆₀⋊₃C₄	φ: S₃/C₃ → C₂ ⊆ Out C₄⋊F₅	60	8+	C4:F5:2S3	480,997
C₄⋊F₅⋊₃S₃ = C₄⋊F₅⋊₃S₃	φ: trivial image	120	8	C4:F5:3S3	480,983

Non-split extensions G=N.Q with N=C₄⋊F₅ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
C₄⋊F₅.₁S₃ = Dic₆⋊F₅	φ: S₃/C₃ → C₂ ⊆ Out C₄⋊F₅	120	8-	C4:F5.1S3	480,229
C₄⋊F₅.₂S₃ = Dic₆⋊₅F₅	φ: S₃/C₃ → C₂ ⊆ Out C₄⋊F₅	120	8-	C4:F5.2S3	480,984
C₄⋊F₅.₃S₃ = Dic₅.Dic₆	φ: S₃/C₃ → C₂ ⊆ Out C₄⋊F₅	120	8	C4:F5.3S3	480,235
C₄⋊F₅.₄S₃ = Dic₅.₄Dic₆	φ: S₃/C₃ → C₂ ⊆ Out C₄⋊F₅	120	8	C4:F5.4S3	480,236

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁