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
C₄×S₃×F₅		60	8	C4xS3xF5	480,994

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

extension	φ:Q→Out N	d	ρ	Label	ID
(C₄×F₅)⋊₁S₃ = D₁₂⋊₂F₅	φ: S₃/C₃ → C₂ ⊆ Out C₄×F₅	120	8-	(C4xF5):1S3	480,232
(C₄×F₅)⋊₂S₃ = D₆₀⋊₅C₄	φ: S₃/C₃ → C₂ ⊆ Out C₄×F₅	120	8+	(C4xF5):2S3	480,234
(C₄×F₅)⋊₃S₃ = F₅×D₁₂	φ: S₃/C₃ → C₂ ⊆ Out C₄×F₅	60	8+	(C4xF5):3S3	480,995
(C₄×F₅)⋊₄S₃ = (C₄×S₃)⋊F₅	φ: S₃/C₃ → C₂ ⊆ Out C₄×F₅	120	8	(C4xF5):4S3	480,985

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 = F₅×Dic₆	φ: S₃/C₃ → C₂ ⊆ Out C₄×F₅	120	8-	(C4xF5).1S3	480,982
(C₄×F₅).₂S₃ = C₃₀.₃C₄²	φ: S₃/C₃ → C₂ ⊆ Out C₄×F₅	120	8	(C4xF5).2S3	480,225
(C₄×F₅).₃S₃ = F₅×C₃⋊C₈	φ: trivial image	120	8	(C4xF5).3S3	480,223

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁