Extensions 1→N→G→Q→1 with N=C₄×D₅ and Q=S₃

Direct product G=N×Q with N=C₄×D₅ and Q=S₃

		d	ρ	Label	ID
C₄×S₃×D₅		60	4	C4xS3xD5	240,135

Semidirect products G=N:Q with N=C₄×D₅ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(C₄×D₅)⋊₁S₃ = D₁₂⋊₅D₅	φ: S₃/C₃ → C₂ ⊆ Out C₄×D₅	120	4-	(C4xD5):1S3	240,133
(C₄×D₅)⋊₂S₃ = C₁₂.₂₈D₁₀	φ: S₃/C₃ → C₂ ⊆ Out C₄×D₅	120	4+	(C4xD5):2S3	240,134
(C₄×D₅)⋊₃S₃ = D₅×D₁₂	φ: S₃/C₃ → C₂ ⊆ Out C₄×D₅	60	4+	(C4xD5):3S3	240,136
(C₄×D₅)⋊₄S₃ = D₆.D₁₀	φ: S₃/C₃ → C₂ ⊆ Out C₄×D₅	120	4	(C4xD5):4S3	240,132

Non-split extensions G=N.Q with N=C₄×D₅ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(C₄×D₅).₁S₃ = D₅×Dic₆	φ: S₃/C₃ → C₂ ⊆ Out C₄×D₅	120	4-	(C4xD5).1S3	240,125
(C₄×D₅).₂S₃ = C₂₀.₃₂D₆	φ: S₃/C₃ → C₂ ⊆ Out C₄×D₅	120	4	(C4xD5).2S3	240,10
(C₄×D₅).₃S₃ = C₁₂.F₅	φ: S₃/C₃ → C₂ ⊆ Out C₄×D₅	120	4	(C4xD5).3S3	240,119
(C₄×D₅).₄S₃ = C₆₀⋊C₄	φ: S₃/C₃ → C₂ ⊆ Out C₄×D₅	60	4	(C4xD5).4S3	240,121
(C₄×D₅).₅S₃ = C₆₀.C₄	φ: S₃/C₃ → C₂ ⊆ Out C₄×D₅	120	4	(C4xD5).5S3	240,118
(C₄×D₅).₆S₃ = C₄×C₃⋊F₅	φ: S₃/C₃ → C₂ ⊆ Out C₄×D₅	60	4	(C4xD5).6S3	240,120
(C₄×D₅).₇S₃ = D₅×C₃⋊C₈	φ: trivial image	120	4	(C4xD5).7S3	240,7

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁