Extensions 1→N→G→Q→1 with N=C₆×F₅ and Q=C₂

Direct product G=N×Q with N=C₆×F₅ and Q=C₂

		d	ρ	Label	ID
C₂×C₆×F₅		60		C2xC6xF5	240,200

Semidirect products G=N:Q with N=C₆×F₅ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₆×F₅)⋊₁C₂ = D₆⋊F₅	φ: C₂/C₁ → C₂ ⊆ Out C₆×F₅	60	8+	(C6xF5):1C2	240,96
(C₆×F₅)⋊₂C₂ = C₂×S₃×F₅	φ: C₂/C₁ → C₂ ⊆ Out C₆×F₅	30	8+	(C6xF5):2C2	240,195
(C₆×F₅)⋊₃C₂ = C₃×C₂²⋊F₅	φ: C₂/C₁ → C₂ ⊆ Out C₆×F₅	60	4	(C6xF5):3C2	240,117

Non-split extensions G=N.Q with N=C₆×F₅ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₆×F₅).₁C₂ = Dic₃×F₅	φ: C₂/C₁ → C₂ ⊆ Out C₆×F₅	60	8-	(C6xF5).1C2	240,95
(C₆×F₅).₂C₂ = Dic₃⋊F₅	φ: C₂/C₁ → C₂ ⊆ Out C₆×F₅	60	8-	(C6xF5).2C2	240,97
(C₆×F₅).₃C₂ = C₃×C₄⋊F₅	φ: C₂/C₁ → C₂ ⊆ Out C₆×F₅	60	4	(C6xF5).3C2	240,114
(C₆×F₅).₄C₂ = C₁₂×F₅	φ: trivial image	60	4	(C6xF5).4C2	240,113

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁