Extensions 1→N→G→Q→1 with N=C₂²×C₆ and Q=F₅

Direct product G=N×Q with N=C₂²×C₆ and Q=F₅

		d	ρ	Label	ID
F₅×C₂²×C₆		120		F5xC2^2xC6	480,1205

Semidirect products G=N:Q with N=C₂²×C₆ and Q=F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂²×C₆)⋊₁F₅ = C₃×C₂³⋊F₅	φ: F₅/C₅ → C₄ ⊆ Aut C₂²×C₆	120	4	(C2^2xC6):1F5	480,291
(C₂²×C₆)⋊₂F₅ = C₃⋊(C₂³⋊F₅)	φ: F₅/C₅ → C₄ ⊆ Aut C₂²×C₆	120	4	(C2^2xC6):2F5	480,316
(C₂²×C₆)⋊₃F₅ = C₆×C₂²⋊F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₂²×C₆	120		(C2^2xC6):3F5	480,1059
(C₂²×C₆)⋊₄F₅ = C₂×D₁₀.D₆	φ: F₅/D₅ → C₂ ⊆ Aut C₂²×C₆	120		(C2^2xC6):4F5	480,1072
(C₂²×C₆)⋊₅F₅ = C₂³×C₃⋊F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₂²×C₆	120		(C2^2xC6):5F5	480,1206

Non-split extensions G=N.Q with N=C₂²×C₆ and Q=F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂²×C₆).₁F₅ = C₃×C₂³.F₅	φ: F₅/C₅ → C₄ ⊆ Aut C₂²×C₆	120	4	(C2^2xC6).1F5	480,293
(C₂²×C₆).₂F₅ = C₅⋊(C₁₂.D₄)	φ: F₅/C₅ → C₄ ⊆ Aut C₂²×C₆	120	4	(C2^2xC6).2F5	480,318
(C₂²×C₆).₃F₅ = C₃×C₂³.₂F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₂²×C₆	240		(C2^2xC6).3F5	480,292
(C₂²×C₆).₄F₅ = C₆×C₂².F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₂²×C₆	240		(C2^2xC6).4F5	480,1058
(C₂²×C₆).₅F₅ = C₃₀.₂₂M₄(2)	φ: F₅/D₅ → C₂ ⊆ Aut C₂²×C₆	240		(C2^2xC6).5F5	480,317
(C₂²×C₆).₆F₅ = C₂²×C₁₅⋊C₈	φ: F₅/D₅ → C₂ ⊆ Aut C₂²×C₆	480		(C2^2xC6).6F5	480,1070
(C₂²×C₆).₇F₅ = C₂×C₁₅⋊₈M₄(2)	φ: F₅/D₅ → C₂ ⊆ Aut C₂²×C₆	240		(C2^2xC6).7F5	480,1071
(C₂²×C₆).₈F₅ = C₂×C₆×C₅⋊C₈	central extension (φ=1)	480		(C2^2xC6).8F5	480,1057

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