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

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

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

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

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₆)⋊₁F₅ = C₃×C₂²⋊F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₂×C₆	60	4	(C2xC6):1F5	240,117
(C₂×C₆)⋊₂F₅ = D₁₀.D₆	φ: F₅/D₅ → C₂ ⊆ Aut C₂×C₆	60	4	(C2xC6):2F5	240,124
(C₂×C₆)⋊₃F₅ = C₂²×C₃⋊F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₂×C₆	60		(C2xC6):3F5	240,201

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

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₆).₁F₅ = C₃×C₂².F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₂×C₆	120	4	(C2xC6).1F5	240,116
(C₂×C₆).₂F₅ = C₂×C₁₅⋊C₈	φ: F₅/D₅ → C₂ ⊆ Aut C₂×C₆	240		(C2xC6).2F5	240,122
(C₂×C₆).₃F₅ = C₁₅⋊₈M₄(2)	φ: F₅/D₅ → C₂ ⊆ Aut C₂×C₆	120	4	(C2xC6).3F5	240,123
(C₂×C₆).₄F₅ = C₆×C₅⋊C₈	central extension (φ=1)	240		(C2xC6).4F5	240,115

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