Extensions 1→N→G→Q→1 with N=C₃×C₆ and Q=F₅

Direct product G=N×Q with N=C₃×C₆ and Q=F₅

		d	ρ	Label	ID
C₃×C₆×F₅		90		C3xC6xF5	360,145

Semidirect products G=N:Q with N=C₃×C₆ and Q=F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₆)⋊F₅ = C₂×C₃²⋊F₅	φ: F₅/C₅ → C₄ ⊆ Aut C₃×C₆	60	4+	(C3xC6):F5	360,150
(C₃×C₆)⋊₂F₅ = C₆×C₃⋊F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₃×C₆	60	4	(C3xC6):2F5	360,146
(C₃×C₆)⋊₃F₅ = C₂×C₃²⋊₃F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₃×C₆	90		(C3xC6):3F5	360,147

Non-split extensions G=N.Q with N=C₃×C₆ and Q=F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₆).F₅ = (C₃×C₆).F₅	φ: F₅/C₅ → C₄ ⊆ Aut C₃×C₆	120	4-	(C3xC6).F5	360,57
(C₃×C₆).₂F₅ = C₃×C₁₅⋊C₈	φ: F₅/D₅ → C₂ ⊆ Aut C₃×C₆	120	4	(C3xC6).2F5	360,53
(C₃×C₆).₃F₅ = C₃₀.Dic₃	φ: F₅/D₅ → C₂ ⊆ Aut C₃×C₆	360		(C3xC6).3F5	360,54
(C₃×C₆).₄F₅ = C₃²×C₅⋊C₈	central extension (φ=1)	360		(C3xC6).4F5	360,52

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