Extensions 1→N→G→Q→1 with N=C₁₂ and Q=F₅

Direct product G=N×Q with N=C₁₂ and Q=F₅

		d	ρ	Label	ID
C₁₂×F₅		60	4	C12xF5	240,113

Semidirect products G=N:Q with N=C₁₂ and Q=F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₂⋊₁F₅ = C₆₀⋊C₄	φ: F₅/D₅ → C₂ ⊆ Aut C₁₂	60	4	C12:1F5	240,121
C₁₂⋊₂F₅ = C₄×C₃⋊F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₁₂	60	4	C12:2F5	240,120
C₁₂⋊₃F₅ = C₃×C₄⋊F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₁₂	60	4	C12:3F5	240,114

Non-split extensions G=N.Q with N=C₁₂ and Q=F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₂.₁F₅ = C₁₂.F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₁₂	120	4	C12.1F5	240,119
C₁₂.₂F₅ = C₁₅⋊C₁₆	φ: F₅/D₅ → C₂ ⊆ Aut C₁₂	240	4	C12.2F5	240,6
C₁₂.₃F₅ = C₆₀.C₄	φ: F₅/D₅ → C₂ ⊆ Aut C₁₂	120	4	C12.3F5	240,118
C₁₂.₄F₅ = C₃×C₄.F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₁₂	120	4	C12.4F5	240,112
C₁₂.₅F₅ = C₃×C₅⋊C₁₆	central extension (φ=1)	240	4	C12.5F5	240,5
C₁₂.₆F₅ = C₃×D₅⋊C₈	central extension (φ=1)	120	4	C12.6F5	240,111

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