Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₃⋊F₅

Direct product G=N×Q with N=C₂³ and Q=C₃⋊F₅

		d	ρ	Label	ID
C₂³×C₃⋊F₅		120		C2^3xC3:F5	480,1206

Semidirect products G=N:Q with N=C₂³ and Q=C₃⋊F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊(C₃⋊F₅) = C₂×A₄⋊F₅	φ: C₃⋊F₅/D₅ → S₃ ⊆ Aut C₂³	30	12+	C2^3:(C3:F5)	480,1191
C₂³⋊₂(C₃⋊F₅) = C₃⋊(C₂³⋊F₅)	φ: C₃⋊F₅/C₁₅ → C₄ ⊆ Aut C₂³	120	4	C2^3:2(C3:F5)	480,316
C₂³⋊₃(C₃⋊F₅) = C₂×D₁₀.D₆	φ: C₃⋊F₅/C₃×D₅ → C₂ ⊆ Aut C₂³	120		C2^3:3(C3:F5)	480,1072

Non-split extensions G=N.Q with N=C₂³ and Q=C₃⋊F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.(C₃⋊F₅) = Dic₅.S₄	φ: C₃⋊F₅/D₅ → S₃ ⊆ Aut C₂³	120	12-	C2^3.(C3:F5)	480,963
C₂³.₂(C₃⋊F₅) = C₅⋊(C₁₂.D₄)	φ: C₃⋊F₅/C₁₅ → C₄ ⊆ Aut C₂³	120	4	C2^3.2(C3:F5)	480,318
C₂³.₃(C₃⋊F₅) = C₃₀.₂₂M₄(2)	φ: C₃⋊F₅/C₃×D₅ → C₂ ⊆ Aut C₂³	240		C2^3.3(C3:F5)	480,317
C₂³.₄(C₃⋊F₅) = C₂×C₁₅⋊₈M₄(2)	φ: C₃⋊F₅/C₃×D₅ → C₂ ⊆ Aut C₂³	240		C2^3.4(C3:F5)	480,1071
C₂³.₅(C₃⋊F₅) = C₂²×C₁₅⋊C₈	central extension (φ=1)	480		C2^3.5(C3:F5)	480,1070

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