Extensions 1→N→G→Q→1 with N=C₄ and Q=C₃⋊F₅

Direct product G=N×Q with N=C₄ and Q=C₃⋊F₅

		d	ρ	Label	ID
C₄×C₃⋊F₅		60	4	C4xC3:F5	240,120

Semidirect products G=N:Q with N=C₄ and Q=C₃⋊F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊(C₃⋊F₅) = C₆₀⋊C₄	φ: C₃⋊F₅/C₃×D₅ → C₂ ⊆ Aut C₄	60	4	C4:(C3:F5)	240,121

Non-split extensions G=N.Q with N=C₄ and Q=C₃⋊F₅

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

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C4 and Q=C3⋊F5