Extensions 1→N→G→Q→1 with N=C₄.F₅ and Q=C₆

Direct product G=N×Q with N=C₄.F₅ and Q=C₆

		d	ρ	Label	ID
C₆×C₄.F₅		240		C6xC4.F5	480,1048

Semidirect products G=N:Q with N=C₄.F₅ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
C₄.F₅⋊₁C₆ = C₃×D₄⋊F₅	φ: C₆/C₃ → C₂ ⊆ Out C₄.F₅	120	8	C4.F5:1C6	480,288
C₄.F₅⋊₂C₆ = C₃×Q₈⋊₂F₅	φ: C₆/C₃ → C₂ ⊆ Out C₄.F₅	120	8	C4.F5:2C6	480,290
C₄.F₅⋊₃C₆ = C₃×D₄.F₅	φ: C₆/C₃ → C₂ ⊆ Out C₄.F₅	240	8	C4.F5:3C6	480,1053
C₄.F₅⋊₄C₆ = C₃×Q₈.F₅	φ: C₆/C₃ → C₂ ⊆ Out C₄.F₅	240	8	C4.F5:4C6	480,1055
C₄.F₅⋊₅C₆ = C₃×D₅⋊M₄(2)	φ: trivial image	120	4	C4.F5:5C6	480,1049

Non-split extensions G=N.Q with N=C₄.F₅ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
C₄.F₅.₁C₆ = C₃×C₄₀.C₄	φ: C₆/C₃ → C₂ ⊆ Out C₄.F₅	240	4	C4.F5.1C6	480,275
C₄.F₅.₂C₆ = C₃×D₁₀.Q₈	φ: C₆/C₃ → C₂ ⊆ Out C₄.F₅	240	4	C4.F5.2C6	480,276

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁