Extensions 1→N→G→Q→1 with N=C₄.A₅ and Q=C₂

Direct product G=N×Q with N=C₄.A₅ and Q=C₂

		d	ρ	Label	ID
C₂×C₄.A₅		48		C2xC4.A5	480,955

Semidirect products G=N:Q with N=C₄.A₅ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
C₄.A₅⋊₁C₂ = D₄.A₅	φ: C₂/C₁ → C₂ ⊆ Out C₄.A₅	48	4-	C4.A5:1C2	480,957
C₄.A₅⋊₂C₂ = Q₈.A₅	φ: C₂/C₁ → C₂ ⊆ Out C₄.A₅	48	4+	C4.A5:2C2	480,959
C₄.A₅⋊₃C₂ = C₄.₃S₅	φ: C₂/C₁ → C₂ ⊆ Out C₄.A₅	40	4	C4.A5:3C2	480,948
C₄.A₅⋊₄C₂ = C₄.₆S₅	φ: C₂/C₁ → C₂ ⊆ Out C₄.A₅	48	4	C4.A5:4C2	480,946

Non-split extensions G=N.Q with N=C₄.A₅ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
C₄.A₅.₁C₂ = C₄.S₅	φ: C₂/C₁ → C₂ ⊆ Out C₄.A₅	48	4	C4.A5.1C2	480,947
C₄.A₅.₂C₂ = GL₂(𝔽₅)	φ: C₂/C₁ → C₂ ⊆ Out C₄.A₅	24	4	C4.A5.2C2	480,218
C₄.A₅.₃C₂ = C₈.A₅	φ: trivial image	48	2	C4.A5.3C2	480,221

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁