Extensions 1→N→G→Q→1 with N=C₅ and Q=C₅×C₂₀

Direct product G=N×Q with N=C₅ and Q=C₅×C₂₀

		d	ρ	Label	ID
C₅²×C₂₀		500		C5^2xC20	500,40

Semidirect products G=N:Q with N=C₅ and Q=C₅×C₂₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊(C₅×C₂₀) = F₅×C₅²	φ: C₅×C₂₀/C₅² → C₄ ⊆ Aut C₅	100		C5:(C5xC20)	500,41
C₅⋊₂(C₅×C₂₀) = Dic₅×C₅²	φ: C₅×C₂₀/C₅×C₁₀ → C₂ ⊆ Aut C₅	100		C5:2(C5xC20)	500,37

Non-split extensions G=N.Q with N=C₅ and Q=C₅×C₂₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅.₁(C₅×C₂₀) = C₄×He₅	central stem extension (φ=1)	100	5	C5.1(C5xC20)	500,13
C₅.₂(C₅×C₂₀) = C₄×5_-¹⁺²	central stem extension (φ=1)	100	5	C5.2(C5xC20)	500,14

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C5 and Q=C5×C20