Extensions 1→N→G→Q→1 with N=C₅×C₅₀ and Q=C₂

Direct product G=N×Q with N=C₅×C₅₀ and Q=C₂

		d	ρ	Label	ID
C₁₀×C₅₀		500		C10xC50	500,34

Semidirect products G=N:Q with N=C₅×C₅₀ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₅×C₅₀)⋊₁C₂ = D₅×C₅₀	φ: C₂/C₁ → C₂ ⊆ Aut C₅×C₅₀	100	2	(C5xC50):1C2	500,29
(C₅×C₅₀)⋊₂C₂ = C₁₀×D₂₅	φ: C₂/C₁ → C₂ ⊆ Aut C₅×C₅₀	100	2	(C5xC50):2C2	500,28
(C₅×C₅₀)⋊₃C₂ = C₂×C₂₅⋊D₅	φ: C₂/C₁ → C₂ ⊆ Aut C₅×C₅₀	250		(C5xC50):3C2	500,32

Non-split extensions G=N.Q with N=C₅×C₅₀ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₅×C₅₀).₁C₂ = Dic₅×C₂₅	φ: C₂/C₁ → C₂ ⊆ Aut C₅×C₅₀	100	2	(C5xC50).1C2	500,7
(C₅×C₅₀).₂C₂ = C₅×Dic₂₅	φ: C₂/C₁ → C₂ ⊆ Aut C₅×C₅₀	100	2	(C5xC50).2C2	500,6
(C₅×C₅₀).₃C₂ = C₅₀.D₅	φ: C₂/C₁ → C₂ ⊆ Aut C₅×C₅₀	500		(C5xC50).3C2	500,10

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C5×C50 and Q=C2