Extensions 1→N→G→Q→1 with N=C₂×C₁₀ and Q=D₅

Direct product G=N×Q with N=C₂×C₁₀ and Q=D₅

		d	ρ	Label	ID
D₅×C₂×C₁₀		40		D5xC2xC10	200,50

Semidirect products G=N:Q with N=C₂×C₁₀ and Q=D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₁₀)⋊₁D₅ = C₅×C₅⋊D₄	φ: D₅/C₅ → C₂ ⊆ Aut C₂×C₁₀	20	2	(C2xC10):1D5	200,31
(C₂×C₁₀)⋊₂D₅ = C₅²⋊₇D₄	φ: D₅/C₅ → C₂ ⊆ Aut C₂×C₁₀	100		(C2xC10):2D5	200,36
(C₂×C₁₀)⋊₃D₅ = C₂²×C₅⋊D₅	φ: D₅/C₅ → C₂ ⊆ Aut C₂×C₁₀	100		(C2xC10):3D5	200,51

Non-split extensions G=N.Q with N=C₂×C₁₀ and Q=D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₁₀).₁D₅ = C₂×Dic₂₅	φ: D₅/C₅ → C₂ ⊆ Aut C₂×C₁₀	200		(C2xC10).1D5	200,7
(C₂×C₁₀).₂D₅ = C₂₅⋊D₄	φ: D₅/C₅ → C₂ ⊆ Aut C₂×C₁₀	100	2	(C2xC10).2D5	200,8
(C₂×C₁₀).₃D₅ = C₂²×D₂₅	φ: D₅/C₅ → C₂ ⊆ Aut C₂×C₁₀	100		(C2xC10).3D5	200,13
(C₂×C₁₀).₄D₅ = C₂×C₅²⋊₆C₄	φ: D₅/C₅ → C₂ ⊆ Aut C₂×C₁₀	200		(C2xC10).4D5	200,35
(C₂×C₁₀).₅D₅ = C₁₀×Dic₅	central extension (φ=1)	40		(C2xC10).5D5	200,30

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁