Extensions 1→N→G→Q→1 with N=C₅×C₁₀ and Q=S₃

Direct product G=N×Q with N=C₅×C₁₀ and Q=S₃

		d	ρ	Label	ID
S₃×C₅×C₁₀		150		S3xC5xC10	300,46

Semidirect products G=N:Q with N=C₅×C₁₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₅×C₁₀)⋊S₃ = C₂×C₅²⋊S₃	φ: S₃/C₁ → S₃ ⊆ Aut C₅×C₁₀	30	3	(C5xC10):S3	300,26
(C₅×C₁₀)⋊₂S₃ = C₁₀×D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₅×C₁₀	60	2	(C5xC10):2S3	300,47
(C₅×C₁₀)⋊₃S₃ = C₂×C₅⋊D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₅×C₁₀	150		(C5xC10):3S3	300,48

Non-split extensions G=N.Q with N=C₅×C₁₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₅×C₁₀).S₃ = C₅²⋊₂Dic₃	φ: S₃/C₁ → S₃ ⊆ Aut C₅×C₁₀	60	3	(C5xC10).S3	300,13
(C₅×C₁₀).₂S₃ = C₅×Dic₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₅×C₁₀	60	2	(C5xC10).2S3	300,19
(C₅×C₁₀).₃S₃ = C₃₀.D₅	φ: S₃/C₃ → C₂ ⊆ Aut C₅×C₁₀	300		(C5xC10).3S3	300,20
(C₅×C₁₀).₄S₃ = Dic₃×C₅²	central extension (φ=1)	300		(C5xC10).4S3	300,18

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁