Extensions 1→N→G→Q→1 with N=C₂×C₁₀ and Q=C₃×S₃

Direct product G=N×Q with N=C₂×C₁₀ and Q=C₃×S₃

		d	ρ	Label	ID
S₃×C₂×C₃₀		120		S3xC2xC30	360,158

Semidirect products G=N:Q with N=C₂×C₁₀ and Q=C₃×S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₁₀)⋊₁(C₃×S₃) = C₁₅×S₄	φ: C₃×S₃/C₃ → S₃ ⊆ Aut C₂×C₁₀	60	3	(C2xC10):1(C3xS3)	360,138
(C₂×C₁₀)⋊₂(C₃×S₃) = C₃×C₅⋊S₄	φ: C₃×S₃/C₃ → S₃ ⊆ Aut C₂×C₁₀	60	6	(C2xC10):2(C3xS3)	360,139
(C₂×C₁₀)⋊₃(C₃×S₃) = A₄×D₁₅	φ: C₃×S₃/C₃ → C₆ ⊆ Aut C₂×C₁₀	60	6+	(C2xC10):3(C3xS3)	360,144
(C₂×C₁₀)⋊₄(C₃×S₃) = C₅×S₃×A₄	φ: C₃×S₃/S₃ → C₃ ⊆ Aut C₂×C₁₀	60	6	(C2xC10):4(C3xS3)	360,143
(C₂×C₁₀)⋊₅(C₃×S₃) = C₁₅×C₃⋊D₄	φ: C₃×S₃/C₃² → C₂ ⊆ Aut C₂×C₁₀	60	2	(C2xC10):5(C3xS3)	360,99
(C₂×C₁₀)⋊₆(C₃×S₃) = C₃×C₁₅⋊₇D₄	φ: C₃×S₃/C₃² → C₂ ⊆ Aut C₂×C₁₀	60	2	(C2xC10):6(C3xS3)	360,104
(C₂×C₁₀)⋊₇(C₃×S₃) = C₂×C₆×D₁₅	φ: C₃×S₃/C₃² → C₂ ⊆ Aut C₂×C₁₀	120		(C2xC10):7(C3xS3)	360,159

Non-split extensions G=N.Q with N=C₂×C₁₀ and Q=C₃×S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₁₀).(C₃×S₃) = C₆×Dic₁₅	φ: C₃×S₃/C₃² → C₂ ⊆ Aut C₂×C₁₀	120		(C2xC10).(C3xS3)	360,103
(C₂×C₁₀).₂(C₃×S₃) = Dic₃×C₃₀	central extension (φ=1)	120		(C2xC10).2(C3xS3)	360,98

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