Extensions 1→N→G→Q→1 with N=C₃×C₁₅ and Q=S₃

Direct product G=N×Q with N=C₃×C₁₅ and Q=S₃

		d	ρ	Label	ID
S₃×C₃×C₁₅		90		S3xC3xC15	270,24

Semidirect products G=N:Q with N=C₃×C₁₅ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₁₅)⋊₁S₃ = He₃⋊D₅	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₁₅	45	6+	(C3xC15):1S3	270,14
(C₃×C₁₅)⋊₂S₃ = C₃²⋊D₁₅	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₁₅	45	6	(C3xC15):2S3	270,19
(C₃×C₁₅)⋊₃S₃ = C₅×C₃²⋊C₆	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₁₅	45	6	(C3xC15):3S3	270,10
(C₃×C₁₅)⋊₄S₃ = C₅×He₃⋊C₂	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₁₅	45	3	(C3xC15):4S3	270,17
(C₃×C₁₅)⋊₅S₃ = C₃³⋊D₅	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₁₅	135		(C3xC15):5S3	270,29
(C₃×C₁₅)⋊₆S₃ = C₃×C₃⋊D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₁₅	90		(C3xC15):6S3	270,27
(C₃×C₁₅)⋊₇S₃ = C₃²×D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₁₅	90		(C3xC15):7S3	270,25
(C₃×C₁₅)⋊₈S₃ = C₁₅×C₃⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₁₅	90		(C3xC15):8S3	270,26
(C₃×C₁₅)⋊₉S₃ = C₅×C₃³⋊C₂	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₁₅	135		(C3xC15):9S3	270,28

Non-split extensions G=N.Q with N=C₃×C₁₅ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₁₅).₁S₃ = D₄₅⋊C₃	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₁₅	45	6+	(C3xC15).1S3	270,15
(C₃×C₁₅).₂S₃ = C₅×C₉⋊C₆	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₁₅	45	6	(C3xC15).2S3	270,11
(C₃×C₁₅).₃S₃ = C₃⋊D₄₅	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₁₅	135		(C3xC15).3S3	270,18
(C₃×C₁₅).₄S₃ = C₃×D₄₅	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₁₅	90	2	(C3xC15).4S3	270,12
(C₃×C₁₅).₅S₃ = C₁₅×D₉	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₁₅	90	2	(C3xC15).5S3	270,8
(C₃×C₁₅).₆S₃ = C₅×C₉⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₁₅	135		(C3xC15).6S3	270,16

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