Extensions 1→N→G→Q→1 with N=C₃×C₁₅ and Q=C₆

Direct product G=N×Q with N=C₃×C₁₅ and Q=C₆

		d	ρ	Label	ID
C₃²×C₃₀		270		C3^2xC30	270,30

Semidirect products G=N:Q with N=C₃×C₁₅ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₁₅)⋊₁C₆ = He₃⋊D₅	φ: C₆/C₁ → C₆ ⊆ Aut C₃×C₁₅	45	6+	(C3xC15):1C6	270,14
(C₃×C₁₅)⋊₂C₆ = D₅×He₃	φ: C₆/C₁ → C₆ ⊆ Aut C₃×C₁₅	45	6	(C3xC15):2C6	270,6
(C₃×C₁₅)⋊₃C₆ = C₅×C₃²⋊C₆	φ: C₆/C₁ → C₆ ⊆ Aut C₃×C₁₅	45	6	(C3xC15):3C6	270,10
(C₃×C₁₅)⋊₄C₆ = C₁₀×He₃	φ: C₆/C₂ → C₃ ⊆ Aut C₃×C₁₅	90	3	(C3xC15):4C6	270,21
(C₃×C₁₅)⋊₅C₆ = C₃×C₃⋊D₁₅	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₁₅	90		(C3xC15):5C6	270,27
(C₃×C₁₅)⋊₆C₆ = C₃²×D₁₅	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₁₅	90		(C3xC15):6C6	270,25
(C₃×C₁₅)⋊₇C₆ = D₅×C₃³	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₁₅	135		(C3xC15):7C6	270,23
(C₃×C₁₅)⋊₈C₆ = S₃×C₃×C₁₅	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₁₅	90		(C3xC15):8C6	270,24
(C₃×C₁₅)⋊₉C₆ = C₁₅×C₃⋊S₃	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₁₅	90		(C3xC15):9C6	270,26

Non-split extensions G=N.Q with N=C₃×C₁₅ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₁₅).C₆ = D₅×3_-¹⁺²	φ: C₆/C₁ → C₆ ⊆ Aut C₃×C₁₅	45	6	(C3xC15).C6	270,7
(C₃×C₁₅).₂C₆ = C₁₀×3_-¹⁺²	φ: C₆/C₂ → C₃ ⊆ Aut C₃×C₁₅	90	3	(C3xC15).2C6	270,22
(C₃×C₁₅).₃C₆ = C₉×D₁₅	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₁₅	90	2	(C3xC15).3C6	270,13
(C₃×C₁₅).₄C₆ = D₅×C₃×C₉	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₁₅	135		(C3xC15).4C6	270,5
(C₃×C₁₅).₅C₆ = S₃×C₄₅	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₁₅	90	2	(C3xC15).5C6	270,9

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