Extensions 1→N→G→Q→1 with N=C₃×C₄₅ and Q=C₃

Direct product G=N×Q with N=C₃×C₄₅ and Q=C₃

		d	ρ	Label	ID
C₃²×C₄₅		405		C3^2xC45	405,11

Semidirect products G=N:Q with N=C₃×C₄₅ and Q=C₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₄₅)⋊₁C₃ = C₅×C₃²⋊C₉	φ: C₃/C₁ → C₃ ⊆ Aut C₃×C₄₅	135		(C3xC45):1C3	405,3
(C₃×C₄₅)⋊₂C₃ = C₅×He₃.C₃	φ: C₃/C₁ → C₃ ⊆ Aut C₃×C₄₅	135	3	(C3xC45):2C3	405,8
(C₃×C₄₅)⋊₃C₃ = C₅×He₃⋊C₃	φ: C₃/C₁ → C₃ ⊆ Aut C₃×C₄₅	135	3	(C3xC45):3C3	405,9
(C₃×C₄₅)⋊₄C₃ = C₁₅×3_-¹⁺²	φ: C₃/C₁ → C₃ ⊆ Aut C₃×C₄₅	135		(C3xC45):4C3	405,13
(C₃×C₄₅)⋊₅C₃ = C₅×C₉○He₃	φ: C₃/C₁ → C₃ ⊆ Aut C₃×C₄₅	135	3	(C3xC45):5C3	405,14

Non-split extensions G=N.Q with N=C₃×C₄₅ and Q=C₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₄₅).₁C₃ = C₅×C₉⋊C₉	φ: C₃/C₁ → C₃ ⊆ Aut C₃×C₄₅	405		(C3xC45).1C3	405,4
(C₃×C₄₅).₂C₃ = C₅×C₃.He₃	φ: C₃/C₁ → C₃ ⊆ Aut C₃×C₄₅	135	3	(C3xC45).2C3	405,10
(C₃×C₄₅).₃C₃ = C₅×C₂₇⋊C₃	φ: C₃/C₁ → C₃ ⊆ Aut C₃×C₄₅	135	3	(C3xC45).3C3	405,6

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁