Extensions 1→N→G→Q→1 with N=C₂×C₄ and Q=S₃×C₉

Direct product G=N×Q with N=C₂×C₄ and Q=S₃×C₉

		d	ρ	Label	ID
S₃×C₂×C₃₆		144		S3xC2xC36	432,345

Semidirect products G=N:Q with N=C₂×C₄ and Q=S₃×C₉

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₄)⋊₁(S₃×C₉) = C₉×D₆⋊C₄	φ: S₃×C₉/C₃×C₉ → C₂ ⊆ Aut C₂×C₄	144		(C2xC4):1(S3xC9)	432,135
(C₂×C₄)⋊₂(S₃×C₉) = C₁₈×D₁₂	φ: S₃×C₉/C₃×C₉ → C₂ ⊆ Aut C₂×C₄	144		(C2xC4):2(S3xC9)	432,346
(C₂×C₄)⋊₃(S₃×C₉) = C₉×C₄○D₁₂	φ: S₃×C₉/C₃×C₉ → C₂ ⊆ Aut C₂×C₄	72	2	(C2xC4):3(S3xC9)	432,347

Non-split extensions G=N.Q with N=C₂×C₄ and Q=S₃×C₉

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₄).₁(S₃×C₉) = C₉×Dic₃⋊C₄	φ: S₃×C₉/C₃×C₉ → C₂ ⊆ Aut C₂×C₄	144		(C2xC4).1(S3xC9)	432,132
(C₂×C₄).₂(S₃×C₉) = C₉×C₄.Dic₃	φ: S₃×C₉/C₃×C₉ → C₂ ⊆ Aut C₂×C₄	72	2	(C2xC4).2(S3xC9)	432,127
(C₂×C₄).₃(S₃×C₉) = C₉×C₄⋊Dic₃	φ: S₃×C₉/C₃×C₉ → C₂ ⊆ Aut C₂×C₄	144		(C2xC4).3(S3xC9)	432,133
(C₂×C₄).₄(S₃×C₉) = C₁₈×Dic₆	φ: S₃×C₉/C₃×C₉ → C₂ ⊆ Aut C₂×C₄	144		(C2xC4).4(S3xC9)	432,341
(C₂×C₄).₅(S₃×C₉) = C₁₈×C₃⋊C₈	central extension (φ=1)	144		(C2xC4).5(S3xC9)	432,126
(C₂×C₄).₆(S₃×C₉) = Dic₃×C₃₆	central extension (φ=1)	144		(C2xC4).6(S3xC9)	432,131

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁