Extensions 1→N→G→Q→1 with N=C₂³ and Q=S₃×C₉

Direct product G=N×Q with N=C₂³ and Q=S₃×C₉

		d	ρ	Label	ID
S₃×C₂²×C₁₈		144		S3xC2^2xC18	432,557

Semidirect products G=N:Q with N=C₂³ and Q=S₃×C₉

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊(S₃×C₉) = C₁₈×S₄	φ: S₃×C₉/C₉ → S₃ ⊆ Aut C₂³	54	3	C2^3:(S3xC9)	432,532
C₂³⋊₂(S₃×C₉) = C₂×S₃×C₃.A₄	φ: S₃×C₉/C₃×S₃ → C₃ ⊆ Aut C₂³	36	6	C2^3:2(S3xC9)	432,541
C₂³⋊₃(S₃×C₉) = C₁₈×C₃⋊D₄	φ: S₃×C₉/C₃×C₉ → C₂ ⊆ Aut C₂³	72		C2^3:3(S3xC9)	432,375

Non-split extensions G=N.Q with N=C₂³ and Q=S₃×C₉

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.(S₃×C₉) = C₉×A₄⋊C₄	φ: S₃×C₉/C₉ → S₃ ⊆ Aut C₂³	108	3	C2^3.(S3xC9)	432,242
C₂³.₂(S₃×C₉) = Dic₃×C₃.A₄	φ: S₃×C₉/C₃×S₃ → C₃ ⊆ Aut C₂³	36	6	C2^3.2(S3xC9)	432,271
C₂³.₃(S₃×C₉) = C₉×C₆.D₄	φ: S₃×C₉/C₃×C₉ → C₂ ⊆ Aut C₂³	72		C2^3.3(S3xC9)	432,165
C₂³.₄(S₃×C₉) = Dic₃×C₂×C₁₈	central extension (φ=1)	144		C2^3.4(S3xC9)	432,373

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