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

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

		d	ρ	Label	ID
S₃×C₂³		24		S3xC2^3	48,51

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊S₃ = C₂×S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂³	6	3+	C2^3:S3	48,48
C₂³⋊₂S₃ = C₂×C₃⋊D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂³	24		C2^3:2S3	48,43

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.S₃ = A₄⋊C₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂³	12	3	C2^3.S3	48,30
C₂³.₂S₃ = C₆.D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂³	24		C2^3.2S3	48,19
C₂³.₃S₃ = C₂²×Dic₃	central extension (φ=1)	48		C2^3.3S3	48,42

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