Extensions 1→N→G→Q→1 with N=C₆ and Q=S₄

Direct product G=N×Q with N=C₆ and Q=S₄

		d	ρ	Label	ID
C₆×S₄		18	3	C6xS4	144,188

Semidirect products G=N:Q with N=C₆ and Q=S₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊S₄ = C₂×C₃⋊S₄	φ: S₄/A₄ → C₂ ⊆ Aut C₆	18	6+	C6:S4	144,189

Non-split extensions G=N.Q with N=C₆ and Q=S₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.₁S₄ = Q₈.D₉	φ: S₄/A₄ → C₂ ⊆ Aut C₆	144	4-	C6.1S4	144,31
C₆.₂S₄ = Q₈⋊D₉	φ: S₄/A₄ → C₂ ⊆ Aut C₆	72	4+	C6.2S4	144,32
C₆.₃S₄ = C₆.S₄	φ: S₄/A₄ → C₂ ⊆ Aut C₆	36	6-	C6.3S4	144,33
C₆.₄S₄ = C₂×C₃.S₄	φ: S₄/A₄ → C₂ ⊆ Aut C₆	18	6+	C6.4S4	144,109
C₆.₅S₄ = C₆.₅S₄	φ: S₄/A₄ → C₂ ⊆ Aut C₆	48	4-	C6.5S4	144,124
C₆.₆S₄ = C₆.₆S₄	φ: S₄/A₄ → C₂ ⊆ Aut C₆	24	4+	C6.6S4	144,125
C₆.₇S₄ = C₆.₇S₄	φ: S₄/A₄ → C₂ ⊆ Aut C₆	36	6-	C6.7S4	144,126
C₆.₈S₄ = C₃×CSU₂(𝔽₃)	central extension (φ=1)	48	2	C6.8S4	144,121
C₆.₉S₄ = C₃×GL₂(𝔽₃)	central extension (φ=1)	24	2	C6.9S4	144,122
C₆.₁₀S₄ = C₃×A₄⋊C₄	central extension (φ=1)	36	3	C6.10S4	144,123

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