Extensions 1→N→G→Q→1 with N=C₁₀ and Q=S₄

Direct product G=N×Q with N=C₁₀ and Q=S₄

		d	ρ	Label	ID
C₁₀×S₄		30	3	C10xS4	240,196

Semidirect products G=N:Q with N=C₁₀ and Q=S₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀⋊S₄ = C₂×C₅⋊S₄	φ: S₄/A₄ → C₂ ⊆ Aut C₁₀	30	6+	C10:S4	240,197

Non-split extensions G=N.Q with N=C₁₀ and Q=S₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀.₁S₄ = Q₈.D₁₅	φ: S₄/A₄ → C₂ ⊆ Aut C₁₀	80	4-	C10.1S4	240,105
C₁₀.₂S₄ = Q₈⋊D₁₅	φ: S₄/A₄ → C₂ ⊆ Aut C₁₀	40	4+	C10.2S4	240,106
C₁₀.₃S₄ = A₄⋊Dic₅	φ: S₄/A₄ → C₂ ⊆ Aut C₁₀	60	6-	C10.3S4	240,107
C₁₀.₄S₄ = C₅×CSU₂(𝔽₃)	central extension (φ=1)	80	2	C10.4S4	240,102
C₁₀.₅S₄ = C₅×GL₂(𝔽₃)	central extension (φ=1)	40	2	C10.5S4	240,103
C₁₀.₆S₄ = C₅×A₄⋊C₄	central extension (φ=1)	60	3	C10.6S4	240,104

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