Extensions 1→N→G→Q→1 with N=SL₂(𝔽₃) and Q=F₅

Direct product G=N×Q with N=SL₂(𝔽₃) and Q=F₅

		d	ρ	Label	ID
F₅×SL₂(𝔽₃)		40	8-	F5xSL(2,3)	480,965

Semidirect products G=N:Q with N=SL₂(𝔽₃) and Q=F₅

extension	φ:Q→Out N	d	ρ	Label	ID
SL₂(𝔽₃)⋊₁F₅ = C₅⋊U₂(𝔽₃)	φ: F₅/D₅ → C₂ ⊆ Out SL₂(𝔽₃)	120	8+	SL(2,3):1F5	480,961
SL₂(𝔽₃)⋊₂F₅ = D₁₀.S₄	φ: F₅/D₅ → C₂ ⊆ Out SL₂(𝔽₃)	40	8-	SL(2,3):2F5	480,962

Non-split extensions G=N.Q with N=SL₂(𝔽₃) and Q=F₅

extension	φ:Q→Out N	d	ρ	Label	ID
SL₂(𝔽₃).F₅ = SL₂(𝔽₃).F₅	φ: trivial image	160	8+	SL(2,3).F5	480,964

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Extensions 1→N→G→Q→1 with N=SL2(𝔽3) and Q=F5