Extensions 1→N→G→Q→1 with N=SL₂(𝔽₃) and Q=D₇

Direct product G=N×Q with N=SL₂(𝔽₃) and Q=D₇

		d	ρ	Label	ID
D₇×SL₂(𝔽₃)		56	4-	D7xSL(2,3)	336,132

Semidirect products G=N:Q with N=SL₂(𝔽₃) and Q=D₇

extension	φ:Q→Out N	d	ρ	Label	ID
SL₂(𝔽₃)⋊D₇ = Q₈⋊D₂₁	φ: D₇/C₇ → C₂ ⊆ Out SL₂(𝔽₃)	56	4+	SL(2,3):D7	336,119
SL₂(𝔽₃)⋊₂D₇ = Dic₇.₂A₄	φ: trivial image	112	4+	SL(2,3):2D7	336,131

Non-split extensions G=N.Q with N=SL₂(𝔽₃) and Q=D₇

extension	φ:Q→Out N	d	ρ	Label	ID
SL₂(𝔽₃).D₇ = Q₈.D₂₁	φ: D₇/C₇ → C₂ ⊆ Out SL₂(𝔽₃)	112	4-	SL(2,3).D7	336,118

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Extensions 1→N→G→Q→1 with N=SL2(𝔽3) and Q=D7