Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃×GL₂(𝔽₃)

Direct product G=N×Q with N=C₃ and Q=C₃×GL₂(𝔽₃)

		d	ρ	Label	ID
C₃²×GL₂(𝔽₃)		72		C3^2xGL(2,3)	432,614

Semidirect products G=N:Q with N=C₃ and Q=C₃×GL₂(𝔽₃)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(C₃×GL₂(𝔽₃)) = C₃×C₆.₆S₄	φ: C₃×GL₂(𝔽₃)/C₃×SL₂(𝔽₃) → C₂ ⊆ Aut C₃	48	4	C3:(C3xGL(2,3))	432,617

Non-split extensions G=N.Q with N=C₃ and Q=C₃×GL₂(𝔽₃)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₃×GL₂(𝔽₃)) = C₃².GL₂(𝔽₃)	φ: C₃×GL₂(𝔽₃)/C₃×SL₂(𝔽₃) → C₂ ⊆ Aut C₃	72	12+	C3.1(C3xGL(2,3))	432,245
C₃.₂(C₃×GL₂(𝔽₃)) = C₃×Q₈⋊D₉	φ: C₃×GL₂(𝔽₃)/C₃×SL₂(𝔽₃) → C₂ ⊆ Aut C₃	144	4	C3.2(C3xGL(2,3))	432,246
C₃.₃(C₃×GL₂(𝔽₃)) = C₃²⋊₂GL₂(𝔽₃)	φ: C₃×GL₂(𝔽₃)/C₃×SL₂(𝔽₃) → C₂ ⊆ Aut C₃	72	12+	C3.3(C3xGL(2,3))	432,248
C₃.₄(C₃×GL₂(𝔽₃)) = C₉×GL₂(𝔽₃)	central extension (φ=1)	72	2	C3.4(C3xGL(2,3))	432,241

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