Extensions 1→N→G→Q→1 with N=C₃² and Q=GL₂(𝔽₃)

Direct product G=N×Q with N=C₃² and Q=GL₂(𝔽₃)

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

Semidirect products G=N:Q with N=C₃² and Q=GL₂(𝔽₃)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃²⋊GL₂(𝔽₃) = AGL₂(𝔽₃)	φ: GL₂(𝔽₃)/C₁ → GL₂(𝔽₃) ⊆ Aut C₃²	9	8+	C3^2:GL(2,3)	432,734
C₃²⋊₂GL₂(𝔽₃) = C₃²⋊₂GL₂(𝔽₃)	φ: GL₂(𝔽₃)/Q₈ → S₃ ⊆ Aut C₃²	72	12+	C3^2:2GL(2,3)	432,248
C₃²⋊₃GL₂(𝔽₃) = C₃²⋊₃GL₂(𝔽₃)	φ: GL₂(𝔽₃)/Q₈ → S₃ ⊆ Aut C₃²	72	6	C3^2:3GL(2,3)	432,258
C₃²⋊₄GL₂(𝔽₃) = C₃×C₆.₆S₄	φ: GL₂(𝔽₃)/SL₂(𝔽₃) → C₂ ⊆ Aut C₃²	48	4	C3^2:4GL(2,3)	432,617
C₃²⋊₅GL₂(𝔽₃) = C₃²⋊₅GL₂(𝔽₃)	φ: GL₂(𝔽₃)/SL₂(𝔽₃) → C₂ ⊆ Aut C₃²	72		C3^2:5GL(2,3)	432,620

Non-split extensions G=N.Q with N=C₃² and Q=GL₂(𝔽₃)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃².GL₂(𝔽₃) = C₃².GL₂(𝔽₃)	φ: GL₂(𝔽₃)/Q₈ → S₃ ⊆ Aut C₃²	72	12+	C3^2.GL(2,3)	432,245
C₃².₂GL₂(𝔽₃) = C₃×Q₈⋊D₉	φ: GL₂(𝔽₃)/SL₂(𝔽₃) → C₂ ⊆ Aut C₃²	144	4	C3^2.2GL(2,3)	432,246
C₃².₃GL₂(𝔽₃) = C₃².₃GL₂(𝔽₃)	φ: GL₂(𝔽₃)/SL₂(𝔽₃) → C₂ ⊆ Aut C₃²	216		C3^2.3GL(2,3)	432,256

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