Extensions 1→N→G→Q→1 with N=C₆ and Q=GL₂(𝔽₃)

Direct product G=N×Q with N=C₆ and Q=GL₂(𝔽₃)

		d	ρ	Label	ID
C₆×GL₂(𝔽₃)		48		C6xGL(2,3)	288,900

Semidirect products G=N:Q with N=C₆ and Q=GL₂(𝔽₃)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊GL₂(𝔽₃) = C₂×C₆.₆S₄	φ: GL₂(𝔽₃)/SL₂(𝔽₃) → C₂ ⊆ Aut C₆	48		C6:GL(2,3)	288,911

Non-split extensions G=N.Q with N=C₆ and Q=GL₂(𝔽₃)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.₁GL₂(𝔽₃) = Q₈⋊Dic₉	φ: GL₂(𝔽₃)/SL₂(𝔽₃) → C₂ ⊆ Aut C₆	288		C6.1GL(2,3)	288,69
C₆.₂GL₂(𝔽₃) = C₂×Q₈⋊D₉	φ: GL₂(𝔽₃)/SL₂(𝔽₃) → C₂ ⊆ Aut C₆	144		C6.2GL(2,3)	288,336
C₆.₃GL₂(𝔽₃) = C₆.GL₂(𝔽₃)	φ: GL₂(𝔽₃)/SL₂(𝔽₃) → C₂ ⊆ Aut C₆	96		C6.3GL(2,3)	288,403
C₆.₄GL₂(𝔽₃) = C₃×Q₈⋊Dic₃	central extension (φ=1)	96		C6.4GL(2,3)	288,399

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