Extensions 1→N→G→Q→1 with N=C₂² and Q=GL₂(𝔽₃)

Direct product G=N×Q with N=C₂² and Q=GL₂(𝔽₃)

		d	ρ	Label	ID
C₂²×GL₂(𝔽₃)		32		C2^2xGL(2,3)	192,1475

Semidirect products G=N:Q with N=C₂² and Q=GL₂(𝔽₃)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂²⋊GL₂(𝔽₃) = Q₈⋊S₄	φ: GL₂(𝔽₃)/Q₈ → S₃ ⊆ Aut C₂²	24	6	C2^2:GL(2,3)	192,1490
C₂²⋊₂GL₂(𝔽₃) = C₂³.₁₆S₄	φ: GL₂(𝔽₃)/SL₂(𝔽₃) → C₂ ⊆ Aut C₂²	32		C2^2:2GL(2,3)	192,980

Non-split extensions G=N.Q with N=C₂² and Q=GL₂(𝔽₃)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂².GL₂(𝔽₃) = C₂³.₈S₄	φ: GL₂(𝔽₃)/Q₈ → S₃ ⊆ Aut C₂²	24	6+	C2^2.GL(2,3)	192,181
C₂².₂GL₂(𝔽₃) = C₂×Q₈⋊Dic₃	central extension (φ=1)	64		C2^2.2GL(2,3)	192,977

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Extensions 1→N→G→Q→1 with N=C22 and Q=GL2(𝔽3)