Extensions 1→N→G→Q→1 with N=C₂² and Q=C₄.A₄

Direct product G=N×Q with N=C₂² and Q=C₄.A₄

		d	ρ	Label	ID
C₂²×C₄.A₄		64		C2^2xC4.A4	192,1500

Semidirect products G=N:Q with N=C₂² and Q=C₄.A₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂²⋊(C₄.A₄) = C₄○D₄⋊A₄	φ: C₄.A₄/C₄○D₄ → C₃ ⊆ Aut C₂²	24	6	C2^2:(C4.A4)	192,1507
C₂²⋊₂(C₄.A₄) = SL₂(𝔽₃)⋊₅D₄	φ: C₄.A₄/SL₂(𝔽₃) → C₂ ⊆ Aut C₂²	32		C2^2:2(C4.A4)	192,1003

Non-split extensions G=N.Q with N=C₂² and Q=C₄.A₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂².₁(C₄.A₄) = C₄²⋊₄C₄⋊C₃	φ: C₄.A₄/C₄○D₄ → C₃ ⊆ Aut C₂²	24	6	C2^2.1(C4.A4)	192,190
C₂².₂(C₄.A₄) = C₂³⋊₂D₄⋊C₃	φ: C₄.A₄/C₄○D₄ → C₃ ⊆ Aut C₂²	12	6+	C2^2.2(C4.A4)	192,194
C₂².₃(C₄.A₄) = (C₂²×C₄).A₄	φ: C₄.A₄/C₄○D₄ → C₃ ⊆ Aut C₂²	24	6-	C2^2.3(C4.A4)	192,196
C₂².₄(C₄.A₄) = C₂³.₁₉(C₂×A₄)	φ: C₄.A₄/C₄○D₄ → C₃ ⊆ Aut C₂²	24	6	C2^2.4(C4.A4)	192,199
C₂².₅(C₄.A₄) = C₂×C₄×SL₂(𝔽₃)	central extension (φ=1)	64		C2^2.5(C4.A4)	192,996

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