Extensions 1→N→G→Q→1 with N=C₂⁴ and Q=A₄

Direct product G=N×Q with N=C₂⁴ and Q=A₄

		d	ρ	Label	ID
A₄×C₂⁴		48		A4xC2^4	192,1539

Semidirect products G=N:Q with N=C₂⁴ and Q=A₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂⁴⋊₁A₄ = C₂≀A₄	φ: A₄/C₁ → A₄ ⊆ Aut C₂⁴	8	4+	C2^4:1A4	192,201
C₂⁴⋊₂A₄ = C₂×C₂⁴⋊C₆	φ: A₄/C₁ → A₄ ⊆ Aut C₂⁴	12	6+	C2^4:2A4	192,1000
C₂⁴⋊₃A₄ = C₂⁴⋊A₄	φ: A₄/C₁ → A₄ ⊆ Aut C₂⁴	16	12+	C2^4:3A4	192,1009
C₂⁴⋊₄A₄ = C₄²⋊A₄	φ: A₄/C₁ → A₄ ⊆ Aut C₂⁴	16	12+	C2^4:4A4	192,1023
C₂⁴⋊₅A₄ = C₂⁴⋊₅A₄	φ: A₄/C₁ → A₄ ⊆ Aut C₂⁴	16		C2^4:5A4	192,1024
C₂⁴⋊₆A₄ = C₂×C₂³⋊A₄	φ: A₄/C₁ → A₄ ⊆ Aut C₂⁴	16		C2^4:6A4	192,1508
C₂⁴⋊₇A₄ = C₂²×C₂²⋊A₄	φ: A₄/C₂² → C₃ ⊆ Aut C₂⁴	12		C2^4:7A4	192,1540
C₂⁴⋊₈A₄ = C₂⁶⋊C₃	φ: A₄/C₂² → C₃ ⊆ Aut C₂⁴	24		C2^4:8A4	192,1541

Non-split extensions G=N.Q with N=C₂⁴ and Q=A₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂⁴.₁A₄ = C₂⁴.A₄	φ: A₄/C₁ → A₄ ⊆ Aut C₂⁴	24	6	C2^4.1A4	192,195
C₂⁴.₂A₄ = C₂⁴.₂A₄	φ: A₄/C₁ → A₄ ⊆ Aut C₂⁴	12	6+	C2^4.2A4	192,197
C₂⁴.₃A₄ = C₂⁴.₃A₄	φ: A₄/C₁ → A₄ ⊆ Aut C₂⁴	24	6	C2^4.3A4	192,198
C₂⁴.₄A₄ = C₂×C₄²⋊C₆	φ: A₄/C₁ → A₄ ⊆ Aut C₂⁴	24	6	C2^4.4A4	192,1001
C₂⁴.₅A₄ = C₂×C₂³.A₄	φ: A₄/C₁ → A₄ ⊆ Aut C₂⁴	12	6+	C2^4.5A4	192,1002
C₂⁴.₆A₄ = C₂⁴.₆A₄	φ: A₄/C₁ → A₄ ⊆ Aut C₂⁴	16	12+	C2^4.6A4	192,1008
C₂⁴.₇A₄ = C₂⁴.₇A₄	φ: A₄/C₁ → A₄ ⊆ Aut C₂⁴	16		C2^4.7A4	192,1021
C₂⁴.₈A₄ = C₂×C₂³.₃A₄	φ: A₄/C₂² → C₃ ⊆ Aut C₂⁴	24		C2^4.8A4	192,189
C₂⁴.₉A₄ = C₂²×C₄²⋊C₃	φ: A₄/C₂² → C₃ ⊆ Aut C₂⁴	24		C2^4.9A4	192,992
C₂⁴.₁₀A₄ = C₄²⋊₂A₄	φ: A₄/C₂² → C₃ ⊆ Aut C₂⁴	24		C2^4.10A4	192,1020
C₂⁴.₁₁A₄ = C₂×Q₈⋊A₄	φ: A₄/C₂² → C₃ ⊆ Aut C₂⁴	48		C2^4.11A4	192,1506
C₂⁴.₁₂A₄ = C₂³×SL₂(𝔽₃)	central extension (φ=1)	64		C2^4.12A4	192,1498

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