Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₅×A₄

Direct product G=N×Q with N=C₂³ and Q=C₅×A₄

		d	ρ	Label	ID
A₄×C₂²×C₁₀		120		A4xC2^2xC10	480,1208

Semidirect products G=N:Q with N=C₂³ and Q=C₅×A₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊₁(C₅×A₄) = C₅×C₂⁴⋊C₆	φ: C₅×A₄/C₅ → A₄ ⊆ Aut C₂³	40	6	C2^3:1(C5xA4)	480,656
C₂³⋊₂(C₅×A₄) = C₅×C₂³⋊A₄	φ: C₅×A₄/C₅ → A₄ ⊆ Aut C₂³	40	4	C2^3:2(C5xA4)	480,1134
C₂³⋊₃(C₅×A₄) = C₁₀×C₂²⋊A₄	φ: C₅×A₄/C₂×C₁₀ → C₃ ⊆ Aut C₂³	60		C2^3:3(C5xA4)	480,1209

Non-split extensions G=N.Q with N=C₂³ and Q=C₅×A₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.₁(C₅×A₄) = C₅×C₄²⋊C₆	φ: C₅×A₄/C₅ → A₄ ⊆ Aut C₂³	80	6	C2^3.1(C5xA4)	480,657
C₂³.₂(C₅×A₄) = C₅×C₂³.A₄	φ: C₅×A₄/C₅ → A₄ ⊆ Aut C₂³	60	6	C2^3.2(C5xA4)	480,658
C₂³.₃(C₅×A₄) = C₅×C₂³.₃A₄	φ: C₅×A₄/C₂×C₁₀ → C₃ ⊆ Aut C₂³	60	6	C2^3.3(C5xA4)	480,74
C₂³.₄(C₅×A₄) = C₁₀×C₄²⋊C₃	φ: C₅×A₄/C₂×C₁₀ → C₃ ⊆ Aut C₂³	60	3	C2^3.4(C5xA4)	480,654
C₂³.₅(C₅×A₄) = C₅×Q₈⋊A₄	φ: C₅×A₄/C₂×C₁₀ → C₃ ⊆ Aut C₂³	120	6	C2^3.5(C5xA4)	480,1133
C₂³.₆(C₅×A₄) = C₂×C₁₀×SL₂(𝔽₃)	central extension (φ=1)	160		C2^3.6(C5xA4)	480,1128

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