Extensions 1→N→G→Q→1 with N=C₂⁴ and Q=C₅×S₃

Direct product G=N×Q with N=C₂⁴ and Q=C₅×S₃

		d	ρ	Label	ID
S₃×C₂³×C₁₀		240		S3xC2^3xC10	480,1211

Semidirect products G=N:Q with N=C₂⁴ and Q=C₅×S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂⁴⋊₁(C₅×S₃) = C₅×A₄⋊D₄	φ: C₅×S₃/C₅ → S₃ ⊆ Aut C₂⁴	60	6	C2^4:1(C5xS3)	480,1023
C₂⁴⋊₂(C₅×S₃) = C₂×C₁₀×S₄	φ: C₅×S₃/C₅ → S₃ ⊆ Aut C₂⁴	60		C2^4:2(C5xS3)	480,1198
C₂⁴⋊₃(C₅×S₃) = C₅×C₂²⋊S₄	φ: C₅×S₃/C₅ → S₃ ⊆ Aut C₂⁴	40	6	C2^4:3(C5xS3)	480,1200
C₂⁴⋊₄(C₅×S₃) = S₃×C₂⁴⋊C₅	φ: C₅×S₃/S₃ → C₅ ⊆ Aut C₂⁴	30	10+	C2^4:4(C5xS3)	480,1196
C₂⁴⋊₅(C₅×S₃) = C₅×C₂⁴⋊₄S₃	φ: C₅×S₃/C₁₅ → C₂ ⊆ Aut C₂⁴	120		C2^4:5(C5xS3)	480,832
C₂⁴⋊₆(C₅×S₃) = C₂×C₁₀×C₃⋊D₄	φ: C₅×S₃/C₁₅ → C₂ ⊆ Aut C₂⁴	240		C2^4:6(C5xS3)	480,1164

Non-split extensions G=N.Q with N=C₂⁴ and Q=C₅×S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂⁴.(C₅×S₃) = C₁₀×A₄⋊C₄	φ: C₅×S₃/C₅ → S₃ ⊆ Aut C₂⁴	120		C2^4.(C5xS3)	480,1022
C₂⁴.₂(C₅×S₃) = C₁₀×C₆.D₄	φ: C₅×S₃/C₁₅ → C₂ ⊆ Aut C₂⁴	240		C2^4.2(C5xS3)	480,831
C₂⁴.₃(C₅×S₃) = Dic₃×C₂²×C₁₀	central extension (φ=1)	480		C2^4.3(C5xS3)	480,1163

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