Extensions 1→N→G→Q→1 with N=C₂⁵ and Q=S₃

Direct product G=N×Q with N=C₂⁵ and Q=S₃

		d	ρ	Label	ID
S₃×C₂⁵		96		S3xC2^5	192,1542

Semidirect products G=N:Q with N=C₂⁵ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂⁵⋊₁S₃ = C₂×A₄⋊D₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂⁵	24		C2^5:1S3	192,1488
C₂⁵⋊₂S₃ = C₂³×S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂⁵	24		C2^5:2S3	192,1537
C₂⁵⋊₃S₃ = C₂×C₂²⋊S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂⁵	12	6+	C2^5:3S3	192,1538
C₂⁵⋊₄S₃ = C₂×C₂⁴⋊₄S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₂⁵	48		C2^5:4S3	192,1399
C₂⁵⋊₅S₃ = C₂³×C₃⋊D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂⁵	96		C2^5:5S3	192,1529

Non-split extensions G=N.Q with N=C₂⁵ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂⁵.₁S₃ = C₂⁵.S₃	φ: S₃/C₁ → S₃ ⊆ Aut C₂⁵	24		C2^5.1S3	192,991
C₂⁵.₂S₃ = C₂²×A₄⋊C₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂⁵	48		C2^5.2S3	192,1487
C₂⁵.₃S₃ = C₂⁴⋊₄Dic₃	φ: S₃/C₁ → S₃ ⊆ Aut C₂⁵	12	6+	C2^5.3S3	192,1495
C₂⁵.₄S₃ = C₂⁵.₄S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₂⁵	48		C2^5.4S3	192,806
C₂⁵.₅S₃ = C₂²×C₆.D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂⁵	96		C2^5.5S3	192,1398
C₂⁵.₆S₃ = Dic₃×C₂⁴	central extension (φ=1)	192		C2^5.6S3	192,1528

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