Extensions 1→N→G→Q→1 with N=C₁₀ and Q=S₃²

Direct product G=N×Q with N=C₁₀ and Q=S₃²

		d	ρ	Label	ID
S₃²×C₁₀		60	4	S3^2xC10	360,153

Semidirect products G=N:Q with N=C₁₀ and Q=S₃²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀⋊₁S₃² = C₂×S₃×D₁₅	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₀	60	4+	C10:1S3^2	360,154
C₁₀⋊₂S₃² = C₂×D₁₅⋊S₃	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₀	60	4	C10:2S3^2	360,155

Non-split extensions G=N.Q with N=C₁₀ and Q=S₃²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀.₁S₃² = Dic₃×D₁₅	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₀	120	4-	C10.1S3^2	360,77
C₁₀.₂S₃² = S₃×Dic₁₅	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₀	120	4-	C10.2S3^2	360,78
C₁₀.₃S₃² = C₆.D₃₀	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₀	60	4+	C10.3S3^2	360,79
C₁₀.₄S₃² = D₆⋊D₁₅	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₀	120	4-	C10.4S3^2	360,80
C₁₀.₅S₃² = C₃⋊D₆₀	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₀	60	4+	C10.5S3^2	360,81
C₁₀.₆S₃² = D₆⋊₂D₁₅	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₀	60	4+	C10.6S3^2	360,82
C₁₀.₇S₃² = C₃⋊Dic₃₀	φ: S₃²/C₃×S₃ → C₂ ⊆ Aut C₁₀	120	4-	C10.7S3^2	360,83
C₁₀.₈S₃² = D₃₀.S₃	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₀	120	4	C10.8S3^2	360,84
C₁₀.₉S₃² = Dic₁₅⋊S₃	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₀	60	4	C10.9S3^2	360,85
C₁₀.₁₀S₃² = D₃₀⋊S₃	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₀	60	4	C10.10S3^2	360,86
C₁₀.₁₁S₃² = C₃²⋊₃D₂₀	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₀	120	4	C10.11S3^2	360,87
C₁₀.₁₂S₃² = C₃²⋊₃Dic₁₀	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Aut C₁₀	120	4	C10.12S3^2	360,88
C₁₀.₁₃S₃² = C₅×S₃×Dic₃	central extension (φ=1)	120	4	C10.13S3^2	360,72
C₁₀.₁₄S₃² = C₅×C₆.D₆	central extension (φ=1)	60	4	C10.14S3^2	360,73
C₁₀.₁₅S₃² = C₅×D₆⋊S₃	central extension (φ=1)	120	4	C10.15S3^2	360,74
C₁₀.₁₆S₃² = C₅×C₃⋊D₁₂	central extension (φ=1)	60	4	C10.16S3^2	360,75
C₁₀.₁₇S₃² = C₅×C₃²⋊₂Q₈	central extension (φ=1)	120	4	C10.17S3^2	360,76

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