Extensions 1→N→G→Q→1 with N=C₁₀ and Q=D₆

Direct product G=N×Q with N=C₁₀ and Q=D₆

		d	ρ	Label	ID
S₃×C₂×C₁₀		60		S3xC2xC10	120,45

Semidirect products G=N:Q with N=C₁₀ and Q=D₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀⋊₁D₆ = C₂×S₃×D₅	φ: D₆/S₃ → C₂ ⊆ Aut C₁₀	30	4+	C10:1D6	120,42
C₁₀⋊₂D₆ = C₂²×D₁₅	φ: D₆/C₆ → C₂ ⊆ Aut C₁₀	60		C10:2D6	120,46

Non-split extensions G=N.Q with N=C₁₀ and Q=D₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀.₁D₆ = D₅×Dic₃	φ: D₆/S₃ → C₂ ⊆ Aut C₁₀	60	4-	C10.1D6	120,8
C₁₀.₂D₆ = S₃×Dic₅	φ: D₆/S₃ → C₂ ⊆ Aut C₁₀	60	4-	C10.2D6	120,9
C₁₀.₃D₆ = D₃₀.C₂	φ: D₆/S₃ → C₂ ⊆ Aut C₁₀	60	4+	C10.3D6	120,10
C₁₀.₄D₆ = C₁₅⋊D₄	φ: D₆/S₃ → C₂ ⊆ Aut C₁₀	60	4-	C10.4D6	120,11
C₁₀.₅D₆ = C₃⋊D₂₀	φ: D₆/S₃ → C₂ ⊆ Aut C₁₀	60	4+	C10.5D6	120,12
C₁₀.₆D₆ = C₅⋊D₁₂	φ: D₆/S₃ → C₂ ⊆ Aut C₁₀	60	4+	C10.6D6	120,13
C₁₀.₇D₆ = C₁₅⋊Q₈	φ: D₆/S₃ → C₂ ⊆ Aut C₁₀	120	4-	C10.7D6	120,14
C₁₀.₈D₆ = Dic₃₀	φ: D₆/C₆ → C₂ ⊆ Aut C₁₀	120	2-	C10.8D6	120,26
C₁₀.₉D₆ = C₄×D₁₅	φ: D₆/C₆ → C₂ ⊆ Aut C₁₀	60	2	C10.9D6	120,27
C₁₀.₁₀D₆ = D₆₀	φ: D₆/C₆ → C₂ ⊆ Aut C₁₀	60	2+	C10.10D6	120,28
C₁₀.₁₁D₆ = C₂×Dic₁₅	φ: D₆/C₆ → C₂ ⊆ Aut C₁₀	120		C10.11D6	120,29
C₁₀.₁₂D₆ = C₁₅⋊₇D₄	φ: D₆/C₆ → C₂ ⊆ Aut C₁₀	60	2	C10.12D6	120,30
C₁₀.₁₃D₆ = C₅×Dic₆	central extension (φ=1)	120	2	C10.13D6	120,21
C₁₀.₁₄D₆ = S₃×C₂₀	central extension (φ=1)	60	2	C10.14D6	120,22
C₁₀.₁₅D₆ = C₅×D₁₂	central extension (φ=1)	60	2	C10.15D6	120,23
C₁₀.₁₆D₆ = C₁₀×Dic₃	central extension (φ=1)	120		C10.16D6	120,24
C₁₀.₁₇D₆ = C₅×C₃⋊D₄	central extension (φ=1)	60	2	C10.17D6	120,25

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