Extensions 1→N→G→Q→1 with N=C₂₁ and Q=C₆

Direct product G=N×Q with N=C₂₁ and Q=C₆

		d	ρ	Label	ID
C₃×C₄₂		126		C3xC42	126,16

Semidirect products G=N:Q with N=C₂₁ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₁⋊₁C₆ = C₃⋊F₇	φ: C₆/C₁ → C₆ ⊆ Aut C₂₁	21	6+	C21:1C6	126,9
C₂₁⋊₂C₆ = C₃×F₇	φ: C₆/C₁ → C₆ ⊆ Aut C₂₁	21	6	C21:2C6	126,7
C₂₁⋊₃C₆ = S₃×C₇⋊C₃	φ: C₆/C₁ → C₆ ⊆ Aut C₂₁	21	6	C21:3C6	126,8
C₂₁⋊₄C₆ = C₆×C₇⋊C₃	φ: C₆/C₂ → C₃ ⊆ Aut C₂₁	42	3	C21:4C6	126,10
C₂₁⋊₅C₆ = C₃×D₂₁	φ: C₆/C₃ → C₂ ⊆ Aut C₂₁	42	2	C21:5C6	126,13
C₂₁⋊₆C₆ = C₃²×D₇	φ: C₆/C₃ → C₂ ⊆ Aut C₂₁	63		C21:6C6	126,11
C₂₁⋊₇C₆ = S₃×C₂₁	φ: C₆/C₃ → C₂ ⊆ Aut C₂₁	42	2	C21:7C6	126,12

Non-split extensions G=N.Q with N=C₂₁ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₁.C₆ = C₇⋊C₁₈	φ: C₆/C₁ → C₆ ⊆ Aut C₂₁	63	6	C21.C6	126,1
C₂₁.₂C₆ = C₂×C₇⋊C₉	φ: C₆/C₂ → C₃ ⊆ Aut C₂₁	126	3	C21.2C6	126,2
C₂₁.₃C₆ = C₉×D₇	φ: C₆/C₃ → C₂ ⊆ Aut C₂₁	63	2	C21.3C6	126,4

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