Extensions 1→N→G→Q→1 with N=C₃×C₂₁ and Q=C₃

Direct product G=N×Q with N=C₃×C₂₁ and Q=C₃

		d	ρ	Label	ID
C₃²×C₂₁		189		C3^2xC21	189,13

Semidirect products G=N:Q with N=C₃×C₂₁ and Q=C₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₂₁)⋊₁C₃ = C₇×He₃	φ: C₃/C₁ → C₃ ⊆ Aut C₃×C₂₁	63	3	(C3xC21):1C3	189,10
(C₃×C₂₁)⋊₂C₃ = C₇⋊He₃	φ: C₃/C₁ → C₃ ⊆ Aut C₃×C₂₁	63	3	(C3xC21):2C3	189,8
(C₃×C₂₁)⋊₃C₃ = C₃²×C₇⋊C₃	φ: C₃/C₁ → C₃ ⊆ Aut C₃×C₂₁	63		(C3xC21):3C3	189,12

Non-split extensions G=N.Q with N=C₃×C₂₁ and Q=C₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₂₁).₁C₃ = C₇×3_-¹⁺²	φ: C₃/C₁ → C₃ ⊆ Aut C₃×C₂₁	63	3	(C3xC21).1C3	189,11
(C₃×C₂₁).₂C₃ = C₃×C₇⋊C₉	φ: C₃/C₁ → C₃ ⊆ Aut C₃×C₂₁	189		(C3xC21).2C3	189,6
(C₃×C₂₁).₃C₃ = C₂₁.C₃²	φ: C₃/C₁ → C₃ ⊆ Aut C₃×C₂₁	63	3	(C3xC21).3C3	189,7

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C3×C21 and Q=C3