Extensions 1→N→G→Q→1 with N=C₈₄ and Q=C₃

Direct product G=N×Q with N=C₈₄ and Q=C₃

		d	ρ	Label	ID
C₃×C₈₄		252		C3xC84	252,25

Semidirect products G=N:Q with N=C₈₄ and Q=C₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈₄⋊C₃ = C₁₂×C₇⋊C₃	φ: C₃/C₁ → C₃ ⊆ Aut C₈₄	84	3	C84:C3	252,19

Non-split extensions G=N.Q with N=C₈₄ and Q=C₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈₄.C₃ = C₄×C₇⋊C₉	φ: C₃/C₁ → C₃ ⊆ Aut C₈₄	252	3	C84.C3	252,2

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C84 and Q=C3