Extensions 1→N→G→Q→1 with N=C₉ and Q=C₂×C₇⋊C₃

Direct product G=N×Q with N=C₉ and Q=C₂×C₇⋊C₃

		d	ρ	Label	ID
C₁₈×C₇⋊C₃		126	3	C18xC7:C3	378,23

Semidirect products G=N:Q with N=C₉ and Q=C₂×C₇⋊C₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₉⋊₁(C₂×C₇⋊C₃) = C₆₃⋊C₆	φ: C₂×C₇⋊C₃/C₇ → C₆ ⊆ Aut C₉	63	6	C9:1(C2xC7:C3)	378,13
C₉⋊₂(C₂×C₇⋊C₃) = C₆₃⋊₆C₆	φ: C₂×C₇⋊C₃/C₇ → C₆ ⊆ Aut C₉	63	6	C9:2(C2xC7:C3)	378,14
C₉⋊₃(C₂×C₇⋊C₃) = C₂×C₆₃⋊C₃	φ: C₂×C₇⋊C₃/C₁₄ → C₃ ⊆ Aut C₉	126	3	C9:3(C2xC7:C3)	378,24
C₉⋊₄(C₂×C₇⋊C₃) = C₂×C₆₃⋊₃C₃	φ: C₂×C₇⋊C₃/C₁₄ → C₃ ⊆ Aut C₉	126	3	C9:4(C2xC7:C3)	378,25
C₉⋊₅(C₂×C₇⋊C₃) = D₉×C₇⋊C₃	φ: C₂×C₇⋊C₃/C₇⋊C₃ → C₂ ⊆ Aut C₉	63	6	C9:5(C2xC7:C3)	378,15

Non-split extensions G=N.Q with N=C₉ and Q=C₂×C₇⋊C₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₉.(C₂×C₇⋊C₃) = C₂×C₇⋊C₂₇	central extension (φ=1)	378	3	C9.(C2xC7:C3)	378,2

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁