Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃²⋊C₁₈

Direct product G=N×Q with N=C₃ and Q=C₃²⋊C₁₈

		d	ρ	Label	ID
C₃×C₃²⋊C₁₈		54		C3xC3^2:C18	486,93

Semidirect products G=N:Q with N=C₃ and Q=C₃²⋊C₁₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(C₃²⋊C₁₈) = C₃³⋊C₁₈	φ: C₃²⋊C₁₈/C₃²⋊C₉ → C₂ ⊆ Aut C₃	54		C3:(C3^2:C18)	486,136

Non-split extensions G=N.Q with N=C₃ and Q=C₃²⋊C₁₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₃²⋊C₁₈) = C₉⋊S₃⋊C₉	φ: C₃²⋊C₁₈/C₃²⋊C₉ → C₂ ⊆ Aut C₃	54		C3.1(C3^2:C18)	486,3
C₃.₂(C₃²⋊C₁₈) = C₃³⋊₁C₁₈	φ: C₃²⋊C₁₈/C₃²⋊C₉ → C₂ ⊆ Aut C₃	18	6	C3.2(C3^2:C18)	486,18
C₃.₃(C₃²⋊C₁₈) = (C₃×C₉)⋊C₁₈	φ: C₃²⋊C₁₈/C₃²⋊C₉ → C₂ ⊆ Aut C₃	54	6	C3.3(C3^2:C18)	486,20
C₃.₄(C₃²⋊C₁₈) = C₉⋊S₃⋊₃C₉	φ: C₃²⋊C₁₈/C₃²⋊C₉ → C₂ ⊆ Aut C₃	54	6	C3.4(C3^2:C18)	486,22
C₃.₅(C₃²⋊C₁₈) = C₃²⋊C₅₄	central extension (φ=1)	54	6	C3.5(C3^2:C18)	486,16
C₃.₆(C₃²⋊C₁₈) = He₃⋊C₁₈	central stem extension (φ=1)	81		C3.6(C3^2:C18)	486,24
C₃.₇(C₃²⋊C₁₈) = He₃.C₁₈	central stem extension (φ=1)	81	3	C3.7(C3^2:C18)	486,26
C₃.₈(C₃²⋊C₁₈) = He₃.₂C₁₈	central stem extension (φ=1)	81	3	C3.8(C3^2:C18)	486,28

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁