Extensions 1→N→G→Q→1 with N=C₂³ and Q=S₃×C₃²

Direct product G=N×Q with N=C₂³ and Q=S₃×C₃²

		d	ρ	Label	ID
S₃×C₂×C₆²		144		S3xC2xC6^2	432,772

Semidirect products G=N:Q with N=C₂³ and Q=S₃×C₃²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊(S₃×C₃²) = C₃×C₆×S₄	φ: S₃×C₃²/C₃² → S₃ ⊆ Aut C₂³	54		C2^3:(S3xC3^2)	432,760
C₂³⋊₂(S₃×C₃²) = S₃×C₆×A₄	φ: S₃×C₃²/C₃×S₃ → C₃ ⊆ Aut C₂³	36	6	C2^3:2(S3xC3^2)	432,763
C₂³⋊₃(S₃×C₃²) = C₃×C₆×C₃⋊D₄	φ: S₃×C₃²/C₃³ → C₂ ⊆ Aut C₂³	72		C2^3:3(S3xC3^2)	432,709

Non-split extensions G=N.Q with N=C₂³ and Q=S₃×C₃²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.(S₃×C₃²) = C₃²×A₄⋊C₄	φ: S₃×C₃²/C₃² → S₃ ⊆ Aut C₂³	108		C2^3.(S3xC3^2)	432,615
C₂³.₂(S₃×C₃²) = C₃×Dic₃×A₄	φ: S₃×C₃²/C₃×S₃ → C₃ ⊆ Aut C₂³	36	6	C2^3.2(S3xC3^2)	432,624
C₂³.₃(S₃×C₃²) = C₃²×C₆.D₄	φ: S₃×C₃²/C₃³ → C₂ ⊆ Aut C₂³	72		C2^3.3(S3xC3^2)	432,479
C₂³.₄(S₃×C₃²) = Dic₃×C₆²	central extension (φ=1)	144		C2^3.4(S3xC3^2)	432,708

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁