Extensions 1→N→G→Q→1 with N=D₆ and Q=S₃²

Direct product G=N×Q with N=D₆ and Q=S₃²

		d	ρ	Label	ID
C₂×S₃³		24	8+	C2xS3^3	432,759

Semidirect products G=N:Q with N=D₆ and Q=S₃²

extension	φ:Q→Out N	d	ρ	Label	ID
D₆⋊₁S₃² = S₃×D₆⋊S₃	φ: S₃²/C₃×S₃ → C₂ ⊆ Out D₆	48	8-	D6:1S3^2	432,597
D₆⋊₂S₃² = S₃×C₃⋊D₁₂	φ: S₃²/C₃×S₃ → C₂ ⊆ Out D₆	24	8+	D6:2S3^2	432,598
D₆⋊₃S₃² = D₆⋊S₃²	φ: S₃²/C₃×S₃ → C₂ ⊆ Out D₆	48	8-	D6:3S3^2	432,600
D₆⋊₄S₃² = D₆⋊₄S₃²	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Out D₆	24	8+	D6:4S3^2	432,599
D₆⋊₅S₃² = (S₃×C₆)⋊D₆	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Out D₆	24	8+	D6:5S3^2	432,601
D₆⋊₆S₃² = C₃⋊S₃⋊₄D₁₂	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Out D₆	24	8+	D6:6S3^2	432,602

Non-split extensions G=N.Q with N=D₆ and Q=S₃²

extension	φ:Q→Out N	d	ρ	Label	ID
D₆.₁S₃² = (S₃×C₆).D₆	φ: S₃²/C₃×S₃ → C₂ ⊆ Out D₆	24	8+	D6.1S3^2	432,606
D₆.₂S₃² = D₆.S₃²	φ: S₃²/C₃×S₃ → C₂ ⊆ Out D₆	48	8-	D6.2S3^2	432,607
D₆.₃S₃² = D₆.₃S₃²	φ: S₃²/C₃×S₃ → C₂ ⊆ Out D₆	24	8+	D6.3S3^2	432,609
D₆.₄S₃² = D₆.₄S₃²	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Out D₆	48	8-	D6.4S3^2	432,608
D₆.₅S₃² = D₆⋊S₃⋊S₃	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Out D₆	48	8-	D6.5S3^2	432,610
D₆.₆S₃² = D₆.₆S₃²	φ: S₃²/C₃⋊S₃ → C₂ ⊆ Out D₆	48	8-	D6.6S3^2	432,611
D₆.₇S₃² = S₃²×Dic₃	φ: trivial image	48	8-	D6.7S3^2	432,594
D₆.₈S₃² = S₃×C₆.D₆	φ: trivial image	24	8+	D6.8S3^2	432,595
D₆.₉S₃² = S₃×C₃²⋊₂Q₈	φ: trivial image	48	8-	D6.9S3^2	432,603

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁