Extensions 1→N→G→Q→1 with N=C₅⋊D₅ and Q=S₃

Direct product G=N×Q with N=C₅⋊D₅ and Q=S₃

		d	ρ	Label	ID
S₃×C₅⋊D₅		75		S3xC5:D5	300,38

Semidirect products G=N:Q with N=C₅⋊D₅ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
C₅⋊D₅⋊S₃ = C₅²⋊D₆	φ: S₃/C₁ → S₃ ⊆ Out C₅⋊D₅	15	6+	C5:D5:S3	300,25
C₅⋊D₅⋊₂S₃ = D₁₅⋊D₅	φ: S₃/C₃ → C₂ ⊆ Out C₅⋊D₅	30	4	C5:D5:2S3	300,40

Non-split extensions G=N.Q with N=C₅⋊D₅ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
C₅⋊D₅.S₃ = C₅²⋊Dic₃	φ: S₃/C₁ → S₃ ⊆ Out C₅⋊D₅	15	12+	C5:D5.S3	300,23
C₅⋊D₅.₂S₃ = C₁₅⋊F₅	φ: S₃/C₃ → C₂ ⊆ Out C₅⋊D₅	75		C5:D5.2S3	300,34
C₅⋊D₅.₃S₃ = C₁₅⋊₂F₅	φ: S₃/C₃ → C₂ ⊆ Out C₅⋊D₅	30	4	C5:D5.3S3	300,35

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C5⋊D5 and Q=S3