Extensions 1→N→G→Q→1 with N=Q₈ and Q=C₃×D₅

Direct product G=N×Q with N=Q₈ and Q=C₃×D₅

		d	ρ	Label	ID
C₃×Q₈×D₅		120	4	C3xQ8xD5	240,161

Semidirect products G=N:Q with N=Q₈ and Q=C₃×D₅

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈⋊(C₃×D₅) = D₅×SL₂(𝔽₃)	φ: C₃×D₅/D₅ → C₃ ⊆ Out Q₈	40	4-	Q8:(C3xD5)	240,109
Q₈⋊₂(C₃×D₅) = C₃×Q₈⋊D₅	φ: C₃×D₅/C₁₅ → C₂ ⊆ Out Q₈	120	4	Q8:2(C3xD5)	240,46
Q₈⋊₃(C₃×D₅) = C₃×Q₈⋊₂D₅	φ: trivial image	120	4	Q8:3(C3xD5)	240,162

Non-split extensions G=N.Q with N=Q₈ and Q=C₃×D₅

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈.(C₃×D₅) = Dic₅.A₄	φ: C₃×D₅/D₅ → C₃ ⊆ Out Q₈	80	4+	Q8.(C3xD5)	240,108
Q₈.₂(C₃×D₅) = C₃×C₅⋊Q₁₆	φ: C₃×D₅/C₁₅ → C₂ ⊆ Out Q₈	240	4	Q8.2(C3xD5)	240,47

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=Q8 and Q=C3×D5