Extensions 1→N→G→Q→1 with N=C₅ and Q=Q₈⋊₂D₅

Direct product G=N×Q with N=C₅ and Q=Q₈⋊₂D₅

		d	ρ	Label	ID
C₅×Q₈⋊₂D₅		80	4	C5xQ8:2D5	400,188

Semidirect products G=N:Q with N=C₅ and Q=Q₈⋊₂D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊₁(Q₈⋊₂D₅) = Dic₁₀⋊₅D₅	φ: Q₈⋊₂D₅/C₄×D₅ → C₂ ⊆ Aut C₅	40	4+	C5:1(Q8:2D5)	400,168
C₅⋊₂(Q₈⋊₂D₅) = D₂₀⋊D₅	φ: Q₈⋊₂D₅/D₂₀ → C₂ ⊆ Aut C₅	40	4	C5:2(Q8:2D5)	400,165
C₅⋊₃(Q₈⋊₂D₅) = C₂₀.₂₆D₁₀	φ: Q₈⋊₂D₅/C₅×Q₈ → C₂ ⊆ Aut C₅	200		C5:3(Q8:2D5)	400,198

Non-split extensions G=N.Q with N=C₅ and Q=Q₈⋊₂D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅.(Q₈⋊₂D₅) = Q₈⋊₂D₂₅	φ: Q₈⋊₂D₅/C₅×Q₈ → C₂ ⊆ Aut C₅	200	4+	C5.(Q8:2D5)	400,42

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C5 and Q=Q8⋊2D5