Extensions 1→N→G→Q→1 with N=C₅ and Q=Q₈○M₄(2)

Direct product G=N×Q with N=C₅ and Q=Q₈○M₄(2)

		d	ρ	Label	ID
C₅×Q₈○M₄(2)		80	4	C5xQ8oM4(2)	320,1570

Semidirect products G=N:Q with N=C₅ and Q=Q₈○M₄(2)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊₁(Q₈○M₄(2)) = Dic₅.C₂⁴	φ: Q₈○M₄(2)/C₂×D₄ → C₄ ⊆ Aut C₅	80	8-	C5:1(Q8oM4(2))	320,1594
C₅⋊₂(Q₈○M₄(2)) = Dic₅.₂₀C₂⁴	φ: Q₈○M₄(2)/C₂×Q₈ → C₄ ⊆ Aut C₅	80	8+	C5:2(Q8oM4(2))	320,1598
C₅⋊₃(Q₈○M₄(2)) = Dic₅.₂₂C₂⁴	φ: Q₈○M₄(2)/C₄○D₄ → C₄ ⊆ Aut C₅	80	8	C5:3(Q8oM4(2))	320,1602
C₅⋊₄(Q₈○M₄(2)) = C₄₀.₄₇C₂³	φ: Q₈○M₄(2)/C₂×M₄(2) → C₂ ⊆ Aut C₅	80	4	C5:4(Q8oM4(2))	320,1417
C₅⋊₅(Q₈○M₄(2)) = C₂₀.₇₂C₂⁴	φ: Q₈○M₄(2)/C₈○D₄ → C₂ ⊆ Aut C₅	80	4	C5:5(Q8oM4(2))	320,1422
C₅⋊₆(Q₈○M₄(2)) = C₂₀.₇₆C₂⁴	φ: Q₈○M₄(2)/C₂×C₄○D₄ → C₂ ⊆ Aut C₅	80	4	C5:6(Q8oM4(2))	320,1491

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁