Extensions 1→N→G→Q→1 with N=C₅ and Q=C₂³.₄Q₈

Direct product G=N×Q with N=C₅ and Q=C₂³.₄Q₈

		d	ρ	Label	ID
C₅×C₂³.₄Q₈		160		C5xC2^3.4Q8	320,900

Semidirect products G=N:Q with N=C₅ and Q=C₂³.₄Q₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊₁(C₂³.₄Q₈) = (C₂×C₂₀).₃₃D₄	φ: C₂³.₄Q₈/C₂.C₄² → C₂ ⊆ Aut C₅	160		C5:1(C2^3.4Q8)	320,304
C₅⋊₂(C₂³.₄Q₈) = C₂⁴.₇D₁₀	φ: C₂³.₄Q₈/C₂×C₂²⋊C₄ → C₂ ⊆ Aut C₅	160		C5:2(C2^3.4Q8)	320,576
C₅⋊₃(C₂³.₄Q₈) = (C₂×C₂₀).₂₈₉D₄	φ: C₂³.₄Q₈/C₂×C₄⋊C₄ → C₂ ⊆ Aut C₅	160		C5:3(C2^3.4Q8)	320,619

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁