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

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

		d	ρ	Label	ID
Q₈×C₂²×C₁₀		320		Q8xC2^2xC10	320,1630

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊₁(C₅×Q₈) = C₅×C₂³⋊Q₈	φ: C₅×Q₈/C₁₀ → C₂² ⊆ Aut C₂³	160		C2^3:1(C5xQ8)	320,894
C₂³⋊₂(C₅×Q₈) = C₅×C₂³⋊₂Q₈	φ: C₅×Q₈/C₁₀ → C₂² ⊆ Aut C₂³	80		C2^3:2(C5xQ8)	320,1545
C₂³⋊₃(C₅×Q₈) = C₁₀×C₂²⋊Q₈	φ: C₅×Q₈/C₂₀ → C₂ ⊆ Aut C₂³	160		C2^3:3(C5xQ8)	320,1525

Non-split extensions G=N.Q with N=C₂³ and Q=C₅×Q₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.₁(C₅×Q₈) = C₅×C₄.₁₀C₄²	φ: C₅×Q₈/C₁₀ → C₂² ⊆ Aut C₂³	80	4	C2^3.1(C5xQ8)	320,143
C₂³.₂(C₅×Q₈) = C₅×C₂³.₉D₄	φ: C₅×Q₈/C₁₀ → C₂² ⊆ Aut C₂³	80		C2^3.2(C5xQ8)	320,147
C₂³.₃(C₅×Q₈) = C₅×C₂³.Q₈	φ: C₅×Q₈/C₁₀ → C₂² ⊆ Aut C₂³	160		C2^3.3(C5xQ8)	320,897
C₂³.₄(C₅×Q₈) = C₅×C₂³.₄Q₈	φ: C₅×Q₈/C₁₀ → C₂² ⊆ Aut C₂³	160		C2^3.4(C5xQ8)	320,900
C₂³.₅(C₅×Q₈) = C₅×M₄(2).C₄	φ: C₅×Q₈/C₁₀ → C₂² ⊆ Aut C₂³	80	4	C2^3.5(C5xQ8)	320,931
C₂³.₆(C₅×Q₈) = C₅×C₄.C₄²	φ: C₅×Q₈/C₂₀ → C₂ ⊆ Aut C₂³	160		C2^3.6(C5xQ8)	320,146
C₂³.₇(C₅×Q₈) = C₅×C₂³.₇Q₈	φ: C₅×Q₈/C₂₀ → C₂ ⊆ Aut C₂³	160		C2^3.7(C5xQ8)	320,881
C₂³.₈(C₅×Q₈) = C₅×C₂³.₈Q₈	φ: C₅×Q₈/C₂₀ → C₂ ⊆ Aut C₂³	160		C2^3.8(C5xQ8)	320,886
C₂³.₉(C₅×Q₈) = C₁₀×C₈.C₄	φ: C₅×Q₈/C₂₀ → C₂ ⊆ Aut C₂³	160		C2^3.9(C5xQ8)	320,930
C₂³.₁₀(C₅×Q₈) = C₁₀×C₂.C₄²	central extension (φ=1)	320		C2^3.10(C5xQ8)	320,876
C₂³.₁₁(C₅×Q₈) = C₄⋊C₄×C₂×C₁₀	central extension (φ=1)	320		C2^3.11(C5xQ8)	320,1515

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁