Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₂×C₁₀

Direct product G=N×Q with N=C₂³ and Q=C₂×C₁₀

		d	ρ	Label	ID
C₂⁴×C₁₀		160		C2^4xC10	160,238

Semidirect products G=N:Q with N=C₂³ and Q=C₂×C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊₁(C₂×C₁₀) = C₅×C₂²≀C₂	φ: C₂×C₁₀/C₅ → C₂² ⊆ Aut C₂³	40		C2^3:1(C2xC10)	160,181
C₂³⋊₂(C₂×C₁₀) = C₅×2₊¹⁺⁴	φ: C₂×C₁₀/C₅ → C₂² ⊆ Aut C₂³	40	4	C2^3:2(C2xC10)	160,232
C₂³⋊₃(C₂×C₁₀) = D₄×C₂×C₁₀	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂³	80		C2^3:3(C2xC10)	160,229

Non-split extensions G=N.Q with N=C₂³ and Q=C₂×C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.₁(C₂×C₁₀) = C₅×C₂³⋊C₄	φ: C₂×C₁₀/C₅ → C₂² ⊆ Aut C₂³	40	4	C2^3.1(C2xC10)	160,49
C₂³.₂(C₂×C₁₀) = C₅×C₄.₄D₄	φ: C₂×C₁₀/C₅ → C₂² ⊆ Aut C₂³	80		C2^3.2(C2xC10)	160,185
C₂³.₃(C₂×C₁₀) = C₅×C₄²⋊₂C₂	φ: C₂×C₁₀/C₅ → C₂² ⊆ Aut C₂³	80		C2^3.3(C2xC10)	160,187
C₂³.₄(C₂×C₁₀) = C₅×C₄⋊₁D₄	φ: C₂×C₁₀/C₅ → C₂² ⊆ Aut C₂³	80		C2^3.4(C2xC10)	160,188
C₂³.₅(C₂×C₁₀) = C₁₀×C₂²⋊C₄	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂³	80		C2^3.5(C2xC10)	160,176
C₂³.₆(C₂×C₁₀) = C₅×C₄²⋊C₂	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂³	80		C2^3.6(C2xC10)	160,178
C₂³.₇(C₂×C₁₀) = D₄×C₂₀	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂³	80		C2^3.7(C2xC10)	160,179
C₂³.₈(C₂×C₁₀) = C₅×C₄⋊D₄	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂³	80		C2^3.8(C2xC10)	160,182
C₂³.₉(C₂×C₁₀) = C₅×C₂²⋊Q₈	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂³	80		C2^3.9(C2xC10)	160,183
C₂³.₁₀(C₂×C₁₀) = C₅×C₂².D₄	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂³	80		C2^3.10(C2xC10)	160,184
C₂³.₁₁(C₂×C₁₀) = C₁₀×C₄○D₄	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₂³	80		C2^3.11(C2xC10)	160,231
C₂³.₁₂(C₂×C₁₀) = C₅×C₂.C₄²	central extension (φ=1)	160		C2^3.12(C2xC10)	160,45
C₂³.₁₃(C₂×C₁₀) = C₁₀×C₄⋊C₄	central extension (φ=1)	160		C2^3.13(C2xC10)	160,177
C₂³.₁₄(C₂×C₁₀) = Q₈×C₂×C₁₀	central extension (φ=1)	160		C2^3.14(C2xC10)	160,230

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