Extensions 1→N→G→Q→1 with N=C₁₀ and Q=C₈⋊C₄

Direct product G=N×Q with N=C₁₀ and Q=C₈⋊C₄

		d	ρ	Label	ID
C₁₀×C₈⋊C₄		320		C10xC8:C4	320,904

Semidirect products G=N:Q with N=C₁₀ and Q=C₈⋊C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀⋊₁(C₈⋊C₄) = C₂×C₈⋊F₅	φ: C₈⋊C₄/C₈ → C₄ ⊆ Aut C₁₀	80		C10:1(C8:C4)	320,1055
C₁₀⋊₂(C₈⋊C₄) = C₂×C₁₀.C₄²	φ: C₈⋊C₄/C₂×C₄ → C₄ ⊆ Aut C₁₀	320		C10:2(C8:C4)	320,1087
C₁₀⋊₃(C₈⋊C₄) = C₂×C₄².D₅	φ: C₈⋊C₄/C₄² → C₂ ⊆ Aut C₁₀	320		C10:3(C8:C4)	320,548
C₁₀⋊₄(C₈⋊C₄) = C₂×C₄₀⋊₈C₄	φ: C₈⋊C₄/C₂×C₈ → C₂ ⊆ Aut C₁₀	320		C10:4(C8:C4)	320,727

Non-split extensions G=N.Q with N=C₁₀ and Q=C₈⋊C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀.₁(C₈⋊C₄) = C₁₆⋊F₅	φ: C₈⋊C₄/C₈ → C₄ ⊆ Aut C₁₀	80	4	C10.1(C8:C4)	320,183
C₁₀.₂(C₈⋊C₄) = C₁₆⋊₄F₅	φ: C₈⋊C₄/C₈ → C₄ ⊆ Aut C₁₀	80	4	C10.2(C8:C4)	320,184
C₁₀.₃(C₈⋊C₄) = C₄₀⋊C₈	φ: C₈⋊C₄/C₈ → C₄ ⊆ Aut C₁₀	320		C10.3(C8:C4)	320,217
C₁₀.₄(C₈⋊C₄) = D₁₀.₃M₄(2)	φ: C₈⋊C₄/C₈ → C₄ ⊆ Aut C₁₀	80		C10.4(C8:C4)	320,230
C₁₀.₅(C₈⋊C₄) = C₄².₃F₅	φ: C₈⋊C₄/C₂×C₄ → C₄ ⊆ Aut C₁₀	80	4	C10.5(C8:C4)	320,198
C₁₀.₆(C₈⋊C₄) = C₂₀.₃₁M₄(2)	φ: C₈⋊C₄/C₂×C₄ → C₄ ⊆ Aut C₁₀	320		C10.6(C8:C4)	320,218
C₁₀.₇(C₈⋊C₄) = C₂₀.₂₃C₄²	φ: C₈⋊C₄/C₂×C₄ → C₄ ⊆ Aut C₁₀	80	4	C10.7(C8:C4)	320,228
C₁₀.₈(C₈⋊C₄) = C₁₀.(C₄⋊C₈)	φ: C₈⋊C₄/C₂×C₄ → C₄ ⊆ Aut C₁₀	320		C10.8(C8:C4)	320,256
C₁₀.₉(C₈⋊C₄) = C₄².₂₇₉D₁₀	φ: C₈⋊C₄/C₄² → C₂ ⊆ Aut C₁₀	320		C10.9(C8:C4)	320,12
C₁₀.₁₀(C₈⋊C₄) = C₂₀.₄₅C₄²	φ: C₈⋊C₄/C₄² → C₂ ⊆ Aut C₁₀	80	4	C10.10(C8:C4)	320,24
C₁₀.₁₁(C₈⋊C₄) = (C₂×C₂₀)⋊₈C₈	φ: C₈⋊C₄/C₄² → C₂ ⊆ Aut C₁₀	320		C10.11(C8:C4)	320,82
C₁₀.₁₂(C₈⋊C₄) = C₄₀⋊₈C₈	φ: C₈⋊C₄/C₂×C₈ → C₂ ⊆ Aut C₁₀	320		C10.12(C8:C4)	320,13
C₁₀.₁₃(C₈⋊C₄) = C₈₀⋊C₄	φ: C₈⋊C₄/C₂×C₈ → C₂ ⊆ Aut C₁₀	80	4	C10.13(C8:C4)	320,70
C₁₀.₁₄(C₈⋊C₄) = (C₂×C₄₀)⋊₁₅C₄	φ: C₈⋊C₄/C₂×C₈ → C₂ ⊆ Aut C₁₀	320		C10.14(C8:C4)	320,108
C₁₀.₁₅(C₈⋊C₄) = C₅×C₈⋊C₈	central extension (φ=1)	320		C10.15(C8:C4)	320,127
C₁₀.₁₆(C₈⋊C₄) = C₅×C₂².₇C₄²	central extension (φ=1)	320		C10.16(C8:C4)	320,141
C₁₀.₁₇(C₈⋊C₄) = C₅×C₁₆⋊C₄	central extension (φ=1)	80	4	C10.17(C8:C4)	320,152

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁