Extensions 1→N→G→Q→1 with N=C₈ and Q=C₅⋊C₈

Direct product G=N×Q with N=C₈ and Q=C₅⋊C₈

		d	ρ	Label	ID
C₈×C₅⋊C₈		320		C8xC5:C8	320,216

Semidirect products G=N:Q with N=C₈ and Q=C₅⋊C₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈⋊₁(C₅⋊C₈) = C₄₀⋊₁C₈	φ: C₅⋊C₈/Dic₅ → C₂ ⊆ Aut C₈	320		C8:1(C5:C8)	320,220
C₈⋊₂(C₅⋊C₈) = C₄₀⋊₂C₈	φ: C₅⋊C₈/Dic₅ → C₂ ⊆ Aut C₈	320		C8:2(C5:C8)	320,219
C₈⋊₃(C₅⋊C₈) = C₄₀⋊C₈	φ: C₅⋊C₈/Dic₅ → C₂ ⊆ Aut C₈	320		C8:3(C5:C8)	320,217

Non-split extensions G=N.Q with N=C₈ and Q=C₅⋊C₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈.₁(C₅⋊C₈) = C₄₀.₁C₈	φ: C₅⋊C₈/Dic₅ → C₂ ⊆ Aut C₈	80	4	C8.1(C5:C8)	320,227
C₈.₂(C₅⋊C₈) = C₅⋊M₆(2)	φ: C₅⋊C₈/Dic₅ → C₂ ⊆ Aut C₈	160	4	C8.2(C5:C8)	320,215
C₈.₃(C₅⋊C₈) = C₄₀.C₈	φ: C₅⋊C₈/Dic₅ → C₂ ⊆ Aut C₈	320		C8.3(C5:C8)	320,224
C₈.₄(C₅⋊C₈) = C₅⋊C₆₄	central extension (φ=1)	320	4	C8.4(C5:C8)	320,3
C₈.₅(C₅⋊C₈) = C₂×C₅⋊C₃₂	central extension (φ=1)	320		C8.5(C5:C8)	320,214
C₈.₆(C₅⋊C₈) = Dic₅⋊C₁₆	central extension (φ=1)	320		C8.6(C5:C8)	320,223

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁