Extensions 1→N→G→Q→1 with N=C₁₀ and Q=Dic₅

Direct product G=N×Q with N=C₁₀ and Q=Dic₅

		d	ρ	Label	ID
C₁₀×Dic₅		40		C10xDic5	200,30

Semidirect products G=N:Q with N=C₁₀ and Q=Dic₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀⋊Dic₅ = C₂×D₅.D₅	φ: Dic₅/C₅ → C₄ ⊆ Aut C₁₀	40	4	C10:Dic5	200,46
C₁₀⋊₂Dic₅ = C₂×C₅²⋊₆C₄	φ: Dic₅/C₁₀ → C₂ ⊆ Aut C₁₀	200		C10:2Dic5	200,35

Non-split extensions G=N.Q with N=C₁₀ and Q=Dic₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀.Dic₅ = C₅²⋊₃C₈	φ: Dic₅/C₅ → C₄ ⊆ Aut C₁₀	40	4	C10.Dic5	200,19
C₁₀.₂Dic₅ = C₂₅⋊₂C₈	φ: Dic₅/C₁₀ → C₂ ⊆ Aut C₁₀	200	2	C10.2Dic5	200,1
C₁₀.₃Dic₅ = C₂×Dic₂₅	φ: Dic₅/C₁₀ → C₂ ⊆ Aut C₁₀	200		C10.3Dic5	200,7
C₁₀.₄Dic₅ = C₅²⋊₇C₈	φ: Dic₅/C₁₀ → C₂ ⊆ Aut C₁₀	200		C10.4Dic5	200,16
C₁₀.₅Dic₅ = C₅×C₅⋊₂C₈	central extension (φ=1)	40	2	C10.5Dic5	200,15

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁