Extensions 1→N→G→Q→1 with N=C₁₈ and Q=C₂×C₁₀

Direct product G=N×Q with N=C₁₈ and Q=C₂×C₁₀

		d	ρ	Label	ID
C₂²×C₉₀		360		C2^2xC90	360,50

Semidirect products G=N:Q with N=C₁₈ and Q=C₂×C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₈⋊(C₂×C₁₀) = D₉×C₂×C₁₀	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₁₈	180		C18:(C2xC10)	360,48

Non-split extensions G=N.Q with N=C₁₈ and Q=C₂×C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₈.₁(C₂×C₁₀) = C₅×Dic₁₈	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₁₈	360	2	C18.1(C2xC10)	360,20
C₁₈.₂(C₂×C₁₀) = D₉×C₂₀	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₁₈	180	2	C18.2(C2xC10)	360,21
C₁₈.₃(C₂×C₁₀) = C₅×D₃₆	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₁₈	180	2	C18.3(C2xC10)	360,22
C₁₈.₄(C₂×C₁₀) = C₁₀×Dic₉	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₁₈	360		C18.4(C2xC10)	360,23
C₁₈.₅(C₂×C₁₀) = C₅×C₉⋊D₄	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Aut C₁₈	180	2	C18.5(C2xC10)	360,24
C₁₈.₆(C₂×C₁₀) = D₄×C₄₅	central extension (φ=1)	180	2	C18.6(C2xC10)	360,31
C₁₈.₇(C₂×C₁₀) = Q₈×C₄₅	central extension (φ=1)	360	2	C18.7(C2xC10)	360,32

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁