Extensions 1→N→G→Q→1 with N=C₁₀ and Q=C₂₄⋊C₂

Direct product G=N×Q with N=C₁₀ and Q=C₂₄⋊C₂

		d	ρ	Label	ID
C₁₀×C₂₄⋊C₂		240		C10xC24:C2	480,781

Semidirect products G=N:Q with N=C₁₀ and Q=C₂₄⋊C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀⋊₁(C₂₄⋊C₂) = C₂×C₂₄⋊D₅	φ: C₂₄⋊C₂/C₂₄ → C₂ ⊆ Aut C₁₀	240		C10:1(C24:C2)	480,867
C₁₀⋊₂(C₂₄⋊C₂) = C₂×Dic₆⋊D₅	φ: C₂₄⋊C₂/Dic₆ → C₂ ⊆ Aut C₁₀	240		C10:2(C24:C2)	480,393
C₁₀⋊₃(C₂₄⋊C₂) = C₂×D₁₂.D₅	φ: C₂₄⋊C₂/D₁₂ → C₂ ⊆ Aut C₁₀	240		C10:3(C24:C2)	480,392

Non-split extensions G=N.Q with N=C₁₀ and Q=C₂₄⋊C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀.₁(C₂₄⋊C₂) = Dic₃₀⋊₈C₄	φ: C₂₄⋊C₂/C₂₄ → C₂ ⊆ Aut C₁₀	480		C10.1(C24:C2)	480,176
C₁₀.₂(C₂₄⋊C₂) = C₁₂₀⋊₁₀C₄	φ: C₂₄⋊C₂/C₂₄ → C₂ ⊆ Aut C₁₀	480		C10.2(C24:C2)	480,177
C₁₀.₃(C₂₄⋊C₂) = D₆₀⋊₈C₄	φ: C₂₄⋊C₂/C₂₄ → C₂ ⊆ Aut C₁₀	240		C10.3(C24:C2)	480,181
C₁₀.₄(C₂₄⋊C₂) = D₆₀⋊₁₅C₄	φ: C₂₄⋊C₂/Dic₆ → C₂ ⊆ Aut C₁₀	240		C10.4(C24:C2)	480,45
C₁₀.₅(C₂₄⋊C₂) = C₁₀.Dic₁₂	φ: C₂₄⋊C₂/Dic₆ → C₂ ⊆ Aut C₁₀	480		C10.5(C24:C2)	480,49
C₁₀.₆(C₂₄⋊C₂) = C₆₀.₇Q₈	φ: C₂₄⋊C₂/Dic₆ → C₂ ⊆ Aut C₁₀	480		C10.6(C24:C2)	480,61
C₁₀.₇(C₂₄⋊C₂) = C₁₀.D₂₄	φ: C₂₄⋊C₂/D₁₂ → C₂ ⊆ Aut C₁₀	240		C10.7(C24:C2)	480,43
C₁₀.₈(C₂₄⋊C₂) = Dic₃₀⋊₁₅C₄	φ: C₂₄⋊C₂/D₁₂ → C₂ ⊆ Aut C₁₀	480		C10.8(C24:C2)	480,51
C₁₀.₉(C₂₄⋊C₂) = C₅×C₂.Dic₁₂	central extension (φ=1)	480		C10.9(C24:C2)	480,135
C₁₀.₁₀(C₂₄⋊C₂) = C₅×C₈⋊Dic₃	central extension (φ=1)	480		C10.10(C24:C2)	480,136
C₁₀.₁₁(C₂₄⋊C₂) = C₅×C₂.D₂₄	central extension (φ=1)	240		C10.11(C24:C2)	480,140

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