Extensions 1→N→G→Q→1 with N=C₁₀ and Q=C₃×M₄(2)

Direct product G=N×Q with N=C₁₀ and Q=C₃×M₄(2)

		d	ρ	Label	ID
M₄(2)×C₃₀		240		M4(2)xC30	480,935

Semidirect products G=N:Q with N=C₁₀ and Q=C₃×M₄(2)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀⋊₁(C₃×M₄(2)) = C₆×C₄.F₅	φ: C₃×M₄(2)/C₁₂ → C₄ ⊆ Aut C₁₀	240		C10:1(C3xM4(2))	480,1048
C₁₀⋊₂(C₃×M₄(2)) = C₆×C₂².F₅	φ: C₃×M₄(2)/C₂×C₆ → C₄ ⊆ Aut C₁₀	240		C10:2(C3xM4(2))	480,1058
C₁₀⋊₃(C₃×M₄(2)) = C₆×C₈⋊D₅	φ: C₃×M₄(2)/C₂₄ → C₂ ⊆ Aut C₁₀	240		C10:3(C3xM4(2))	480,693
C₁₀⋊₄(C₃×M₄(2)) = C₆×C₄.Dic₅	φ: C₃×M₄(2)/C₂×C₁₂ → C₂ ⊆ Aut C₁₀	240		C10:4(C3xM4(2))	480,714

Non-split extensions G=N.Q with N=C₁₀ and Q=C₃×M₄(2)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₀.₁(C₃×M₄(2)) = C₃×C₂₀⋊C₈	φ: C₃×M₄(2)/C₁₂ → C₄ ⊆ Aut C₁₀	480		C10.1(C3xM4(2))	480,281
C₁₀.₂(C₃×M₄(2)) = C₃×D₁₀⋊C₈	φ: C₃×M₄(2)/C₁₂ → C₄ ⊆ Aut C₁₀	240		C10.2(C3xM4(2))	480,283
C₁₀.₃(C₃×M₄(2)) = C₃×C₁₀.C₄²	φ: C₃×M₄(2)/C₂×C₆ → C₄ ⊆ Aut C₁₀	480		C10.3(C3xM4(2))	480,282
C₁₀.₄(C₃×M₄(2)) = C₃×Dic₅⋊C₈	φ: C₃×M₄(2)/C₂×C₆ → C₄ ⊆ Aut C₁₀	480		C10.4(C3xM4(2))	480,284
C₁₀.₅(C₃×M₄(2)) = C₃×C₂³.₂F₅	φ: C₃×M₄(2)/C₂×C₆ → C₄ ⊆ Aut C₁₀	240		C10.5(C3xM4(2))	480,292
C₁₀.₆(C₃×M₄(2)) = C₃×C₂₀.₈Q₈	φ: C₃×M₄(2)/C₂₄ → C₂ ⊆ Aut C₁₀	480		C10.6(C3xM4(2))	480,92
C₁₀.₇(C₃×M₄(2)) = C₃×C₄₀⋊₈C₄	φ: C₃×M₄(2)/C₂₄ → C₂ ⊆ Aut C₁₀	480		C10.7(C3xM4(2))	480,93
C₁₀.₈(C₃×M₄(2)) = C₃×D₁₀⋊₁C₈	φ: C₃×M₄(2)/C₂₄ → C₂ ⊆ Aut C₁₀	240		C10.8(C3xM4(2))	480,98
C₁₀.₉(C₃×M₄(2)) = C₃×C₄².D₅	φ: C₃×M₄(2)/C₂×C₁₂ → C₂ ⊆ Aut C₁₀	480		C10.9(C3xM4(2))	480,81
C₁₀.₁₀(C₃×M₄(2)) = C₃×C₂₀⋊₃C₈	φ: C₃×M₄(2)/C₂×C₁₂ → C₂ ⊆ Aut C₁₀	480		C10.10(C3xM4(2))	480,82
C₁₀.₁₁(C₃×M₄(2)) = C₃×C₂₀.₅₅D₄	φ: C₃×M₄(2)/C₂×C₁₂ → C₂ ⊆ Aut C₁₀	240		C10.11(C3xM4(2))	480,108
C₁₀.₁₂(C₃×M₄(2)) = C₁₅×C₈⋊C₄	central extension (φ=1)	480		C10.12(C3xM4(2))	480,200
C₁₀.₁₃(C₃×M₄(2)) = C₁₅×C₂²⋊C₈	central extension (φ=1)	240		C10.13(C3xM4(2))	480,201
C₁₀.₁₄(C₃×M₄(2)) = C₁₅×C₄⋊C₈	central extension (φ=1)	480		C10.14(C3xM4(2))	480,208

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁