Extensions 1→N→G→Q→1 with N=C₄ and Q=C₃×M₄(2)

Direct product G=N×Q with N=C₄ and Q=C₃×M₄(2)

		d	ρ	Label	ID
C₁₂×M₄(2)		96		C12xM4(2)	192,837

Semidirect products G=N:Q with N=C₄ and Q=C₃×M₄(2)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊₁(C₃×M₄(2)) = C₃×C₈⋊₆D₄	φ: C₃×M₄(2)/C₂₄ → C₂ ⊆ Aut C₄	96		C4:1(C3xM4(2))	192,869
C₄⋊₂(C₃×M₄(2)) = C₃×C₄⋊M₄(2)	φ: C₃×M₄(2)/C₂×C₁₂ → C₂ ⊆ Aut C₄	96		C4:2(C3xM4(2))	192,856

Non-split extensions G=N.Q with N=C₄ and Q=C₃×M₄(2)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₃×M₄(2)) = C₃×D₄⋊C₈	φ: C₃×M₄(2)/C₂₄ → C₂ ⊆ Aut C₄	96		C4.1(C3xM4(2))	192,131
C₄.₂(C₃×M₄(2)) = C₃×Q₈⋊C₈	φ: C₃×M₄(2)/C₂₄ → C₂ ⊆ Aut C₄	192		C4.2(C3xM4(2))	192,132
C₄.₃(C₃×M₄(2)) = C₃×C₈⋊₄Q₈	φ: C₃×M₄(2)/C₂₄ → C₂ ⊆ Aut C₄	192		C4.3(C3xM4(2))	192,879
C₄.₄(C₃×M₄(2)) = C₃×C₈⋊₂C₈	φ: C₃×M₄(2)/C₂×C₁₂ → C₂ ⊆ Aut C₄	192		C4.4(C3xM4(2))	192,140
C₄.₅(C₃×M₄(2)) = C₃×C₈⋊₁C₈	φ: C₃×M₄(2)/C₂×C₁₂ → C₂ ⊆ Aut C₄	192		C4.5(C3xM4(2))	192,141
C₄.₆(C₃×M₄(2)) = C₃×C₁₆⋊C₄	φ: C₃×M₄(2)/C₂×C₁₂ → C₂ ⊆ Aut C₄	48	4	C4.6(C3xM4(2))	192,153
C₄.₇(C₃×M₄(2)) = C₃×C₂³.C₈	φ: C₃×M₄(2)/C₂×C₁₂ → C₂ ⊆ Aut C₄	48	4	C4.7(C3xM4(2))	192,155
C₄.₈(C₃×M₄(2)) = C₃×C₄².₆C₄	φ: C₃×M₄(2)/C₂×C₁₂ → C₂ ⊆ Aut C₄	96		C4.8(C3xM4(2))	192,865
C₄.₉(C₃×M₄(2)) = C₃×C₈⋊C₈	central extension (φ=1)	192		C4.9(C3xM4(2))	192,128
C₄.₁₀(C₃×M₄(2)) = C₃×C₂²⋊C₁₆	central extension (φ=1)	96		C4.10(C3xM4(2))	192,154
C₄.₁₁(C₃×M₄(2)) = C₃×C₄⋊C₁₆	central extension (φ=1)	192		C4.11(C3xM4(2))	192,169
C₄.₁₂(C₃×M₄(2)) = C₃×C₄².₁₂C₄	central extension (φ=1)	96		C4.12(C3xM4(2))	192,864

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁