Extensions 1→N→G→Q→1 with N=C₃ and Q=C₂₄⋊C₄

Direct product G=N×Q with N=C₃ and Q=C₂₄⋊C₄

		d	ρ	Label	ID
C₃×C₂₄⋊C₄		96		C3xC24:C4	288,249

Semidirect products G=N:Q with N=C₃ and Q=C₂₄⋊C₄

extension	φ:Q→Aut N	d	Label	ID
C₃⋊₁(C₂₄⋊C₄) = C₂.Dic₃²	φ: C₂₄⋊C₄/C₂×C₃⋊C₈ → C₂ ⊆ Aut C₃	96	C3:1(C24:C4)	288,203
C₃⋊₂(C₂₄⋊C₄) = C₃⋊C₈⋊Dic₃	φ: C₂₄⋊C₄/C₄×Dic₃ → C₂ ⊆ Aut C₃	96	C3:2(C24:C4)	288,202
C₃⋊₃(C₂₄⋊C₄) = C₂₄⋊Dic₃	φ: C₂₄⋊C₄/C₂×C₂₄ → C₂ ⊆ Aut C₃	288	C3:3(C24:C4)	288,290

Non-split extensions G=N.Q with N=C₃ and Q=C₂₄⋊C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₂₄⋊C₄) = C₇₂⋊C₄	φ: C₂₄⋊C₄/C₂×C₂₄ → C₂ ⊆ Aut C₃	288		C3.(C24:C4)	288,23

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C3 and Q=C24⋊C4