Extensions 1→N→G→Q→1 with N=C₆ and Q=C₃×C₂₄

Direct product G=N×Q with N=C₆ and Q=C₃×C₂₄

		d	ρ	Label	ID
C₃×C₆×C₂₄		432		C3xC6xC24	432,515

Semidirect products G=N:Q with N=C₆ and Q=C₃×C₂₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊(C₃×C₂₄) = C₃×C₆×C₃⋊C₈	φ: C₃×C₂₄/C₃×C₁₂ → C₂ ⊆ Aut C₆	144		C6:(C3xC24)	432,469

Non-split extensions G=N.Q with N=C₆ and Q=C₃×C₂₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.(C₃×C₂₄) = C₃²×C₃⋊C₁₆	φ: C₃×C₂₄/C₃×C₁₂ → C₂ ⊆ Aut C₆	144		C6.(C3xC24)	432,229
C₆.₂(C₃×C₂₄) = C₁₆×He₃	central extension (φ=1)	144	3	C6.2(C3xC24)	432,35
C₆.₃(C₃×C₂₄) = C₁₆×3_-¹⁺²	central extension (φ=1)	144	3	C6.3(C3xC24)	432,36
C₆.₄(C₃×C₂₄) = C₂×C₈×He₃	central extension (φ=1)	144		C6.4(C3xC24)	432,210
C₆.₅(C₃×C₂₄) = C₂×C₈×3_-¹⁺²	central extension (φ=1)	144		C6.5(C3xC24)	432,211

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