Extensions 1→N→G→Q→1 with N=C₆ and Q=C₃xC₂₄

Direct product G=NxQ with N=C₆ and Q=C₃xC₂₄

		d	ρ	Label	ID
C₃xC₆xC₂₄		432		C3xC6xC24	432,515

Semidirect products G=N:Q with N=C₆ and Q=C₃xC₂₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆:(C₃xC₂₄) = C₃xC₆xC₃:C₈	φ: C₃xC₂₄/C₃xC₁₂ → C₂ ⊆ Aut C₆	144		C6:(C3xC24)	432,469

Non-split extensions G=N.Q with N=C₆ and Q=C₃xC₂₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.(C₃xC₂₄) = C₃²xC₃:C₁₆	φ: C₃xC₂₄/C₃xC₁₂ → C₂ ⊆ Aut C₆	144		C6.(C3xC24)	432,229
C₆.₂(C₃xC₂₄) = C₁₆xHe₃	central extension (φ=1)	144	3	C6.2(C3xC24)	432,35
C₆.₃(C₃xC₂₄) = C₁₆x3_-¹⁺²	central extension (φ=1)	144	3	C6.3(C3xC24)	432,36
C₆.₄(C₃xC₂₄) = C₂xC₈xHe₃	central extension (φ=1)	144		C6.4(C3xC24)	432,210
C₆.₅(C₃xC₂₄) = C₂xC₈x3_-¹⁺²	central extension (φ=1)	144		C6.5(C3xC24)	432,211

׿

x

:

Z

F

o

wr

Q

<