Extensions 1→N→G→Q→1 with N=C₃xC₆ and Q=A₄

Direct product G=NxQ with N=C₃xC₆ and Q=A₄

		d	ρ	Label	ID
A₄xC₃xC₆		54		A4xC3xC6	216,173

Semidirect products G=N:Q with N=C₃xC₆ and Q=A₄

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃xC₆):A₄ = C₂xC₃²:A₄	φ: A₄/C₂² → C₃ ⊆ Aut C₃xC₆	18	3	(C3xC6):A4	216,107

Non-split extensions G=N.Q with N=C₃xC₆ and Q=A₄

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃xC₆).₁A₄ = Q₈:3_-¹⁺²	φ: A₄/C₂² → C₃ ⊆ Aut C₃xC₆	72	6	(C3xC6).1A4	216,41
(C₃xC₆).₂A₄ = Q₈:He₃	φ: A₄/C₂² → C₃ ⊆ Aut C₃xC₆	72	6	(C3xC6).2A4	216,42
(C₃xC₆).₃A₄ = C₂xC₃².A₄	φ: A₄/C₂² → C₃ ⊆ Aut C₃xC₆	18	3	(C3xC6).3A4	216,106
(C₃xC₆).₄A₄ = C₃xQ₈:C₉	central extension (φ=1)	216		(C3xC6).4A4	216,40
(C₃xC₆).₅A₄ = C₆xC₃.A₄	central extension (φ=1)	54		(C3xC6).5A4	216,105
(C₃xC₆).₆A₄ = C₃²xSL₂(F₃)	central extension (φ=1)	72		(C3xC6).6A4	216,134

׿

x

:

Z

F

o

wr

Q

<