Extensions 1→N→G→Q→1 with N=Q₈ and Q=C₃xS₃

Direct product G=NxQ with N=Q₈ and Q=C₃xS₃

		d	ρ	Label	ID
C₃xS₃xQ₈		48	4	C3xS3xQ8	144,164

Semidirect products G=N:Q with N=Q₈ and Q=C₃xS₃

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈:(C₃xS₃) = C₃xGL₂(F₃)	φ: C₃xS₃/C₃ → S₃ ⊆ Out Q₈	24	2	Q8:(C3xS3)	144,122
Q₈:₂(C₃xS₃) = S₃xSL₂(F₃)	φ: C₃xS₃/S₃ → C₃ ⊆ Out Q₈	24	4-	Q8:2(C3xS3)	144,128
Q₈:₃(C₃xS₃) = C₃xQ₈:₂S₃	φ: C₃xS₃/C₃² → C₂ ⊆ Out Q₈	48	4	Q8:3(C3xS3)	144,82
Q₈:₄(C₃xS₃) = C₃xQ₈:₃S₃	φ: trivial image	48	4	Q8:4(C3xS3)	144,165

Non-split extensions G=N.Q with N=Q₈ and Q=C₃xS₃

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈.(C₃xS₃) = C₃xCSU₂(F₃)	φ: C₃xS₃/C₃ → S₃ ⊆ Out Q₈	48	2	Q8.(C3xS3)	144,121
Q₈.₂(C₃xS₃) = Dic₃.A₄	φ: C₃xS₃/S₃ → C₃ ⊆ Out Q₈	48	4+	Q8.2(C3xS3)	144,127
Q₈.₃(C₃xS₃) = C₃xC₃:Q₁₆	φ: C₃xS₃/C₃² → C₂ ⊆ Out Q₈	48	4	Q8.3(C3xS3)	144,83

׿

x

:

Z

F

o

wr

Q

<