Extensions 1→N→G→Q→1 with N=C₃² and Q=SL₂(𝔽₃)

Direct product G=N×Q with N=C₃² and Q=SL₂(𝔽₃)

		d	ρ	Label	ID
C₃²×SL₂(𝔽₃)		72		C3^2xSL(2,3)	216,134

Semidirect products G=N:Q with N=C₃² and Q=SL₂(𝔽₃)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃²⋊SL₂(𝔽₃) = ASL₂(𝔽₃)	φ: SL₂(𝔽₃)/C₁ → SL₂(𝔽₃) ⊆ Aut C₃²	9	8+	C3^2:SL(2,3)	216,153
C₃²⋊₂SL₂(𝔽₃) = Q₈⋊He₃	φ: SL₂(𝔽₃)/Q₈ → C₃ ⊆ Aut C₃²	72	6	C3^2:2SL(2,3)	216,42

Non-split extensions G=N.Q with N=C₃² and Q=SL₂(𝔽₃)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃².SL₂(𝔽₃) = Q₈⋊3_-¹⁺²	φ: SL₂(𝔽₃)/Q₈ → C₃ ⊆ Aut C₃²	72	6	C3^2.SL(2,3)	216,41
C₃².₂SL₂(𝔽₃) = C₃×Q₈⋊C₉	central extension (φ=1)	216		C3^2.2SL(2,3)	216,40

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C32 and Q=SL2(𝔽3)