Extensions 1→N→G→Q→1 with N=SL₂(𝔽₃) and Q=C₁₈

Direct product G=N×Q with N=SL₂(𝔽₃) and Q=C₁₈

		d	ρ	Label	ID
C₁₈×SL₂(𝔽₃)		144		C18xSL(2,3)	432,327

Semidirect products G=N:Q with N=SL₂(𝔽₃) and Q=C₁₈

extension	φ:Q→Out N	d	ρ	Label	ID
SL₂(𝔽₃)⋊C₁₈ = C₉×GL₂(𝔽₃)	φ: C₁₈/C₉ → C₂ ⊆ Out SL₂(𝔽₃)	72	2	SL(2,3):C18	432,241
SL₂(𝔽₃)⋊₂C₁₈ = C₉×C₄.A₄	φ: trivial image	144	2	SL(2,3):2C18	432,329

Non-split extensions G=N.Q with N=SL₂(𝔽₃) and Q=C₁₈

extension	φ:Q→Out N	d	ρ	Label	ID
SL₂(𝔽₃).C₁₈ = C₉×CSU₂(𝔽₃)	φ: C₁₈/C₉ → C₂ ⊆ Out SL₂(𝔽₃)	144	2	SL(2,3).C18	432,240

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=SL2(𝔽3) and Q=C18