Extensions 1→N→G→Q→1 with N=C₁₂₂ and Q=C₂²

Direct product G=N×Q with N=C₁₂₂ and Q=C₂²

		d	ρ	Label	ID
C₂²×C₁₂₂		488		C2^2xC122	488,14

Semidirect products G=N:Q with N=C₁₂₂ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₂₂⋊C₂² = C₂²×D₆₁	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₂₂	244		C122:C2^2	488,13

Non-split extensions G=N.Q with N=C₁₂₂ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₂₂.₁C₂² = Dic₁₂₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₂₂	488	2-	C122.1C2^2	488,4
C₁₂₂.₂C₂² = C₄×D₆₁	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₂₂	244	2	C122.2C2^2	488,5
C₁₂₂.₃C₂² = D₂₄₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₂₂	244	2+	C122.3C2^2	488,6
C₁₂₂.₄C₂² = C₂×Dic₆₁	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₂₂	488		C122.4C2^2	488,7
C₁₂₂.₅C₂² = C₆₁⋊D₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₂₂	244	2	C122.5C2^2	488,8
C₁₂₂.₆C₂² = D₄×C₆₁	central extension (φ=1)	244	2	C122.6C2^2	488,10
C₁₂₂.₇C₂² = Q₈×C₆₁	central extension (φ=1)	488	2	C122.7C2^2	488,11

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁