C_n D_n S_n A_n ...

Extensions 1→N→G→Q→1 with N=2₊⁽¹⁺⁴⁾ and Q=C₂²

Direct product G=N×Q with N=2₊⁽¹⁺⁴⁾ and Q=C₂²

		d	ρ	Label	ID
C₂²×2₊⁽¹⁺⁴⁾		32		C2^2xES+(2,2)	128,2323

Semidirect products G=N:Q with N=2₊⁽¹⁺⁴⁾ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
2₊⁽¹⁺⁴⁾⋊₁C₂² = C₂≀D₄	φ: C₂²/C₁ → C₂² ⊆ Out 2₊⁽¹⁺⁴⁾	8	4+	ES+(2,2):1C2^2	128,928
2₊⁽¹⁺⁴⁾⋊₂C₂² = D₈⋊₁₁D₄	φ: C₂²/C₁ → C₂² ⊆ Out 2₊⁽¹⁺⁴⁾	16	8+	ES+(2,2):2C2^2	128,2020
2₊⁽¹⁺⁴⁾⋊₃C₂² = D₈⋊₆D₄	φ: C₂²/C₁ → C₂² ⊆ Out 2₊⁽¹⁺⁴⁾	16	4	ES+(2,2):3C2^2	128,2023
2₊⁽¹⁺⁴⁾⋊₄C₂² = D₈○D₈	φ: C₂²/C₁ → C₂² ⊆ Out 2₊⁽¹⁺⁴⁾	16	4+	ES+(2,2):4C2^2	128,2024
2₊⁽¹⁺⁴⁾⋊₅C₂² = C₂×D₄⋊₄D₄	φ: C₂²/C₂ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	16		ES+(2,2):5C2^2	128,1746
2₊⁽¹⁺⁴⁾⋊₆C₂² = C₄².₁₂C₂³	φ: C₂²/C₂ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	16	8+	ES+(2,2):6C2^2	128,1753
2₊⁽¹⁺⁴⁾⋊₇C₂² = C₂×C₂≀C₂²	φ: C₂²/C₂ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	16		ES+(2,2):7C2^2	128,1755
2₊⁽¹⁺⁴⁾⋊₈C₂² = C₂×D₄○D₈	φ: C₂²/C₂ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	32		ES+(2,2):8C2^2	128,2313
2₊⁽¹⁺⁴⁾⋊₉C₂² = C₂×D₄○SD₁₆	φ: C₂²/C₂ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	32		ES+(2,2):9C2^2	128,2314
2₊⁽¹⁺⁴⁾⋊₁₀C₂² = C₈.C₂⁴	φ: C₂²/C₂ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	32	4	ES+(2,2):10C2^2	128,2316
2₊⁽¹⁺⁴⁾⋊₁₁C₂² = D₈⋊C₂³	φ: C₂²/C₂ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	16	8+	ES+(2,2):11C2^2	128,2317
2₊⁽¹⁺⁴⁾⋊₁₂C₂² = C₄.C₂⁵	φ: C₂²/C₂ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	32	8-	ES+(2,2):12C2^2	128,2318
2₊⁽¹⁺⁴⁾⋊₁₃C₂² = C₂×C₂.C₂⁵	φ: trivial image	32		ES+(2,2):13C2^2	128,2325
2₊⁽¹⁺⁴⁾⋊₁₄C₂² = 2₊⁽¹⁺⁶⁾	φ: trivial image	16	8+	ES+(2,2):14C2^2	128,2326
2₊⁽¹⁺⁴⁾⋊₁₅C₂² = 2_-⁽¹⁺⁶⁾	φ: trivial image	32	8-	ES+(2,2):15C2^2	128,2327

Non-split extensions G=N.Q with N=2₊⁽¹⁺⁴⁾ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
2₊⁽¹⁺⁴⁾.₁C₂² = C₄²⋊₄D₄	φ: C₂²/C₁ → C₂² ⊆ Out 2₊⁽¹⁺⁴⁾	16	4	ES+(2,2).1C2^2	128,929
2₊⁽¹⁺⁴⁾.₂C₂² = C₄².₁₃D₄	φ: C₂²/C₁ → C₂² ⊆ Out 2₊⁽¹⁺⁴⁾	16	4	ES+(2,2).2C2^2	128,930
2₊⁽¹⁺⁴⁾.₃C₂² = C₂⁴⋊₃D₄	φ: C₂²/C₁ → C₂² ⊆ Out 2₊⁽¹⁺⁴⁾	16	8+	ES+(2,2).3C2^2	128,931
2₊⁽¹⁺⁴⁾.₄C₂² = C₄²⋊₆D₄	φ: C₂²/C₁ → C₂² ⊆ Out 2₊⁽¹⁺⁴⁾	16	8+	ES+(2,2).4C2^2	128,932
2₊⁽¹⁺⁴⁾.₅C₂² = C₄².₁₄D₄	φ: C₂²/C₁ → C₂² ⊆ Out 2₊⁽¹⁺⁴⁾	32	8-	ES+(2,2).5C2^2	128,933
2₊⁽¹⁺⁴⁾.₆C₂² = D₈.₁₃D₄	φ: C₂²/C₁ → C₂² ⊆ Out 2₊⁽¹⁺⁴⁾	32	8-	ES+(2,2).6C2^2	128,2021
2₊⁽¹⁺⁴⁾.₇C₂² = D₈○SD₁₆	φ: C₂²/C₁ → C₂² ⊆ Out 2₊⁽¹⁺⁴⁾	32	4	ES+(2,2).7C2^2	128,2022
2₊⁽¹⁺⁴⁾.₈C₂² = C₂×D₄.₉D₄	φ: C₂²/C₂ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	32		ES+(2,2).8C2^2	128,1747
2₊⁽¹⁺⁴⁾.₉C₂² = C₄².₃₁₃C₂³	φ: C₂²/C₂ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	16	4	ES+(2,2).9C2^2	128,1750
2₊⁽¹⁺⁴⁾.₁₀C₂² = M₄(2)⋊C₂³	φ: C₂²/C₂ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	16	8+	ES+(2,2).10C2^2	128,1751
2₊⁽¹⁺⁴⁾.₁₁C₂² = C₄².₁₃C₂³	φ: C₂²/C₂ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	32	8-	ES+(2,2).11C2^2	128,1754
2₊⁽¹⁺⁴⁾.₁₂C₂² = C₂×C₂³.₇D₄	φ: C₂²/C₂ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	32		ES+(2,2).12C2^2	128,1756
2₊⁽¹⁺⁴⁾.₁₃C₂² = C₂³.₇C₂⁴	φ: C₂²/C₂ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	16	4	ES+(2,2).13C2^2	128,1757
2₊⁽¹⁺⁴⁾.₁₄C₂² = C₂⁴⋊C₂³	φ: C₂²/C₂ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	16	8+	ES+(2,2).14C2^2	128,1758
2₊⁽¹⁺⁴⁾.₁₅C₂² = C₂³.₉C₂⁴	φ: C₂²/C₂ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	16	8+	ES+(2,2).15C2^2	128,1759
2₊⁽¹⁺⁴⁾.₁₆C₂² = C₂³.₁₀C₂⁴	φ: C₂²/C₂ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	32	8-	ES+(2,2).16C2^2	128,1760

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