Extensions 1→N→G→Q→1 with N=C₄ and Q=D₅₂

Direct product G=N×Q with N=C₄ and Q=D₅₂

		d	ρ	Label	ID
C₄×D₅₂		208		C4xD52	416,94

Semidirect products G=N:Q with N=C₄ and Q=D₅₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊₁D₅₂ = C₄⋊D₅₂	φ: D₅₂/C₅₂ → C₂ ⊆ Aut C₄	208		C4:1D52	416,95
C₄⋊₂D₅₂ = C₄⋊₂D₅₂	φ: D₅₂/D₂₆ → C₂ ⊆ Aut C₄	208		C4:2D52	416,116

Non-split extensions G=N.Q with N=C₄ and Q=D₅₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁D₅₂ = D₂₀₈	φ: D₅₂/C₅₂ → C₂ ⊆ Aut C₄	208	2+	C4.1D52	416,6
C₄.₂D₅₂ = C₁₆⋊D₁₃	φ: D₅₂/C₅₂ → C₂ ⊆ Aut C₄	208	2	C4.2D52	416,7
C₄.₃D₅₂ = Dic₁₀₄	φ: D₅₂/C₅₂ → C₂ ⊆ Aut C₄	416	2-	C4.3D52	416,8
C₄.₄D₅₂ = C₅₂⋊₂Q₈	φ: D₅₂/C₅₂ → C₂ ⊆ Aut C₄	416		C4.4D52	416,90
C₄.₅D₅₂ = C₄.D₅₂	φ: D₅₂/C₅₂ → C₂ ⊆ Aut C₄	208		C4.5D52	416,96
C₄.₆D₅₂ = C₂×C₁₀₄⋊C₂	φ: D₅₂/C₅₂ → C₂ ⊆ Aut C₄	208		C4.6D52	416,123
C₄.₇D₅₂ = C₂×D₁₀₄	φ: D₅₂/C₅₂ → C₂ ⊆ Aut C₄	208		C4.7D52	416,124
C₄.₈D₅₂ = C₂×Dic₅₂	φ: D₅₂/C₅₂ → C₂ ⊆ Aut C₄	416		C4.8D52	416,126
C₄.₉D₅₂ = D₅₂⋊₆C₄	φ: D₅₂/D₂₆ → C₂ ⊆ Aut C₄	208		C4.9D52	416,16
C₄.₁₀D₅₂ = C₂₆.Q₁₆	φ: D₅₂/D₂₆ → C₂ ⊆ Aut C₄	416		C4.10D52	416,17
C₄.₁₁D₅₂ = C₅₂.₄₆D₄	φ: D₅₂/D₂₆ → C₂ ⊆ Aut C₄	104	4+	C4.11D52	416,30
C₄.₁₂D₅₂ = C₄.₁₂D₅₂	φ: D₅₂/D₂₆ → C₂ ⊆ Aut C₄	208	4-	C4.12D52	416,31
C₄.₁₃D₅₂ = D₂₆⋊₂Q₈	φ: D₅₂/D₂₆ → C₂ ⊆ Aut C₄	208		C4.13D52	416,118
C₄.₁₄D₅₂ = C₈⋊D₂₆	φ: D₅₂/D₂₆ → C₂ ⊆ Aut C₄	104	4+	C4.14D52	416,129
C₄.₁₅D₅₂ = C₈.D₂₆	φ: D₅₂/D₂₆ → C₂ ⊆ Aut C₄	208	4-	C4.15D52	416,130
C₄.₁₆D₅₂ = C₅₂⋊₃C₈	central extension (φ=1)	416		C4.16D52	416,11
C₄.₁₇D₅₂ = D₅₂⋊₄C₄	central extension (φ=1)	104	2	C4.17D52	416,12
C₄.₁₈D₅₂ = C₁₀₄.₆C₄	central extension (φ=1)	208	2	C4.18D52	416,26
C₄.₁₉D₅₂ = D₂₆⋊₁C₈	central extension (φ=1)	208		C4.19D52	416,27
C₄.₂₀D₅₂ = D₁₀₄⋊₇C₂	central extension (φ=1)	208	2	C4.20D52	416,125

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Extensions 1→N→G→Q→1 with N=C4 and Q=D52

Extensions 1→N→G→Q→1 with N=C₄ and Q=D₅₂