Extensions 1→N→G→Q→1 with N=C₅₂ and Q=C₄

Direct product G=N×Q with N=C₅₂ and Q=C₄

		d	ρ	Label	ID
C₄×C₅₂		208		C4xC52	208,20

Semidirect products G=N:Q with N=C₅₂ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₂⋊₁C₄ = C₅₂⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₅₂	52	4	C52:1C4	208,31
C₅₂⋊₂C₄ = C₄×C₁₃⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₅₂	52	4	C52:2C4	208,30
C₅₂⋊₃C₄ = C₅₂⋊₃C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₅₂	208		C52:3C4	208,13
C₅₂⋊₄C₄ = C₄×Dic₁₃	φ: C₄/C₂ → C₂ ⊆ Aut C₅₂	208		C52:4C4	208,11
C₅₂⋊₅C₄ = C₁₃×C₄⋊C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₅₂	208		C52:5C4	208,22

Non-split extensions G=N.Q with N=C₅₂ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₂.₁C₄ = C₅₂.C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₅₂	104	4	C52.1C4	208,29
C₅₂.₂C₄ = C₁₃⋊C₁₆	φ: C₄/C₁ → C₄ ⊆ Aut C₅₂	208	4	C52.2C4	208,3
C₅₂.₃C₄ = D₁₃⋊C₈	φ: C₄/C₁ → C₄ ⊆ Aut C₅₂	104	4	C52.3C4	208,28
C₅₂.₄C₄ = C₅₂.₄C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₅₂	104	2	C52.4C4	208,10
C₅₂.₅C₄ = C₁₃⋊₂C₁₆	φ: C₄/C₂ → C₂ ⊆ Aut C₅₂	208	2	C52.5C4	208,1
C₅₂.₆C₄ = C₂×C₁₃⋊₂C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₅₂	208		C52.6C4	208,9
C₅₂.₇C₄ = C₁₃×M₄(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₅₂	104	2	C52.7C4	208,24

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