Extensions 1→N→G→Q→1 with N=C₇₈ and Q=S₃

Direct product G=NxQ with N=C₇₈ and Q=S₃

		d	ρ	Label	ID
S₃xC₇₈		156	2	S3xC78	468,51

Semidirect products G=N:Q with N=C₇₈ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇₈:₁S₃ = C₂xC₃:D₃₉	φ: S₃/C₃ → C₂ ⊆ Aut C₇₈	234		C78:1S3	468,54
C₇₈:₂S₃ = C₆xD₃₉	φ: S₃/C₃ → C₂ ⊆ Aut C₇₈	156	2	C78:2S3	468,52
C₇₈:₃S₃ = C₃:S₃xC₂₆	φ: S₃/C₃ → C₂ ⊆ Aut C₇₈	234		C78:3S3	468,53

Non-split extensions G=N.Q with N=C₇₈ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇₈.₁S₃ = Dic₁₁₇	φ: S₃/C₃ → C₂ ⊆ Aut C₇₈	468	2-	C78.1S3	468,5
C₇₈.₂S₃ = D₂₃₄	φ: S₃/C₃ → C₂ ⊆ Aut C₇₈	234	2+	C78.2S3	468,17
C₇₈.₃S₃ = C₃:Dic₃₉	φ: S₃/C₃ → C₂ ⊆ Aut C₇₈	468		C78.3S3	468,27
C₇₈.₄S₃ = C₃xDic₃₉	φ: S₃/C₃ → C₂ ⊆ Aut C₇₈	156	2	C78.4S3	468,25
C₇₈.₅S₃ = C₁₃xDic₉	φ: S₃/C₃ → C₂ ⊆ Aut C₇₈	468	2	C78.5S3	468,3
C₇₈.₆S₃ = D₉xC₂₆	φ: S₃/C₃ → C₂ ⊆ Aut C₇₈	234	2	C78.6S3	468,16
C₇₈.₇S₃ = C₁₃xC₃:Dic₃	φ: S₃/C₃ → C₂ ⊆ Aut C₇₈	468		C78.7S3	468,26
C₇₈.₈S₃ = Dic₃xC₃₉	central extension (φ=1)	156	2	C78.8S3	468,24

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