Extensions 1→N→G→Q→1 with N=C₇₂ and Q=C₆

Direct product G=N×Q with N=C₇₂ and Q=C₆

		d	ρ	Label	ID
C₆×C₇₂		432		C6xC72	432,209

Semidirect products G=N:Q with N=C₇₂ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇₂⋊₁C₆ = D₇₂⋊C₃	φ: C₆/C₁ → C₆ ⊆ Aut C₇₂	72	6+	C72:1C6	432,123
C₇₂⋊₂C₆ = C₇₂⋊₂C₆	φ: C₆/C₁ → C₆ ⊆ Aut C₇₂	72	6	C72:2C6	432,122
C₇₂⋊₃C₆ = C₈×C₉⋊C₆	φ: C₆/C₁ → C₆ ⊆ Aut C₇₂	72	6	C72:3C6	432,120
C₇₂⋊₄C₆ = C₇₂⋊C₆	φ: C₆/C₁ → C₆ ⊆ Aut C₇₂	72	6	C72:4C6	432,121
C₇₂⋊₅C₆ = D₈×3_-¹⁺²	φ: C₆/C₁ → C₆ ⊆ Aut C₇₂	72	6	C72:5C6	432,217
C₇₂⋊₆C₆ = SD₁₆×3_-¹⁺²	φ: C₆/C₁ → C₆ ⊆ Aut C₇₂	72	6	C72:6C6	432,220
C₇₂⋊₇C₆ = M₄(2)×3_-¹⁺²	φ: C₆/C₁ → C₆ ⊆ Aut C₇₂	72	6	C72:7C6	432,214
C₇₂⋊₈C₆ = C₂×C₈×3_-¹⁺²	φ: C₆/C₂ → C₃ ⊆ Aut C₇₂	144		C72:8C6	432,211
C₇₂⋊₉C₆ = C₃×D₇₂	φ: C₆/C₃ → C₂ ⊆ Aut C₇₂	144	2	C72:9C6	432,108
C₇₂⋊₁₀C₆ = C₃×C₇₂⋊C₂	φ: C₆/C₃ → C₂ ⊆ Aut C₇₂	144	2	C72:10C6	432,107
C₇₂⋊₁₁C₆ = D₉×C₂₄	φ: C₆/C₃ → C₂ ⊆ Aut C₇₂	144	2	C72:11C6	432,105
C₇₂⋊₁₂C₆ = C₃×C₈⋊D₉	φ: C₆/C₃ → C₂ ⊆ Aut C₇₂	144	2	C72:12C6	432,106
C₇₂⋊₁₃C₆ = D₈×C₃×C₉	φ: C₆/C₃ → C₂ ⊆ Aut C₇₂	216		C72:13C6	432,215
C₇₂⋊₁₄C₆ = SD₁₆×C₃×C₉	φ: C₆/C₃ → C₂ ⊆ Aut C₇₂	216		C72:14C6	432,218
C₇₂⋊₁₅C₆ = M₄(2)×C₃×C₉	φ: C₆/C₃ → C₂ ⊆ Aut C₇₂	216		C72:15C6	432,212

Non-split extensions G=N.Q with N=C₇₂ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇₂.₁C₆ = C₇₂.C₆	φ: C₆/C₁ → C₆ ⊆ Aut C₇₂	144	6-	C72.1C6	432,119
C₇₂.₂C₆ = C₉⋊C₄₈	φ: C₆/C₁ → C₆ ⊆ Aut C₇₂	144	6	C72.2C6	432,31
C₇₂.₃C₆ = Q₁₆×3_-¹⁺²	φ: C₆/C₁ → C₆ ⊆ Aut C₇₂	144	6	C72.3C6	432,223
C₇₂.₄C₆ = C₁₆×3_-¹⁺²	φ: C₆/C₂ → C₃ ⊆ Aut C₇₂	144	3	C72.4C6	432,36
C₇₂.₅C₆ = C₃×Dic₃₆	φ: C₆/C₃ → C₂ ⊆ Aut C₇₂	144	2	C72.5C6	432,104
C₇₂.₆C₆ = C₃×C₉⋊C₁₆	φ: C₆/C₃ → C₂ ⊆ Aut C₇₂	144	2	C72.6C6	432,28
C₇₂.₇C₆ = D₈×C₂₇	φ: C₆/C₃ → C₂ ⊆ Aut C₇₂	216	2	C72.7C6	432,25
C₇₂.₈C₆ = Q₁₆×C₂₇	φ: C₆/C₃ → C₂ ⊆ Aut C₇₂	432	2	C72.8C6	432,27
C₇₂.₉C₆ = Q₁₆×C₃×C₉	φ: C₆/C₃ → C₂ ⊆ Aut C₇₂	432		C72.9C6	432,221
C₇₂.₁₀C₆ = SD₁₆×C₂₇	φ: C₆/C₃ → C₂ ⊆ Aut C₇₂	216	2	C72.10C6	432,26
C₇₂.₁₁C₆ = M₄(2)×C₂₇	φ: C₆/C₃ → C₂ ⊆ Aut C₇₂	216	2	C72.11C6	432,24

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