Extensions 1→N→G→Q→1 with N=C₃ and Q=He₃.C₆

Direct product G=N×Q with N=C₃ and Q=He₃.C₆

		d	ρ	Label	ID
C₃×He₃.C₆		81		C3xHe3.C6	486,118

Semidirect products G=N:Q with N=C₃ and Q=He₃.C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(He₃.C₆) = He₃.C₃⋊S₃	φ: He₃.C₆/He₃.C₃ → C₂ ⊆ Aut C₃	54	6	C3:(He3.C6)	486,169

Non-split extensions G=N.Q with N=C₃ and Q=He₃.C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(He₃.C₆) = C₃²⋊C₉⋊S₃	φ: He₃.C₆/He₃.C₃ → C₂ ⊆ Aut C₃	18	6	C3.1(He3.C6)	486,7
C₃.₂(He₃.C₆) = C₃³.(C₃×S₃)	φ: He₃.C₆/He₃.C₃ → C₂ ⊆ Aut C₃	54	6	C3.2(He3.C6)	486,11
C₃.₃(He₃.C₆) = C₃²⋊₂D₉.C₃	φ: He₃.C₆/He₃.C₃ → C₂ ⊆ Aut C₃	54	6	C3.3(He3.C6)	486,12
C₃.₄(He₃.C₆) = (C₃×C₉)⋊D₉	φ: He₃.C₆/He₃.C₃ → C₂ ⊆ Aut C₃	54	6	C3.4(He3.C6)	486,21
C₃.₅(He₃.C₆) = He₃⋊C₁₈	central extension (φ=1)	81		C3.5(He3.C6)	486,24

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