Extensions 1→N→G→Q→1 with N=C₃ and Q=He₃.₄C₆

Direct product G=N×Q with N=C₃ and Q=He₃.₄C₆

		d	ρ	Label	ID
C₃×He₃.₄C₆		81		C3xHe3.4C6	486,235

Semidirect products G=N:Q with N=C₃ and Q=He₃.₄C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(He₃.₄C₆) = C₉○He₃⋊₄S₃	φ: He₃.₄C₆/C₉○He₃ → C₂ ⊆ Aut C₃	54	6	C3:(He3.4C6)	486,246

Non-split extensions G=N.Q with N=C₃ and Q=He₃.₄C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(He₃.₄C₆) = C₉²⋊₄S₃	φ: He₃.₄C₆/C₉○He₃ → C₂ ⊆ Aut C₃	54	6	C3.1(He3.4C6)	486,140
C₃.₂(He₃.₄C₆) = (C₃²×C₉)⋊₈S₃	φ: He₃.₄C₆/C₉○He₃ → C₂ ⊆ Aut C₃	54	6	C3.2(He3.4C6)	486,150
C₃.₃(He₃.₄C₆) = C₉⋊C₉⋊₂S₃	φ: He₃.₄C₆/C₉○He₃ → C₂ ⊆ Aut C₃	54	6	C3.3(He3.4C6)	486,152
C₃.₄(He₃.₄C₆) = C₉²⋊₆S₃	φ: He₃.₄C₆/C₉○He₃ → C₂ ⊆ Aut C₃	18	6	C3.4(He3.4C6)	486,153
C₃.₅(He₃.₄C₆) = C₉²⋊₅S₃	φ: He₃.₄C₆/C₉○He₃ → C₂ ⊆ Aut C₃	54	6	C3.5(He3.4C6)	486,156
C₃.₆(He₃.₄C₆) = C₉×He₃⋊C₂	central extension (φ=1)	81		C3.6(He3.4C6)	486,143

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁