Extensions 1→N→G→Q→1 with N=C₂xC₄ and Q=He₃:C₂

Direct product G=NxQ with N=C₂xC₄ and Q=He₃:C₂

		d	ρ	Label	ID
C₂xC₄xHe₃:C₂		72		C2xC4xHe3:C2	432,385

Semidirect products G=N:Q with N=C₂xC₄ and Q=He₃:C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂xC₄):₁(He₃:C₂) = C₆².₃₁D₆	φ: He₃:C₂/He₃ → C₂ ⊆ Aut C₂xC₄	72		(C2xC4):1(He3:C2)	432,189
(C₂xC₄):₂(He₃:C₂) = C₂xHe₃:₅D₄	φ: He₃:C₂/He₃ → C₂ ⊆ Aut C₂xC₄	72		(C2xC4):2(He3:C2)	432,386
(C₂xC₄):₃(He₃:C₂) = C₆².₄₇D₆	φ: He₃:C₂/He₃ → C₂ ⊆ Aut C₂xC₄	72	6	(C2xC4):3(He3:C2)	432,387

Non-split extensions G=N.Q with N=C₂xC₄ and Q=He₃:C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂xC₄).₁(He₃:C₂) = C₆².₂₉D₆	φ: He₃:C₂/He₃ → C₂ ⊆ Aut C₂xC₄	144		(C2xC4).1(He3:C2)	432,187
(C₂xC₄).₂(He₃:C₂) = He₃:₈M₄(2)	φ: He₃:C₂/He₃ → C₂ ⊆ Aut C₂xC₄	72	6	(C2xC4).2(He3:C2)	432,185
(C₂xC₄).₃(He₃:C₂) = C₆².₃₀D₆	φ: He₃:C₂/He₃ → C₂ ⊆ Aut C₂xC₄	144		(C2xC4).3(He3:C2)	432,188
(C₂xC₄).₄(He₃:C₂) = C₂xHe₃:₄Q₈	φ: He₃:C₂/He₃ → C₂ ⊆ Aut C₂xC₄	144		(C2xC4).4(He3:C2)	432,384
(C₂xC₄).₅(He₃:C₂) = C₂xHe₃:₄C₈	central extension (φ=1)	144		(C2xC4).5(He3:C2)	432,184
(C₂xC₄).₆(He₃:C₂) = C₄xHe₃:₃C₄	central extension (φ=1)	144		(C2xC4).6(He3:C2)	432,186

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