Extensions 1→N→G→Q→1 with N=C₆ and Q=C₃²⋊C₄

Direct product G=N×Q with N=C₆ and Q=C₃²⋊C₄

		d	ρ	Label	ID
C₆×C₃²⋊C₄		24	4	C6xC3^2:C4	216,168

Semidirect products G=N:Q with N=C₆ and Q=C₃²⋊C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊(C₃²⋊C₄) = C₂×C₃³⋊C₄	φ: C₃²⋊C₄/C₃⋊S₃ → C₂ ⊆ Aut C₆	24	4	C6:(C3^2:C4)	216,169

Non-split extensions G=N.Q with N=C₆ and Q=C₃²⋊C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.(C₃²⋊C₄) = C₃³⋊₄C₈	φ: C₃²⋊C₄/C₃⋊S₃ → C₂ ⊆ Aut C₆	24	4	C6.(C3^2:C4)	216,118
C₆.₂(C₃²⋊C₄) = He₃⋊₂C₈	central extension (φ=1)	72	3	C6.2(C3^2:C4)	216,25
C₆.₃(C₃²⋊C₄) = C₂×He₃⋊C₄	central extension (φ=1)	36	3	C6.3(C3^2:C4)	216,100
C₆.₄(C₃²⋊C₄) = C₃×C₃²⋊₂C₈	central extension (φ=1)	24	4	C6.4(C3^2:C4)	216,117

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁