A₄×(C₂×D₃)⋊Dic₃ #13166165

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂³

Aliases

direct product	A₄×(C₂×D₃)⋊Dic₃
unambiguous semidirect product	(C₂×D₃)⋊(Dic₃×A₄)
unambiguous semidirect product	(C₂²×(C₂×D₃)⋊Dic₃)⋊C₃

	subgroup	G/H
center, Frattini, hypercenter	C₂²	D₃²×A₄
commutator	C₂³×C₃²	C₂×C₃×C₄
Fitting, socle, cosocle	C₂⁴×C₃²	C₂²×C₃
prime radical	C₂²×C₃×D₃×A₄	C₂
hypocenter	C₂²×C₃²	C₃×C₂²⋊C₄
LCS	G ▷ C₂³×C₃² ▷ C₂²×C₃²
UCS	C₁ ◁ C₂²

858 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 858 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 144

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 32228);