A₄×#3775 #13180229

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	A₄×#3775
unambiguous semidirect product	(C₂²×#3775)⋊C₃

	subgroup	G/H
center, Frattini, hypercenter	C₂	A₄×GO⁺(4,𝔽₂)
commutator, cosocle	C₂²×C₃⋊Dic₃	C₂²×C₃
Fitting, socle	C₂³×C₃²	C₃×D₄
prime radical	A₄×#625	C₂
hypocenter	C₂²×C₃²	C₃×SD₁₆
LCS	G ▷ C₂²×C₃⋊Dic₃ ▷ C₂³×C₃² ▷ C₂²×C₃²
UCS	C₁ ◁ C₂

310 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.

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

μ_t(G) = 72

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 46292);