A₄×#3777 #13180233

order	1728
isoclinism	isoclinic class of A₄×PSU(3,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂²×C₃

Aliases

direct product	A₄×#3777
unambiguous semidirect product	(C₂²×#3777)⋊C₃

	subgroup	G/H
center, Frattini, hypercenter	C₂	A₄×PSU(3,𝔽₂)
commutator	C₂²×C₃⋊D₃	C₂×C₃×C₄
Fitting, socle	C₂³×C₃²	C₃×Q₈
prime radical	C₂×A₄×C₃⋊D₃	C₂²
cosocle	C₂³×C₃⋊D₃	C₂²×C₃
hypocenter	C₂²×C₃²	C₃×C₄⋊C₄
LCS	G ▷ C₂²×C₃⋊D₃ ▷ C₂²×C₃²
UCS	C₁ ◁ C₂

273 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 273 conjugacy classes of subgroups — too many to draw. Only its 39 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, 46296);