A₄×D₃²⋊C₄ #13180226

order	1728
isoclinism	isoclinic class of A₄×GO⁺(4,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂³

Aliases

direct product	A₄×D₃²⋊C₄
unambiguous semidirect product	D₃²⋊(C₄×A₄)
unambiguous semidirect product	(C₂²×D₃²⋊C₄)⋊C₃

	subgroup	G/H
center, Frattini, hypercenter	C₂	A₄×GO⁺(4,𝔽₂)
commutator	C₂²×C₃⋊D₃	C₂×C₃×C₄
Fitting, socle	C₂³×C₃²	C₃×D₄
prime radical	C₂×D₃²×A₄	C₂
cosocle	C₂³×C₃⋊D₃	C₂²×C₃
hypocenter	C₂²×C₃²	C₃×C₂²⋊C₄
LCS	G ▷ C₂²×C₃⋊D₃ ▷ C₂²×C₃²
UCS	C₁ ◁ C₂

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

normal subgroups only

This group has 614 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) = 36

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 46289);