D₃²×C₄²⋊C₃ #13166117

order	1728
isoclinism	isoclinic class of D₃²×C₄²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product	D₃²×C₄²⋊C₃
unambiguous semidirect product	(C₃×D₃)⋊(C₂×C₄²⋊C₃)
unambiguous semidirect product	(C₄²×D₃²)⋊C₃

C₃²×C₄² ⋊ C₂²×C₃

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃²×C₄²	C₂²×C₃
Frattini	C₂²	D₃²×A₄
socle	C₂²×C₃²	C₂²×A₄
LCS	G ▷ C₃²×C₄²
UCS	C₁

490 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 40 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, 32180);