D₃×#63703 #13164660

order	1728
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product	D₃×#63703
unambiguous semidirect product	C₃⋊(C₂×#63703)

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	D₃×C₂²⋊A₄
commutator, hypocenter	C₃×H(5,𝔽₂)	C₂×C₉
Fitting, cosocle	C₃²×H(5,𝔽₂)	C₂×C₃
socle	C₂×C₃²	C₂×C₂²⋊A₄
prime radical	C₃×D₃×H(5,𝔽₂)	C₃
LCS	G ▷ C₃×H(5,𝔽₂)
UCS	C₁ ◁ C₂×C₃

766 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 766 conjugacy classes of subgroups — too many to draw. Only its 53 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, 30723);