D₃×C₃⋊(C₃⋊C₃₂) #13145484

order	1728
isoclinism	isoclinic class of D₃×C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃₂ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	D₃×C₃⋊(C₃⋊C₃₂)
unambiguous semidirect product	(C₃×D₃)⋊(C₃⋊C₃₂)

C₃³ ⋊ C₂×C₃₂

	subgroup	G/H
center, Frattini, hypercenter	C₁₆	D₃×C₃⋊D₃
commutator, hypocenter	C₃³	C₂×C₃₂
Fitting, cosocle	C₃³×C₁₆	C₂²
socle	C₂×C₃³	C₂×C₁₆
prime radical	C₂×C₃²×D₃	C₁₆
LCS	G ▷ C₃³
UCS	C₁ ◁ C₁₆

252 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.

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

μ_t(G) = 576

288 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 11547);