D₃×((C₃⋊D₃)⋊C₃)⋊D₃ #14519175

order	1944
isoclinism	isoclinic class of D₃×((C₃⋊D₃)⋊C₃)⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³×C₃

Aliases

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

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃²×H(3,𝔽₃)	C₂³
Frattini	C₃	D₃²×C₃⋊D₃
socle	C₃³	C₂×D₃²
LCS	G ▷ C₃²×H(3,𝔽₃)
UCS	C₁

1119 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 1119 conjugacy classes of subgroups — too many to draw. Only its 84 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(1944, 3569);