C₃×C₃⋊(((C₂²⋊C₉)⋊C₂)⋊C₃) #14519209

order	1944
isoclinism	isoclinic class of C₃⋊(((C₂²⋊C₉)⋊C₂)⋊C₃)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₂×C₃²

Aliases

direct product	C₃×C₃⋊(((C₂²⋊C₉)⋊C₂)⋊C₃)
unambiguous semidirect product	C₃⋊(C₃×((C₂²⋊C₉)⋊C₂)⋊C₃)

	subgroup	G/H
center, hypercenter	C₃	C₃⋊(((C₂²⋊C₉)⋊C₂)⋊C₃)
commutator, cosocle, hypocenter	C₃×C₂²⋊C₉	C₂×C₃²
Frattini	C₃	C₃²×C₃⋊S₄
Fitting	C₂²×C₃⁴	D₃
socle	C₂²×C₃³	C₃×D₃
LCS	G ▷ C₃×C₂²⋊C₉
UCS	C₁ ◁ C₃

664 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 664 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

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

μ_t(G) = 108

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3603);