C₃×C₉⋊((C₂²⋊C₉)⋊C₂) #14518044

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

Aliases

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

339 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 339 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.

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

μ_t(G) = 324

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2438);