C₂²×C₃⋊#4181 #14518543

order	1944
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³×C₃²

Aliases

Fitting	C₂²×C₃×C₃²⋊C₉ ⋊ C₂
derived, Sylow	C₃×C₃²⋊C₉ ⋊ C₂³

	subgroup	G/H
center, hypercenter	C₂²×C₃	C₃⋊(C₃⋊D₉)
commutator, cosocle, hypocenter	C₃×C₃²⋊C₉	C₂³
Frattini	C₃²	C₂²×C₃⋊(C₃⋊D₃)
Fitting	C₂²×C₃×C₃²⋊C₉	C₂
socle	C₂²×C₃³	C₃⋊D₃
LCS	G ▷ C₃×C₃²⋊C₉
UCS	C₁ ◁ C₂²×C₃

1575 conjugacy classes of subgroups; only the 291 normal subgroups are shown.

normal subgroups only

This group has 1575 conjugacy classes of subgroups — too many to draw. Only its 291 normal subgroups are shown.

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

μ_t(G) = 216

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2937);