C₃×#10620044 #14519194

order	1944
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

C₂²×C₃²×C₉ ⋊ D₃

	subgroup	G/H
center, hypercenter	C₃×C₉	C₃⋊S₄
commutator, cosocle, hypocenter	C₂²⋊H(3,𝔽₃)	C₂×C₃²
Frattini	C₃	C₃²×C₃⋊S₄
Fitting	C₂²×C₃²×C₉	D₃
socle	C₂²×C₃²	C₃×C₃⋊D₃
prime radical	C₃×#6258	C₃
LCS	G ▷ C₂²⋊H(3,𝔽₃)
UCS	C₁ ◁ C₃×C₉

483 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 483 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.

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

μ_t(G) = 162

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3588);