C₂²×C₃⋊#4176 #14518531

order	1944
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³×C₃

Aliases

Fitting	C₂²×C₃×#731 ⋊ C₂
Sylow	C₃×#731 ⋊ C₂³

	subgroup	G/H
center, hypercenter	C₂²×C₃	C₃⋊((C₃⋊D₃)⋊C₃)
commutator, cosocle, hypocenter	C₃×H(3,𝔽₃)	C₂³×C₃
Frattini	C₃²	C₂²×C₃×C₃⋊D₃
Fitting	C₂²×C₃×#731	C₂
socle	C₂²×C₃²	(C₃⋊D₃)⋊C₃
prime radical	C₂²×C₃⋊#272	C₃
LCS	G ▷ C₃×H(3,𝔽₃)
UCS	C₁ ◁ C₂²×C₃

666 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 666 conjugacy classes of subgroups — too many to draw. Only its 112 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, 2925);