C₂²×C₃⋊(C₃⋊#226) #13181399

order	1728
isoclinism	isoclinic class of C₃⋊(C₃⋊#226)
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³×C₃³

Aliases

	subgroup	G/H
center, hypercenter	C₂³	C₃⋊(C₃⋊S₄)
commutator, cosocle, hypocenter	C₃²×SL(2,𝔽₃)	C₂³
Frattini	C₂	C₂²×C₃⋊(C₃⋊S₄)
Fitting	C₂²×C₃²×Q₈	D₃
socle	C₂³×C₃²	S₄
prime radical	C₂²×C₃²×SL(2,𝔽₃)	C₂
LCS	G ▷ C₃²×SL(2,𝔽₃)
UCS	C₁ ◁ C₂³

1606 conjugacy classes of subgroups; only the 247 normal subgroups are shown.

normal subgroups only

This group has 1606 conjugacy classes of subgroups — too many to draw. Only its 247 normal subgroups are shown.

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

μ_t(G) = 576

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 47462);