C₂²×(C₃⋊#226)⋊C₃ #13164414

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

Aliases

	subgroup	G/H
center, hypercenter	C₂³	(C₃⋊S₄)⋊C₃
commutator, cosocle, hypocenter	C₃×SL(2,𝔽₃)	C₂³×C₃
Frattini	C₂×C₃	C₂²×C₃×S₄
Fitting	C₂²×C₃²×Q₈	D₃
socle	C₂³×C₃	C₃×S₄
prime radical	C₂²×Q₈⋊H(3,𝔽₃)	C₂
LCS	G ▷ C₃×SL(2,𝔽₃)
UCS	C₁ ◁ C₂³

630 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 95 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, 30477);