C₃×(C₃⋊#226)⋊C₃ #13048373

order	1296
isoclinism	isoclinic class of (C₃⋊#226)⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃²

Aliases

direct product	C₃×(C₃⋊#226)⋊C₃
unambiguous semidirect product	(C₃⋊#226)⋊C₃²
unambiguous semidirect product	(C₃×C₃⋊#226)⋊C₃

	subgroup	G/H
center, hypercenter	C₂×C₃	(C₃⋊S₄)⋊C₃
commutator, cosocle, hypocenter	C₃×SL(2,𝔽₃)	C₂×C₃²
Frattini	C₂×C₃	C₃²×S₄
Fitting	C₃³×Q₈	D₃
socle	C₂×C₃²	C₃×S₄
prime radical	C₃×Q₈⋊H(3,𝔽₃)	C₂
LCS	G ▷ C₃×SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₃

198 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.

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

μ_t(G) = 144

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 2091);