#32915347

order	18549
automorphism	?
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₃

Aliases

No aliases for this group.

C₂₂₉ ⋊ #733

	subgroup	G/H
center	C₃	C₃²⋊(C₂₂₉⋊C₃)
commutator, prime radical, cosocle	C₃²×C₂₂₉	C₃²
Frattini	C₃²	C₃×C₂₂₉⋊C₃
Fitting	C₃×C₉×C₂₂₉	C₃
socle	C₃×C₂₂₉	H(3,𝔽₃)
hypercenter	C₃×C₉	C₂₂₉⋊C₃
hypocenter	C₂₂₉	#733
LCS	G ▷ C₃²×C₂₂₉ ▷ C₃×C₂₂₉ ▷ C₂₂₉
UCS	C₁ ◁ C₃ ◁ C₃² ◁ C₃×C₉

26 conjugacy classes of subgroups.

μ_t(G) = 6183

Polycyclic presentation:

3^4,229|a^3=d,b^3=d^2,b^a=bc,c^a=cd,e^a=e^134

2069 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18549, 37);