#31825596

order	18063
automorphism	?
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₃

Aliases

No aliases for this group.

C₂₂₃ ⋊ #733

	subgroup	G/H
center	C₃	C₃²⋊(C₂₂₃⋊C₃)
commutator, prime radical, cosocle	C₃²×C₂₂₃	C₃²
Frattini	C₃²	C₃×C₂₂₃⋊C₃
Fitting	C₃×C₉×C₂₂₃	C₃
socle	C₃×C₂₂₃	H(3,𝔽₃)
hypercenter	C₃×C₉	C₂₂₃⋊C₃
hypocenter	C₂₂₃	#733
LCS	G ▷ C₃²×C₂₂₃ ▷ C₃×C₂₂₃ ▷ C₂₂₃
UCS	C₁ ◁ C₃ ◁ C₃² ◁ C₃×C₉

26 conjugacy classes of subgroups.

μ_t(G) = 6021

Polycyclic presentation:

3^4,223|a^3=d,b^3=d^2,b^a=bc,c^a=cd,e^a=e^183

2015 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18063, 37);