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#30627655

order	15633
automorphism	?
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₃²

Aliases

No aliases for this group.

Splittings

Fitting	H(3,𝔽₃)×C₁₉₃ ⋊ C₃
Sylow	C₁₉₃ ⋊ #732

Subgroups

	subgroup	G/H
center	C₃	C₃²⋊(C₁₉₃⋊C₃)
commutator, cosocle	C₃²×C₁₉₃	C₃²
Frattini	C₃²	C₃×C₁₉₃⋊C₃
Fitting	H(3,𝔽₃)×C₁₉₃	C₃
socle	C₃×C₁₉₃	H(3,𝔽₃)
hypercenter	H(3,𝔽₃)	C₁₉₃⋊C₃
hypocenter	C₁₉₃	#732
LCS	G ▷ C₃²×C₁₉₃ ▷ C₃×C₁₉₃ ▷ C₁₉₃
UCS	C₁ ◁ C₃ ◁ C₃² ◁ H(3,𝔽₃)

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 5211

Polycyclic presentation:

3^4,193|b^3=d^2,b^a=bc,c^a=cd,e^b=e^84

Conjugacy classes & character table

721 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15633, 34);