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C₃×#14578899 #21419382

order	7533
automorphism	?
homology	Abelianization (H₁) = C₃³ · Schur multiplier (H₂) = C₃⁴

Aliases

C₃×#14578899

Splittings

Fitting	C₃×H(3,𝔽₃)×C₃₁ ⋊ C₃
Sylow	C₃₁ ⋊ C₃×#732

Subgroups

	subgroup	G/H
center	C₃²	C₃²⋊(C₃₁⋊C₃)
commutator	C₃²×C₃₁	C₃³
Frattini	C₃²	C₃²×C₃₁⋊C₃
Fitting	C₃×H(3,𝔽₃)×C₃₁	C₃
socle	C₃²×C₃₁	H(3,𝔽₃)
hypercenter	C₃×H(3,𝔽₃)	C₃₁⋊C₃
hypocenter	C₃₁	C₃×#732
LCS	G ▷ C₃²×C₃₁ ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃×H(3,𝔽₃)

168 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

381 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₉×#14578899, #36381135, #36381167, …
maximal normal subgroup of	C₉×#14578899, #36381135, #36381167, …
maximal quotient of	C₃×#21419200, C₃×#21419201, C₃×#21419209, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7533, 252);