Finite Group Databasebeta

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C₃×(C₃³⋊C₁₃)⋊C₉ #23748636

order	9477
automorphism	?
homology	Abelianization (H₁) = C₃×C₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×(C₃³⋊C₁₃)⋊C₉
unambiguous semidirect product	(C₃×C₃³⋊C₁₃)⋊C₉

Splittings

C₃³⋊C₁₃ ⋊ C₃×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃²	(C₃³⋊C₁₃)⋊C₃
commutator, hypocenter	C₃³⋊C₁₃	C₃×C₉
Frattini	C₃	C₃×(C₃³⋊C₁₃)⋊C₃
Fitting, socle	C₃⁵	C₁₃⋊C₃
prime radical	C₃²×C₃³⋊C₁₃	C₃
cosocle	C₃×C₃³⋊C₁₃	C₃²
LCS	G ▷ C₃³⋊C₁₃
UCS	C₁ ◁ C₃²

198 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

117 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9477, 4045);