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C₃×D₃×C₅₂₉ #23749004

order	9522
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₃×C₅₂₉
unambiguous semidirect product	C₃⋊(C₂×C₃×C₅₂₉)

Splittings

Fitting, Hall	C₃²×C₅₂₉ ⋊ C₂
derived	C₃ ⋊ C₂×C₃×C₅₂₉
Sylow	C₃² ⋊ C₂×C₅₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₅₂₉	D₃
commutator, hypocenter	C₃	C₂×C₃×C₅₂₉
Frattini	C₂₃	C₃×D₃×C₂₃
Fitting	C₃²×C₅₂₉	C₂
socle	C₃²×C₂₃	C₂×C₂₃
prime radical	C₃×D₃×C₂₃	C₂₃
cosocle	C₃×C₂₃	C₂×C₃×C₂₃
LCS	G ▷ C₃
UCS	C₁ ◁ C₃×C₅₂₉

27 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4761 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×D₃×D₅₂₉, D₃²×C₅₂₉, D₃×D₁₅₈₇, …
maximal normal subgroup of	C₃×D₃×D₅₂₉, D₃²×C₅₂₉, D₃×D₁₅₈₇, …
maximal quotient of	C₃×Dic₃×C₅₂₉, C₂×C₃×D₃×C₅₂₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9522, 7);