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C₉×D₅₂₉ #23749000

order	9522
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₅₂₉
unambiguous semidirect product	C₅₂₉⋊(C₂×C₉)

Splittings

Fitting, Hall	C₉×C₅₂₉ ⋊ C₂
derived, Sylow	C₅₂₉ ⋊ C₂×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₅₂₉
commutator, hypocenter	C₅₂₉	C₂×C₉
Frattini, socle	C₃×C₂₃	C₃×D₂₃
Fitting	C₉×C₅₂₉	C₂
prime radical	C₃×D₅₂₉	C₃
cosocle	C₃×C₅₂₉	C₂×C₃
LCS	G ▷ C₅₂₉
UCS	C₁ ◁ C₉

18 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2394 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₉×D₅₂₉, C₂×C₉×D₅₂₉
maximal normal subgroup of	D₉×D₅₂₉, C₂×C₉×D₅₂₉
maximal quotient of	C₉×Dic₅₂₉, C₂×C₉×D₅₂₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9522, 3);