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C₉×D₅₂₃ #22627907

order	9414
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₅₂₃

Splittings

Fitting, Hall	C₉×C₅₂₃ ⋊ C₂
derived, Sylow	C₅₂₃ ⋊ C₂×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₅₂₃
commutator, hypocenter	C₅₂₃	C₂×C₉
Frattini	C₃	C₃×D₅₂₃
Fitting	C₉×C₅₂₃	C₂
socle	C₃×C₅₂₃	C₂×C₃
LCS	G ▷ C₅₂₃
UCS	C₁ ◁ C₉

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2367 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₉×D₅₂₃, C₂×C₉×D₅₂₃
maximal normal subgroup of	D₉×D₅₂₃, C₂×C₉×D₅₂₃
maximal quotient of	C₉×Dic₅₂₃, C₂×C₉×D₅₂₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9414, 5);