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C₉×D₅₅₉ #23758444

order	10062
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₅₅₉

Splittings

Fitting, Hall	C₉×C₁₃×C₄₃ ⋊ C₂
derived, Hall	C₁₃×C₄₃ ⋊ C₂×C₉
Hall	C₉×C₄₃ ⋊ D₁₃
Hall	C₉×C₁₃ ⋊ D₄₃
Sylow	C₄₃ ⋊ C₉×D₁₃
Sylow	C₁₃ ⋊ C₉×D₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₅₅₉
commutator, hypocenter	C₁₃×C₄₃	C₂×C₉
Frattini	C₃	C₃×D₅₅₉
Fitting	C₉×C₁₃×C₄₃	C₂
socle, cosocle	C₃×C₁₃×C₄₃	C₂×C₃
prime radical	C₃×D₅₅₉	C₃
LCS	G ▷ C₁₃×C₄₃
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2529 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₁₃×D₄₃, D₉×D₅₅₉, D₁₁₇⋊D₄₃, …
maximal normal subgroup of	C₉×D₁₃×D₄₃, D₉×D₅₅₉, D₁₁₇⋊D₄₃, …
maximal quotient of	C₉×Dic₅₅₉, C₂×C₉×D₅₅₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10062, 8);