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C₉×D₈₈₉ #30630653

order	16002
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₈₈₉

Splittings

Fitting, Hall	C₇×C₉×C₁₂₇ ⋊ C₂
derived, Hall	C₇×C₁₂₇ ⋊ C₂×C₉
Hall	C₉×C₁₂₇ ⋊ D₇
Sylow	C₁₂₇ ⋊ C₉×D₇
Hall	C₇×C₉ ⋊ D₁₂₇
Sylow	C₇ ⋊ C₉×D₁₂₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₈₈₉
commutator, hypocenter	C₇×C₁₂₇	C₂×C₉
Frattini	C₃	C₃×D₈₈₉
Fitting	C₇×C₉×C₁₂₇	C₂
socle, cosocle	C₃×C₇×C₁₂₇	C₂×C₃
prime radical	C₃×D₈₈₉	C₃
LCS	G ▷ C₇×C₁₂₇
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4014 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₇×D₁₂₇, D₉×D₈₈₉, D₆₃⋊D₁₂₇, …
maximal normal subgroup of	C₉×D₇×D₁₂₇, D₉×D₈₈₉, D₆₃⋊D₁₂₇, …
maximal quotient of	C₉×Dic₈₈₉, C₂×C₉×D₈₈₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16002, 10);