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C₉×D₇×C₈₉ #26014237

order	11214
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₈₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₇×C₈₉

Splittings

Fitting, Hall	C₇×C₉×C₈₉ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₉×C₈₉
Hall	C₇×C₈₉ ⋊ C₂×C₉
Hall	C₇×C₉ ⋊ C₂×C₈₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₈₉	D₇
commutator, hypocenter	C₇	C₂×C₉×C₈₉
Frattini	C₃	C₃×D₇×C₈₉
Fitting	C₇×C₉×C₈₉	C₂
socle	C₃×C₇×C₈₉	C₂×C₃
prime radical	C₃×D₇×C₈₉	C₃
cosocle	C₃×C₇	C₂×C₃×C₈₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₉×C₈₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4005 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₇×D₈₉, D₇×D₉×C₈₉, D₇×D₈₀₁, …
maximal normal subgroup of	C₉×D₇×D₈₉, D₇×D₉×C₈₉, D₇×D₈₀₁, …
maximal quotient of	C₉×Dic₇×C₈₉, C₂×C₉×D₇×C₈₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11214, 4);