Finite Group Databasebeta

← Prev (#26014235) Next (#26014237) →

C₇×C₉×D₈₉ #26014236

order	11214
isoclinism	isoclinic class of D₈₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₉×D₈₉
unambiguous semidirect product	C₈₉⋊(C₂×C₇×C₉)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₉	D₈₉
commutator, hypocenter	C₈₉	C₂×C₇×C₉
Frattini	C₃	C₃×C₇×D₈₉
Fitting	C₇×C₉×C₈₉	C₂
socle	C₃×C₇×C₈₉	C₂×C₃
prime radical	C₃×C₇×D₈₉	C₃
cosocle	C₃×C₈₉	C₂×C₃×C₇
LCS	G ▷ C₈₉
UCS	C₁ ◁ C₇×C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2898 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×C₉×#67063, C₉×C₇⋊#67063, C₉×D₇×D₈₉, …
maximal normal subgroup of	C₇×C₉×#67063, C₉×C₇⋊#67063, C₉×D₇×D₈₉, …
maximal quotient of	C₇×C₉×Dic₈₉, C₂×C₇×C₉×D₈₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11214, 3);