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C₈₉×D₇⋊C₉ #26014244

order	11214
isoclinism	isoclinic class of AGL(1,𝔽₇)
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₈₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₈₉×D₇⋊C₉
unambiguous semidirect product	D₇⋊(C₉×C₈₉)
unambiguous semidirect product	(C₇⋊C₉)⋊(C₂×C₈₉)
unambiguous semidirect product	(D₇×C₈₉)⋊C₉

Splittings

derived, Sylow	C₇ ⋊ C₂×C₉×C₈₉
Hall	C₇⋊C₉×C₈₉ ⋊ C₂
Hall	D₇×C₈₉ ⋊ C₉
Hall	C₇×C₈₉ ⋊ C₂×C₉
Hall	C₇⋊C₉ ⋊ C₂×C₈₉
Hall	D₇ ⋊ C₉×C₈₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₈₉	AGL(1,𝔽₇)
commutator, hypocenter	C₇	C₂×C₉×C₈₉
Frattini	C₃	AGL(1,𝔽₇)×C₈₉
Fitting, socle	C₃×C₇×C₈₉	C₂×C₃
prime radical	C₃×D₇×C₈₉	C₃
cosocle	C₃×C₇	C₂×C₃×C₈₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₈₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1869 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₇⋊C₉×D₈₉, C₂×C₈₉×D₇⋊C₉
maximal normal subgroup of	D₇⋊C₉×D₈₉, C₂×C₈₉×D₇⋊C₉
maximal quotient of	C₈₉×Dic₇⋊C₉, C₂×C₈₉×D₇⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11214, 11);