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C₈₉×D₄₅ #22547935

order	8010
isoclinism	isoclinic class of D₄₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₈₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₈₉×D₄₅
unambiguous semidirect product	C₅⋊(D₉×C₈₉)
unambiguous semidirect product	C₉⋊(D₅×C₈₉)

Splittings

Fitting, Hall	C₅×C₉×C₈₉ ⋊ C₂
derived, Hall	C₅×C₉ ⋊ C₂×C₈₉
Hall	C₉×C₈₉ ⋊ D₅
Hall	C₅×C₈₉ ⋊ D₉
Sylow	C₉ ⋊ D₅×C₈₉
Sylow	C₅ ⋊ D₉×C₈₉

Subgroups

	subgroup	G/H
center, hypercenter	C₈₉	D₄₅
commutator, hypocenter	C₅×C₉	C₂×C₈₉
Frattini	C₃	D₁₅×C₈₉
Fitting	C₅×C₉×C₈₉	C₂
socle	C₃×C₅×C₈₉	D₃
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₈₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2136 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₄₅×D₈₉, D₅×D₉×C₈₉, D₄₅⋊D₈₉, …
maximal normal subgroup of	D₄₅×D₈₉, D₅×D₉×C₈₉, D₄₅⋊D₈₉, …
maximal quotient of	C₈₉×Dic₄₅, C₂×C₈₉×D₄₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8010, 7);