Finite Group Databasebeta

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C₂×C₉×D₅×C₈₉ #30630830

order	16020
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₈₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₉×D₅×C₈₉
unambiguous semidirect product	C₅⋊(C₂²×C₉×C₈₉)
unambiguous semidirect product	(C₂×C₅)⋊(C₂×C₉×C₈₉)

Splittings

Fitting	C₂×C₅×C₉×C₈₉ ⋊ C₂
derived, Sylow	C₅ ⋊ C₂²×C₉×C₈₉
Hall	C₅×C₉×C₈₉ ⋊ C₂²
Hall	C₅×C₈₉ ⋊ C₂²×C₉
Hall	C₅×C₉ ⋊ C₂²×C₈₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₈₉	D₅
commutator, hypocenter	C₅	C₂²×C₉×C₈₉
Frattini	C₃	C₂×C₃×D₅×C₈₉
Fitting	C₂×C₅×C₉×C₈₉	C₂
socle	C₂×C₃×C₅×C₈₉	C₂×C₃
prime radical	C₂×C₃×D₅×C₈₉	C₃
cosocle	C₃×C₅	C₂²×C₃×C₈₉
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₉×C₈₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8010

Conjugacy classes & character table

6408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16020, 35);