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C₂×C₉×D₄₄₅ #30630829

order	16020
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₉×D₄₄₅
unambiguous semidirect product	(C₂×C₅)⋊(C₉×D₈₉)
unambiguous semidirect product	(C₂×C₈₉)⋊(C₉×D₅)

Splittings

Fitting	C₂×C₅×C₉×C₈₉ ⋊ C₂
derived, Hall	C₅×C₈₉ ⋊ C₂²×C₉
Hall	C₅×C₉×C₈₉ ⋊ C₂²
Hall	C₉×C₈₉ ⋊ C₂×D₅
Sylow	C₈₉ ⋊ C₂×C₉×D₅
Hall	C₅×C₉ ⋊ C₂×D₈₉
Sylow	C₅ ⋊ C₂×C₉×D₈₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉	D₄₄₅
commutator, hypocenter	C₅×C₈₉	C₂²×C₉
Frattini	C₃	C₂×C₃×D₄₄₅
Fitting	C₂×C₅×C₉×C₈₉	C₂
socle	C₂×C₃×C₅×C₈₉	C₂×C₃
prime radical	C₂×C₃×D₄₄₅	C₃
cosocle	C₃×C₅×C₈₉	C₂²×C₃
LCS	G ▷ C₅×C₈₉
UCS	C₁ ◁ C₂×C₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8010

Conjugacy classes & character table

4032 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16020, 34);