Finite Group Databasebeta

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C₂×C₉×D₅₅₁ #34090620

order	19836
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₉×D₅₅₁
unambiguous semidirect product	(C₂×C₂₉)⋊(C₉×D₁₉)

Splittings

Fitting	C₂×C₉×C₁₉×C₂₉ ⋊ C₂
derived, Hall	C₁₉×C₂₉ ⋊ C₂²×C₉
Hall	C₉×C₁₉×C₂₉ ⋊ C₂²
Hall	C₉×C₂₉ ⋊ C₂×D₁₉
Hall	C₉×C₁₉ ⋊ C₂×D₂₉
Sylow	C₂₉ ⋊ C₂×C₉×D₁₉
Sylow	C₁₉ ⋊ C₂×C₉×D₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉	D₅₅₁
commutator, hypocenter	C₁₉×C₂₉	C₂²×C₉
Frattini	C₃	C₂×C₃×D₅₅₁
Fitting	C₂×C₉×C₁₉×C₂₉	C₂
socle	C₂×C₃×C₁₉×C₂₉	C₂×C₃
prime radical	C₂×C₃×D₅₅₁	C₃
cosocle	C₃×C₁₉×C₂₉	C₂²×C₃
LCS	G ▷ C₁₉×C₂₉
UCS	C₁ ◁ C₂×C₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9918

Conjugacy classes & character table

4986 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19836, 36);