Finite Group Databasebeta

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C₉×D₁₃×C₈₉ #35209693

order	20826
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₈₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₁₃×C₈₉

Splittings

Fitting, Hall	C₉×C₁₃×C₈₉ ⋊ C₂
derived, Sylow	C₁₃ ⋊ C₂×C₉×C₈₉
Hall	C₁₃×C₈₉ ⋊ C₂×C₉
Hall	C₉×C₁₃ ⋊ C₂×C₈₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₈₉	D₁₃
commutator, hypocenter	C₁₃	C₂×C₉×C₈₉
Frattini	C₃	C₃×D₁₃×C₈₉
Fitting	C₉×C₁₃×C₈₉	C₂
socle	C₃×C₁₃×C₈₉	C₂×C₃
prime radical	C₃×D₁₃×C₈₉	C₃
cosocle	C₃×C₁₃	C₂×C₃×C₈₉
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₉×C₈₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 10413

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(20826, 4);