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C₉×C₁₃×D₈₉ #35209692

order	20826
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₁₃×D₈₉
unambiguous semidirect product	C₈₉⋊(C₂×C₉×C₁₃)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₃	D₈₉
commutator, hypocenter	C₈₉	C₂×C₉×C₁₃
Frattini	C₃	C₃×C₁₃×D₈₉
Fitting	C₉×C₁₃×C₈₉	C₂
socle	C₃×C₁₃×C₈₉	C₂×C₃
prime radical	C₃×C₁₃×D₈₉	C₃
cosocle	C₃×C₈₉	C₂×C₃×C₁₃
LCS	G ▷ C₈₉
UCS	C₁ ◁ C₉×C₁₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 10413

Conjugacy classes & character table

5382 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20826, 3);