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C₉×D₈₉₉ #30633640

order	16182
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₈₉₉
unambiguous semidirect product	C₂₉⋊(C₉×D₃₁)

Splittings

Fitting, Hall	C₉×C₂₉×C₃₁ ⋊ C₂
derived, Hall	C₂₉×C₃₁ ⋊ C₂×C₉
Hall	C₉×C₃₁ ⋊ D₂₉
Hall	C₉×C₂₉ ⋊ D₃₁
Sylow	C₃₁ ⋊ C₉×D₂₉
Sylow	C₂₉ ⋊ C₉×D₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₈₉₉
commutator, hypocenter	C₂₉×C₃₁	C₂×C₉
Frattini	C₃	C₃×D₈₉₉
Fitting	C₉×C₂₉×C₃₁	C₂
socle, cosocle	C₃×C₂₉×C₃₁	C₂×C₃
prime radical	C₃×D₈₉₉	C₃
LCS	G ▷ C₂₉×C₃₁
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8091

Conjugacy classes & character table

4059 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₂₉×D₃₁, D₉×D₈₉₉, D₂₆₁⋊D₃₁, …
maximal normal subgroup of	C₉×D₂₉×D₃₁, D₉×D₈₉₉, D₂₆₁⋊D₃₁, …
maximal quotient of	C₉×Dic₈₉₉, C₂×C₉×D₈₉₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16182, 5);