Finite Group Databasebeta

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C₉×C₃₁×D₂₉ #30633639

order	16182
isoclinism	isoclinic class of D₂₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₃₁×D₂₉
unambiguous semidirect product	C₂₉⋊(C₂×C₉×C₃₁)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₃₁	D₂₉
commutator, hypocenter	C₂₉	C₂×C₉×C₃₁
Frattini	C₃	C₃×C₃₁×D₂₉
Fitting	C₉×C₂₉×C₃₁	C₂
socle	C₃×C₂₉×C₃₁	C₂×C₃
prime radical	C₃×C₃₁×D₂₉	C₃
cosocle	C₃×C₂₉	C₂×C₃×C₃₁
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₉×C₃₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8091

Conjugacy classes & character table

4464 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×C₃₁×#1181, C₉×C₃₁⋊#1181, C₉×D₂₉×D₃₁, …
maximal normal subgroup of	C₉×C₃₁×#1181, C₉×C₃₁⋊#1181, C₉×D₂₉×D₃₁, …
maximal quotient of	C₉×C₃₁×Dic₂₉, C₂×C₉×C₃₁×D₂₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16182, 4);