Finite Group Databasebeta

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C₉×D₅×C₃₄₉ #44536102

order	31410
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₃₄₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₅×C₃₄₉
unambiguous semidirect product	C₅⋊(C₂×C₉×C₃₄₉)

Splittings

Fitting, Hall	C₅×C₉×C₃₄₉ ⋊ C₂
derived, Sylow	C₅ ⋊ C₂×C₉×C₃₄₉
Hall	C₅×C₃₄₉ ⋊ C₂×C₉
Hall	C₅×C₉ ⋊ C₂×C₃₄₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₃₄₉	D₅
commutator, hypocenter	C₅	C₂×C₉×C₃₄₉
Frattini	C₃	C₃×D₅×C₃₄₉
Fitting	C₅×C₉×C₃₄₉	C₂
socle	C₃×C₅×C₃₄₉	C₂×C₃
prime radical	C₃×D₅×C₃₄₉	C₃
cosocle	C₃×C₅	C₂×C₃×C₃₄₉
LCS	G ▷ C₅
UCS	C₁ ◁ C₉×C₃₄₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 15705

Conjugacy classes & character table

12564 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31410, 4);