Finite Group Databasebeta

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C₉×D₁₇₈₁ #44545383

order	32058
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₁₇₈₁
unambiguous semidirect product	C₁₃₇⋊(C₉×D₁₃)

Splittings

Fitting, Hall	C₉×C₁₃×C₁₃₇ ⋊ C₂
derived, Hall	C₁₃×C₁₃₇ ⋊ C₂×C₉
Hall	C₉×C₁₃₇ ⋊ D₁₃
Sylow	C₁₃₇ ⋊ C₉×D₁₃
Hall	C₉×C₁₃ ⋊ D₁₃₇
Sylow	C₁₃ ⋊ C₉×D₁₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₁₇₈₁
commutator, hypocenter	C₁₃×C₁₃₇	C₂×C₉
Frattini	C₃	C₃×D₁₇₈₁
Fitting	C₉×C₁₃×C₁₃₇	C₂
socle, cosocle	C₃×C₁₃×C₁₃₇	C₂×C₃
prime radical	C₃×D₁₇₈₁	C₃
LCS	G ▷ C₁₃×C₁₃₇
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 16029

Conjugacy classes & character table

8028 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32058, 5);