Finite Group Databasebeta

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C₉×C₁₉×D₁₀₁ #46828801

order	34542
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₁₉×D₁₀₁
unambiguous semidirect product	C₁₀₁⋊(C₂×C₉×C₁₉)

Splittings

Fitting, Hall	C₉×C₁₉×C₁₀₁ ⋊ C₂
derived, Sylow	C₁₀₁ ⋊ C₂×C₉×C₁₉
Hall	C₁₉×C₁₀₁ ⋊ C₂×C₉
Hall	C₉×C₁₀₁ ⋊ C₂×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₉	D₁₀₁
commutator, hypocenter	C₁₀₁	C₂×C₉×C₁₉
Frattini	C₃	C₃×C₁₉×D₁₀₁
Fitting	C₉×C₁₉×C₁₀₁	C₂
socle	C₃×C₁₉×C₁₀₁	C₂×C₃
prime radical	C₃×C₁₉×D₁₀₁	C₃
cosocle	C₃×C₁₀₁	C₂×C₃×C₁₉
LCS	G ▷ C₁₀₁
UCS	C₁ ◁ C₉×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 17271

Conjugacy classes & character table

8892 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34542, 3);