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C₉×D₁₀₆₉ #34064020

order	19242
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₁₀₆₉

Splittings

Fitting, Hall	C₉×C₁₀₆₉ ⋊ C₂
derived, Sylow	C₁₀₆₉ ⋊ C₂×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₁₀₆₉
commutator, hypocenter	C₁₀₆₉	C₂×C₉
Frattini	C₃	C₃×D₁₀₆₉
Fitting	C₉×C₁₀₆₉	C₂
socle, cosocle	C₃×C₁₀₆₉	C₂×C₃
prime radical	C₃×D₁₀₆₉	C₃
LCS	G ▷ C₁₀₆₉
UCS	C₁ ◁ C₉

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9621

Conjugacy classes & character table

4824 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×#16862693, C₉⋊#16862693, D₉×D₁₀₆₉, …
maximal normal subgroup of	C₉×#16862693, C₉⋊#16862693, D₉×D₁₀₆₉, …
maximal quotient of	C₉×Dic₁₀₆₉, C₂×C₉×D₁₀₆₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19242, 5);