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C₉×C₂₉×D₁₉ #23755339

order	9918
isoclinism	isoclinic class of D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×C₂₉×D₁₉

Splittings

Fitting, Hall	C₉×C₁₉×C₂₉ ⋊ C₂
derived, Sylow	C₁₉ ⋊ C₂×C₉×C₂₉
Hall	C₁₉×C₂₉ ⋊ C₂×C₉
Hall	C₉×C₁₉ ⋊ C₂×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₂₉	D₁₉
commutator, hypocenter	C₁₉	C₂×C₉×C₂₉
Frattini	C₃	C₃×C₂₉×D₁₉
Fitting	C₉×C₁₉×C₂₉	C₂
socle	C₃×C₁₉×C₂₉	C₂×C₃
prime radical	C₃×C₂₉×D₁₉	C₃
cosocle	C₃×C₁₉	C₂×C₃×C₂₉
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₉×C₂₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2871 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₁₉×D₂₉, D₉×C₂₉×D₁₉, D₁₉×D₂₆₁, …
maximal normal subgroup of	C₉×D₁₉×D₂₉, D₉×C₂₉×D₁₉, D₁₉×D₂₆₁, …
maximal quotient of	C₉×C₂₉×Dic₁₉, C₂×C₉×C₂₉×D₁₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9918, 4);