Finite Group Databasebeta

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C₉×C₁₉×D₅₃ #31827363

order	18126
isoclinism	isoclinic class of D₅₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₁₉×D₅₃
unambiguous semidirect product	C₅₃⋊(C₂×C₉×C₁₉)

Splittings

Fitting, Hall	C₉×C₁₉×C₅₃ ⋊ C₂
derived, Sylow	C₅₃ ⋊ C₂×C₉×C₁₉
Hall	C₁₉×C₅₃ ⋊ C₂×C₉
Hall	C₉×C₅₃ ⋊ C₂×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₉	D₅₃
commutator, hypocenter	C₅₃	C₂×C₉×C₁₉
Frattini	C₃	C₃×C₁₉×D₅₃
Fitting	C₉×C₁₉×C₅₃	C₂
socle	C₃×C₁₉×C₅₃	C₂×C₃
prime radical	C₃×C₁₉×D₅₃	C₃
cosocle	C₃×C₅₃	C₂×C₃×C₁₉
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₉×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9063

Conjugacy classes & character table

4788 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×C₁₉×#6157, C₉×C₁₉⋊#6157, C₉×D₁₉×D₅₃, …
maximal normal subgroup of	C₉×C₁₉×#6157, C₉×C₁₉⋊#6157, C₉×D₁₉×D₅₃, …
maximal quotient of	C₉×C₁₉×Dic₅₃, C₂×C₉×C₁₉×D₅₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18126, 3);