Finite Group Databasebeta

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C₉×D₁₉×C₅₃ #31827364

order	18126
isoclinism	isoclinic class of D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₅₃ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₁₉×C₅₃

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₅₃	D₁₉
commutator, hypocenter	C₁₉	C₂×C₉×C₅₃
Frattini	C₃	C₃×D₁₉×C₅₃
Fitting	C₉×C₁₉×C₅₃	C₂
socle	C₃×C₁₉×C₅₃	C₂×C₃
prime radical	C₃×D₁₉×C₅₃	C₃
cosocle	C₃×C₁₉	C₂×C₃×C₅₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₉×C₅₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9063

Conjugacy classes & character table

5247 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₁₉×D₅₃, D₉×D₁₉×C₅₃, D₁₉×D₄₇₇, …
maximal normal subgroup of	C₉×D₁₉×D₅₃, D₉×D₁₉×C₅₃, D₁₉×D₄₇₇, …
maximal quotient of	C₉×C₅₃×Dic₁₉, C₂×C₉×D₁₉×C₅₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18126, 4);