Finite Group Databasebeta

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C₉×D₁₁×C₇₉ #30627700

order	15642
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₇₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₁₁×C₇₉
unambiguous semidirect product	C₁₁⋊(C₂×C₉×C₇₉)

Splittings

Fitting, Hall	C₉×C₁₁×C₇₉ ⋊ C₂
derived, Sylow	C₁₁ ⋊ C₂×C₉×C₇₉
Hall	C₁₁×C₇₉ ⋊ C₂×C₉
Hall	C₉×C₁₁ ⋊ C₂×C₇₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₇₉	D₁₁
commutator, hypocenter	C₁₁	C₂×C₉×C₇₉
Frattini	C₃	C₃×D₁₁×C₇₉
Fitting	C₉×C₁₁×C₇₉	C₂
socle	C₃×C₁₁×C₇₉	C₂×C₃
prime radical	C₃×D₁₁×C₇₉	C₃
cosocle	C₃×C₁₁	C₂×C₃×C₇₉
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₉×C₇₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7821

Conjugacy classes & character table

4977 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₁₁×D₇₉, D₉×D₁₁×C₇₉, D₁₁×D₇₁₁, …
maximal normal subgroup of	C₉×D₁₁×D₇₉, D₉×D₁₁×C₇₉, D₁₁×D₇₁₁, …
maximal quotient of	C₉×Dic₁₁×C₇₉, C₂×C₉×D₁₁×C₇₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15642, 4);