Finite Group Databasebeta

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C₉×C₁₃×D₇₉ #32914845

order	18486
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

C₉×C₁₃×D₇₉

Splittings

Fitting, Hall	C₉×C₁₃×C₇₉ ⋊ C₂
derived, Sylow	C₇₉ ⋊ C₂×C₉×C₁₃
Hall	C₁₃×C₇₉ ⋊ C₂×C₉
Hall	C₉×C₇₉ ⋊ C₂×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₃	D₇₉
commutator, hypocenter	C₇₉	C₂×C₉×C₁₃
Frattini	C₃	C₃×C₁₃×D₇₉
Fitting	C₉×C₁₃×C₇₉	C₂
socle	C₃×C₁₃×C₇₉	C₂×C₃
prime radical	C₃×C₁₃×D₇₉	C₃
cosocle	C₃×C₇₉	C₂×C₃×C₁₃
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₉×C₁₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9243

Conjugacy classes & character table

4797 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₁₃×D₇₉, C₁₃×D₉×D₇₉, D₇₉×D₁₁₇, …
maximal normal subgroup of	C₉×D₁₃×D₇₉, C₁₃×D₉×D₇₉, D₇₉×D₁₁₇, …
maximal quotient of	C₉×C₁₃×Dic₇₉, C₂×C₉×C₁₃×D₇₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18486, 8);