Finite Group Databasebeta

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C₉×D₇×C₁₁₃ #28382829

order	14238
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₁₃ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₇×C₁₁₃

Splittings

Fitting, Hall	C₇×C₉×C₁₁₃ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₉×C₁₁₃
Hall	C₇×C₁₁₃ ⋊ C₂×C₉
Hall	C₇×C₉ ⋊ C₂×C₁₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₁₃	D₇
commutator, hypocenter	C₇	C₂×C₉×C₁₁₃
Frattini	C₃	C₃×D₇×C₁₁₃
Fitting	C₇×C₉×C₁₁₃	C₂
socle	C₃×C₇×C₁₁₃	C₂×C₃
prime radical	C₃×D₇×C₁₁₃	C₃
cosocle	C₃×C₇	C₂×C₃×C₁₁₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₉×C₁₁₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7119

Conjugacy classes & character table

5085 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₇×D₁₁₃, D₇×D₉×C₁₁₃, D₇×D₁₀₁₇, …
maximal normal subgroup of	C₉×D₇×D₁₁₃, D₇×D₉×C₁₁₃, D₇×D₁₀₁₇, …
maximal quotient of	C₉×Dic₇×C₁₁₃, C₂×C₉×D₇×C₁₁₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14238, 5);