Finite Group Databasebeta

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C₉×D₇×C₁₃₉ #31776094

order	17514
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₃₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₇×C₁₃₉

Splittings

Fitting, Hall	C₇×C₉×C₁₃₉ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₉×C₁₃₉
Hall	C₇×C₁₃₉ ⋊ C₂×C₉
Hall	C₇×C₉ ⋊ C₂×C₁₃₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₃₉	D₇
commutator, hypocenter	C₇	C₂×C₉×C₁₃₉
Frattini	C₃	C₃×D₇×C₁₃₉
Fitting	C₇×C₉×C₁₃₉	C₂
socle	C₃×C₇×C₁₃₉	C₂×C₃
prime radical	C₃×D₇×C₁₃₉	C₃
cosocle	C₃×C₇	C₂×C₃×C₁₃₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₉×C₁₃₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8757

Conjugacy classes & character table

6255 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₇×D₁₃₉, D₇×D₉×C₁₃₉, D₇×D₁₂₅₁, …
maximal normal subgroup of	C₉×D₇×D₁₃₉, D₇×D₉×C₁₃₉, D₇×D₁₂₅₁, …
maximal quotient of	C₉×Dic₇×C₁₃₉, C₂×C₉×D₇×C₁₃₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17514, 7);