Finite Group Databasebeta

← Prev (#31776092) Next (#31776094) →

C₇×C₉×D₁₃₉ #31776093

order	17514
isoclinism	isoclinic class of D₁₃₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₇×C₉×D₁₃₉

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₉	D₁₃₉
commutator, hypocenter	C₁₃₉	C₂×C₇×C₉
Frattini	C₃	C₃×C₇×D₁₃₉
Fitting	C₇×C₉×C₁₃₉	C₂
socle	C₃×C₇×C₁₃₉	C₂×C₃
prime radical	C₃×C₇×D₁₃₉	C₃
cosocle	C₃×C₁₃₉	C₂×C₃×C₇
LCS	G ▷ C₁₃₉
UCS	C₁ ◁ C₇×C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8757

Conjugacy classes & character table

4473 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₇×D₁₃₉, C₇×D₉×D₁₃₉, D₆₃×D₁₃₉, …
maximal normal subgroup of	C₉×D₇×D₁₃₉, C₇×D₉×D₁₃₉, D₆₃×D₁₃₉, …
maximal quotient of	C₇×C₉×Dic₁₃₉, C₂×C₇×C₉×D₁₃₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17514, 6);