Finite Group Databasebeta

← Prev (#24924189) Next (#24924191) →

C₅×C₉×D₁₁₉ #24924190

order	10710
isoclinism	isoclinic class of D₁₁₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₉×D₁₁₉
unambiguous semidirect product	C₁₇⋊(C₅×C₉×D₇)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₉	D₁₁₉
commutator, hypocenter	C₇×C₁₇	C₂×C₅×C₉
Frattini	C₃	C₃×C₅×D₁₁₉
Fitting	C₅×C₇×C₉×C₁₇	C₂
socle	C₃×C₅×C₇×C₁₇	C₂×C₃
prime radical	C₃×C₅×D₁₁₉	C₃
cosocle	C₃×C₇×C₁₇	C₂×C₃×C₅
LCS	G ▷ C₇×C₁₇
UCS	C₁ ◁ C₅×C₉

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2745 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₉×D₇×D₁₇, C₉×D₅×D₁₁₉, C₉×D₃₅⋊D₁₇, …
maximal normal subgroup of	C₅×C₉×D₇×D₁₇, C₉×D₅×D₁₁₉, C₉×D₃₅⋊D₁₇, …
maximal quotient of	C₅×C₉×Dic₁₁₉, C₂×C₅×C₉×D₁₁₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 5);